Stanford Center for International Development

Working Paper No 461

Intergenerational Co-residence and Schooling

by

Anjini Kochar

November 2012

Stanford University John A and Cynthia Fry Gunn Building 366 Galvez Street

Stanford CA 94305-6015

Intergenerational Co-residence and Schooling

Anjini Kochar

November 2012

Abstract

This paper investigates how parentsrsquo expectations of co-residence with their oldest son affects schooling outcomes Using an overlapping generations model the effect is shown to be ambiguous it depends on how schooling affects life cycle income profiles The empirical analysis utilizes household data that reports young parentsrsquo expectations regarding residence in old age and also provides measures of schooling achievement for their children Identification comes from interactions of demographic shocks that reduce the relative profitability of residence with the oldest son with state-level investments that increase schooling returns Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

Keywords Schooling Old age security Inter-generational co-residence JEL Classification No J12 J14 I25

Stanford Center for International Development Stanford University Emailanjinistanfordedu This paper uses survey data collected as part of a larger study on schooling in the state of Karnataka India Data collection was generously funded by the William and Flora Hewlett Foundation The author alone is responsible for the findings of this paper

Intergenerational Co-residence and Schooling

Anjini Kochar

November 2012

Abstract

This paper investigates how parentsrsquo expectations of co-residence with their oldest son affects schooling outcomes Using an overlapping generations model the effect is shown to be ambiguous it depends on how schooling affects life cycle income profiles The empirical analysis utilizes household data that reports young parentsrsquo expectations regarding residence in old age and also provides measures of schooling achievement for their children Identification comes from interactions of demographic shocks that reduce the relative profitability of residence with the oldest son with state-level investments that increase schooling returns Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

Keywords Schooling Old age security Inter-generational co-residence JEL Classification No J12 J14 I25

Stanford Center for International Development Stanford University Emailanjinistanfordedu This paper uses survey data collected as part of a larger study on schooling in the state of Karnataka India Data collection was generously funded by the William and Flora Hewlett Foundation The author alone is responsible for the findings of this paper

Intergenerational Co-residence and Schooling

By

Anjini Kochar

Stanford Center for International Development Stanford University

November 2012

This paper uses survey data collected as part of a larger study on schooling in the state of Karnataka India Data collection was generously funded by the William and Flora Hewlett Foundation The author alone is responsible for the findings of this paper

1 Introduction

There is an interesting question of why the demand for the schooling of children exists given that it destroys a family structure of which the older generation has always approved and a family economy that brought them benefits in proportion to the number of children they had (Caldwell 1980)

This paper examines how the expectation of future co-residence with the oldest son affects parental investments in schooling In economies with weakly developed financial markets such as India many households lack access to the financial instruments that enable saving to smooth consumption over the life cycle Instead co-residence with sons is the primary method of ensuring consumption requirements in old age Of parents who chose co-residence the majority reside with the oldest son

How does this contract affect the schooling and hence the wealth of future

generations The effect is generally perceived to be positive Researchers have argued that old-age support is just one side of a reciprocal exchange system whereby parents invest in the schooling of their children in anticipation of support in old age (Lillard and Willis 1997) If imperfectly developed financial markets also imply lack of access to the credit necessary to finance educational investments the inter-generational family unit can substitute for formal markets enabling implicit loans for schooling from parents to their young children that when subsequently repaid support the consumption requirements of elderly parents Others however note that collective or social institutions may enhance poverty because default remains a significant concern even in social contracts (Greif 1997) This may be particularly true of implicit intra-family contracts across generations formal legal institutions are generally reluctant to intervene in intra-familial conflicts Reducing the probability of default requires actions to enhance the value of the contract and these may come at the cost of wealth-enhancing investments

I apply these insights to an analysis of the effect of inter-generational co-

residence on schooling building on a theoretical literature that examines loan contracts between overlapping generations when commitment is not possible (Lambertini (1998) and Azariadis and Lambertini (2003)) Theoretical work that utilizes a two-period model with incomes rising between the two periods generally suggests an unambiguous effect of childrenrsquos schooling on support for

1

the elderly In contrast utilizing a model in which adults live three periods I show that the effect of childrenrsquos schooling on the terms of the implicit inter-generational contract and hence the welfare of the elderly is ambiguous This is because the demand for and supply of credit depends not on wealth but on the profile of income over the life cycle If schooling makes income more ldquohump-shapedrdquo then the probability of adherence to the inter-generational loan contract increases with schooling since it increases the demand for old-age support However if schooling also increases incomes in old age the need for the family contract is reduced thereby increasing the likelihood of default

In such cases parents have a strong incentive to identify the child they

will reside with at any early age and invest strategically in his education so as to reduce the probability of default In most Asian economies that exhibit high levels of inter-generational co-residence the preferred arrangement is for elderly parents to reside with their oldest son Accordingly I focus on identifying the effects of expected co-residence with the oldest son on schooling attainment using survey data that queries parents on expected old-age residential arrangements and combines this with administrative data from schools on measures of schooling attainment

An empirical analysis of the effect of expectations of co-residence on

schooling investments is rendered difficult by the possibility of reverse causation Residential choices may be made after observing a childrsquos academic ability so that it is schooling that determines co-residence rather than the other way around Parents may identify the son with the least interest in schooling as their preferred son for co-residence in old-age since this son may be most likely to remain in rural areas and continue with traditional family occupations

Focusing on the effect of co-residence with a specific child the oldest son

facilitates identification Since the profitability of co-residence requires a difference in the profiles of life cycle income of parents and the son in question parents will plan the birth of their first child so as to ensure an optimal age difference that maximizes the profitability of the contract ldquoDemographic shocksrdquo in the form of the birth of a girl or a series of girls cause reductions in profitability and a decline in the value of co-residence with the oldest son These shocks therefore determine the likelihood of co-residence with the oldest son

They will do so however only for households with a demand for life

cycle consumption smoothing Therefore interactions of the age difference between the oldest child and the oldest son with exogenous determinants of life cycle income profiles also constitute valid instruments Building on the

2

hypothesis of this paper that the expansion of education is a primary determinant of the demand for the inter-generational loans I use interactions of the demographic shock with a measure of the quality of the school the child attends the student teacher ratio as instruments

The interaction with measures of school quality imply that identification

of the effect of expected co-residence with the son is possible even in regressions that condition on the childrsquos birth order and on indicators for the gender of the first child These latter variables allow for birth order and the gender of the oldest child to directly affect human capital investments (Ejrnaeligs and Poumlrtner 2004 Behrman and Taubman 1986 Willis and Parish 1994 Garg and Morduch 1998) And similarly it also implies that identification is driven not just by the lower schooling quality of relatively backward regions in these regions identification relies on demographic shocks that make some first sons better suited for co-residence than others

The age difference between the oldest child and the oldest son would not

constitute the basis for a valid instrument if households chose the gender of their first child through for example the use of diagnostic methods such as ultrasounds While this is known to occur in many regions of India particularly in North India it is not a common practice in the survey region of this study the Southern state of Karnataka Supporting this the survey data reveal that the proportion of oldest children that are sons is 050

The primary concern with this identification strategy is the possibility of

bias due to the possible correlation of the demographic shock with total number of children and the effect of the latter on schooling outcomes A strictly positive age difference between the first child and the oldest son suggests that the first child is a daughter with the age difference increasing with the number of older daughters in the family Any form of son preference will generate a positive correlation between low birth order daughters (or equivalently the birth order of the oldest son) and the number of children Thus demographic shocks increase family size and hence can also affect schooling through a classic quantity-quality trade-off

A second concern relates to the interpretation of the results Households

that enter into inter-generational familial contracts do so because they are credit constrained Thus any identified effect of the family contract on schooling may be interpreted as a reflection of credit constraints not of the family contract per se Relatedly in addition to their effect on family size the later-than-expected birth of the first son also generally results in family sex ratios that favor girls If girls are costlier for parents perhaps because of expected expenditure on dowries

3

this may represent a negative wealth shock and affect schooling decisions through this avenue

I address the first issue by also conditioning schooling outcomes on the

total number of children treating this variable as endogenous I use data on the gender and ordering of the first two children in the household as instruments for the number of children The identification strategy is fully described in the body of this paper In addition to providing credible identification of both expectations of co-residence and number of children on educational investments it also allows standard over-identification tests of the instruments as well as additional controls for direct demographic effects on outcomes The second concern is addressed by conditioning results on household savings Allowing for the endogeneity of this variable enables regressions that condition on expected income as well as current and expected credit constraints

The empirical analysis uses household data from rural Karnataka state in South India The data set part of a larger study on the determinants of schooling in the region includes a detailed household survey of all parents with children in 3rd grade in 2009-10 in over 720 government schools yielding a sample of approximately 10000 households The data set provides information on expected residential arrangements in old-age of young parents who are currently investing in their childrenrsquos schooling This is invaluable for several reasons First the data provide the ldquocorrectrdquo independent variable of interest it is only expectations of future residential patterns that can affect schooling investments at the time that they are made Second the availability of data at the time when schooling investments are being made provides ldquocorrectrdquo measures of other relevant variables Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school

The drawback of using data on households at the time of investing in their childrenrsquos schooling is that we cannot examine the effect of expectations of co-residence on completed schooling Instead we examine three other outcomes school attendance (the number of days that the child attended school between June to January of the 2009-10 school year) and test scores in language and mathematics Test scores are from tests that were conducted by an independent testing agency on students in 3rd grade The tests provide measures of their skills relative to state norms for students in grade 3 Attendance data are from school administrative records This is important since it removes the need to rely on parent-provided measures of their investment in their children such as reported hours of work or expenditures on private tuitions While parents do report unequal treatment for girls relative to boys (in terms of expectations of years of schooling

4

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

1 Introduction

There is an interesting question of why the demand for the schooling of children exists given that it destroys a family structure of which the older generation has always approved and a family economy that brought them benefits in proportion to the number of children they had (Caldwell 1980)

This paper examines how the expectation of future co-residence with the oldest son affects parental investments in schooling In economies with weakly developed financial markets such as India many households lack access to the financial instruments that enable saving to smooth consumption over the life cycle Instead co-residence with sons is the primary method of ensuring consumption requirements in old age Of parents who chose co-residence the majority reside with the oldest son

How does this contract affect the schooling and hence the wealth of future

generations The effect is generally perceived to be positive Researchers have argued that old-age support is just one side of a reciprocal exchange system whereby parents invest in the schooling of their children in anticipation of support in old age (Lillard and Willis 1997) If imperfectly developed financial markets also imply lack of access to the credit necessary to finance educational investments the inter-generational family unit can substitute for formal markets enabling implicit loans for schooling from parents to their young children that when subsequently repaid support the consumption requirements of elderly parents Others however note that collective or social institutions may enhance poverty because default remains a significant concern even in social contracts (Greif 1997) This may be particularly true of implicit intra-family contracts across generations formal legal institutions are generally reluctant to intervene in intra-familial conflicts Reducing the probability of default requires actions to enhance the value of the contract and these may come at the cost of wealth-enhancing investments

I apply these insights to an analysis of the effect of inter-generational co-

residence on schooling building on a theoretical literature that examines loan contracts between overlapping generations when commitment is not possible (Lambertini (1998) and Azariadis and Lambertini (2003)) Theoretical work that utilizes a two-period model with incomes rising between the two periods generally suggests an unambiguous effect of childrenrsquos schooling on support for

1

the elderly In contrast utilizing a model in which adults live three periods I show that the effect of childrenrsquos schooling on the terms of the implicit inter-generational contract and hence the welfare of the elderly is ambiguous This is because the demand for and supply of credit depends not on wealth but on the profile of income over the life cycle If schooling makes income more ldquohump-shapedrdquo then the probability of adherence to the inter-generational loan contract increases with schooling since it increases the demand for old-age support However if schooling also increases incomes in old age the need for the family contract is reduced thereby increasing the likelihood of default

In such cases parents have a strong incentive to identify the child they

will reside with at any early age and invest strategically in his education so as to reduce the probability of default In most Asian economies that exhibit high levels of inter-generational co-residence the preferred arrangement is for elderly parents to reside with their oldest son Accordingly I focus on identifying the effects of expected co-residence with the oldest son on schooling attainment using survey data that queries parents on expected old-age residential arrangements and combines this with administrative data from schools on measures of schooling attainment

An empirical analysis of the effect of expectations of co-residence on

schooling investments is rendered difficult by the possibility of reverse causation Residential choices may be made after observing a childrsquos academic ability so that it is schooling that determines co-residence rather than the other way around Parents may identify the son with the least interest in schooling as their preferred son for co-residence in old-age since this son may be most likely to remain in rural areas and continue with traditional family occupations

Focusing on the effect of co-residence with a specific child the oldest son

facilitates identification Since the profitability of co-residence requires a difference in the profiles of life cycle income of parents and the son in question parents will plan the birth of their first child so as to ensure an optimal age difference that maximizes the profitability of the contract ldquoDemographic shocksrdquo in the form of the birth of a girl or a series of girls cause reductions in profitability and a decline in the value of co-residence with the oldest son These shocks therefore determine the likelihood of co-residence with the oldest son

They will do so however only for households with a demand for life

cycle consumption smoothing Therefore interactions of the age difference between the oldest child and the oldest son with exogenous determinants of life cycle income profiles also constitute valid instruments Building on the

2

hypothesis of this paper that the expansion of education is a primary determinant of the demand for the inter-generational loans I use interactions of the demographic shock with a measure of the quality of the school the child attends the student teacher ratio as instruments

The interaction with measures of school quality imply that identification

of the effect of expected co-residence with the son is possible even in regressions that condition on the childrsquos birth order and on indicators for the gender of the first child These latter variables allow for birth order and the gender of the oldest child to directly affect human capital investments (Ejrnaeligs and Poumlrtner 2004 Behrman and Taubman 1986 Willis and Parish 1994 Garg and Morduch 1998) And similarly it also implies that identification is driven not just by the lower schooling quality of relatively backward regions in these regions identification relies on demographic shocks that make some first sons better suited for co-residence than others

The age difference between the oldest child and the oldest son would not

constitute the basis for a valid instrument if households chose the gender of their first child through for example the use of diagnostic methods such as ultrasounds While this is known to occur in many regions of India particularly in North India it is not a common practice in the survey region of this study the Southern state of Karnataka Supporting this the survey data reveal that the proportion of oldest children that are sons is 050

The primary concern with this identification strategy is the possibility of

bias due to the possible correlation of the demographic shock with total number of children and the effect of the latter on schooling outcomes A strictly positive age difference between the first child and the oldest son suggests that the first child is a daughter with the age difference increasing with the number of older daughters in the family Any form of son preference will generate a positive correlation between low birth order daughters (or equivalently the birth order of the oldest son) and the number of children Thus demographic shocks increase family size and hence can also affect schooling through a classic quantity-quality trade-off

A second concern relates to the interpretation of the results Households

that enter into inter-generational familial contracts do so because they are credit constrained Thus any identified effect of the family contract on schooling may be interpreted as a reflection of credit constraints not of the family contract per se Relatedly in addition to their effect on family size the later-than-expected birth of the first son also generally results in family sex ratios that favor girls If girls are costlier for parents perhaps because of expected expenditure on dowries

3

this may represent a negative wealth shock and affect schooling decisions through this avenue

I address the first issue by also conditioning schooling outcomes on the

total number of children treating this variable as endogenous I use data on the gender and ordering of the first two children in the household as instruments for the number of children The identification strategy is fully described in the body of this paper In addition to providing credible identification of both expectations of co-residence and number of children on educational investments it also allows standard over-identification tests of the instruments as well as additional controls for direct demographic effects on outcomes The second concern is addressed by conditioning results on household savings Allowing for the endogeneity of this variable enables regressions that condition on expected income as well as current and expected credit constraints

The empirical analysis uses household data from rural Karnataka state in South India The data set part of a larger study on the determinants of schooling in the region includes a detailed household survey of all parents with children in 3rd grade in 2009-10 in over 720 government schools yielding a sample of approximately 10000 households The data set provides information on expected residential arrangements in old-age of young parents who are currently investing in their childrenrsquos schooling This is invaluable for several reasons First the data provide the ldquocorrectrdquo independent variable of interest it is only expectations of future residential patterns that can affect schooling investments at the time that they are made Second the availability of data at the time when schooling investments are being made provides ldquocorrectrdquo measures of other relevant variables Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school

The drawback of using data on households at the time of investing in their childrenrsquos schooling is that we cannot examine the effect of expectations of co-residence on completed schooling Instead we examine three other outcomes school attendance (the number of days that the child attended school between June to January of the 2009-10 school year) and test scores in language and mathematics Test scores are from tests that were conducted by an independent testing agency on students in 3rd grade The tests provide measures of their skills relative to state norms for students in grade 3 Attendance data are from school administrative records This is important since it removes the need to rely on parent-provided measures of their investment in their children such as reported hours of work or expenditures on private tuitions While parents do report unequal treatment for girls relative to boys (in terms of expectations of years of schooling

4

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

the elderly In contrast utilizing a model in which adults live three periods I show that the effect of childrenrsquos schooling on the terms of the implicit inter-generational contract and hence the welfare of the elderly is ambiguous This is because the demand for and supply of credit depends not on wealth but on the profile of income over the life cycle If schooling makes income more ldquohump-shapedrdquo then the probability of adherence to the inter-generational loan contract increases with schooling since it increases the demand for old-age support However if schooling also increases incomes in old age the need for the family contract is reduced thereby increasing the likelihood of default

In such cases parents have a strong incentive to identify the child they

will reside with at any early age and invest strategically in his education so as to reduce the probability of default In most Asian economies that exhibit high levels of inter-generational co-residence the preferred arrangement is for elderly parents to reside with their oldest son Accordingly I focus on identifying the effects of expected co-residence with the oldest son on schooling attainment using survey data that queries parents on expected old-age residential arrangements and combines this with administrative data from schools on measures of schooling attainment

An empirical analysis of the effect of expectations of co-residence on

schooling investments is rendered difficult by the possibility of reverse causation Residential choices may be made after observing a childrsquos academic ability so that it is schooling that determines co-residence rather than the other way around Parents may identify the son with the least interest in schooling as their preferred son for co-residence in old-age since this son may be most likely to remain in rural areas and continue with traditional family occupations

Focusing on the effect of co-residence with a specific child the oldest son

facilitates identification Since the profitability of co-residence requires a difference in the profiles of life cycle income of parents and the son in question parents will plan the birth of their first child so as to ensure an optimal age difference that maximizes the profitability of the contract ldquoDemographic shocksrdquo in the form of the birth of a girl or a series of girls cause reductions in profitability and a decline in the value of co-residence with the oldest son These shocks therefore determine the likelihood of co-residence with the oldest son

They will do so however only for households with a demand for life

cycle consumption smoothing Therefore interactions of the age difference between the oldest child and the oldest son with exogenous determinants of life cycle income profiles also constitute valid instruments Building on the

2

hypothesis of this paper that the expansion of education is a primary determinant of the demand for the inter-generational loans I use interactions of the demographic shock with a measure of the quality of the school the child attends the student teacher ratio as instruments

The interaction with measures of school quality imply that identification

of the effect of expected co-residence with the son is possible even in regressions that condition on the childrsquos birth order and on indicators for the gender of the first child These latter variables allow for birth order and the gender of the oldest child to directly affect human capital investments (Ejrnaeligs and Poumlrtner 2004 Behrman and Taubman 1986 Willis and Parish 1994 Garg and Morduch 1998) And similarly it also implies that identification is driven not just by the lower schooling quality of relatively backward regions in these regions identification relies on demographic shocks that make some first sons better suited for co-residence than others

The age difference between the oldest child and the oldest son would not

constitute the basis for a valid instrument if households chose the gender of their first child through for example the use of diagnostic methods such as ultrasounds While this is known to occur in many regions of India particularly in North India it is not a common practice in the survey region of this study the Southern state of Karnataka Supporting this the survey data reveal that the proportion of oldest children that are sons is 050

The primary concern with this identification strategy is the possibility of

bias due to the possible correlation of the demographic shock with total number of children and the effect of the latter on schooling outcomes A strictly positive age difference between the first child and the oldest son suggests that the first child is a daughter with the age difference increasing with the number of older daughters in the family Any form of son preference will generate a positive correlation between low birth order daughters (or equivalently the birth order of the oldest son) and the number of children Thus demographic shocks increase family size and hence can also affect schooling through a classic quantity-quality trade-off

A second concern relates to the interpretation of the results Households

that enter into inter-generational familial contracts do so because they are credit constrained Thus any identified effect of the family contract on schooling may be interpreted as a reflection of credit constraints not of the family contract per se Relatedly in addition to their effect on family size the later-than-expected birth of the first son also generally results in family sex ratios that favor girls If girls are costlier for parents perhaps because of expected expenditure on dowries

3

this may represent a negative wealth shock and affect schooling decisions through this avenue

I address the first issue by also conditioning schooling outcomes on the

total number of children treating this variable as endogenous I use data on the gender and ordering of the first two children in the household as instruments for the number of children The identification strategy is fully described in the body of this paper In addition to providing credible identification of both expectations of co-residence and number of children on educational investments it also allows standard over-identification tests of the instruments as well as additional controls for direct demographic effects on outcomes The second concern is addressed by conditioning results on household savings Allowing for the endogeneity of this variable enables regressions that condition on expected income as well as current and expected credit constraints

The empirical analysis uses household data from rural Karnataka state in South India The data set part of a larger study on the determinants of schooling in the region includes a detailed household survey of all parents with children in 3rd grade in 2009-10 in over 720 government schools yielding a sample of approximately 10000 households The data set provides information on expected residential arrangements in old-age of young parents who are currently investing in their childrenrsquos schooling This is invaluable for several reasons First the data provide the ldquocorrectrdquo independent variable of interest it is only expectations of future residential patterns that can affect schooling investments at the time that they are made Second the availability of data at the time when schooling investments are being made provides ldquocorrectrdquo measures of other relevant variables Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school

The drawback of using data on households at the time of investing in their childrenrsquos schooling is that we cannot examine the effect of expectations of co-residence on completed schooling Instead we examine three other outcomes school attendance (the number of days that the child attended school between June to January of the 2009-10 school year) and test scores in language and mathematics Test scores are from tests that were conducted by an independent testing agency on students in 3rd grade The tests provide measures of their skills relative to state norms for students in grade 3 Attendance data are from school administrative records This is important since it removes the need to rely on parent-provided measures of their investment in their children such as reported hours of work or expenditures on private tuitions While parents do report unequal treatment for girls relative to boys (in terms of expectations of years of schooling

4

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

hypothesis of this paper that the expansion of education is a primary determinant of the demand for the inter-generational loans I use interactions of the demographic shock with a measure of the quality of the school the child attends the student teacher ratio as instruments

The interaction with measures of school quality imply that identification

of the effect of expected co-residence with the son is possible even in regressions that condition on the childrsquos birth order and on indicators for the gender of the first child These latter variables allow for birth order and the gender of the oldest child to directly affect human capital investments (Ejrnaeligs and Poumlrtner 2004 Behrman and Taubman 1986 Willis and Parish 1994 Garg and Morduch 1998) And similarly it also implies that identification is driven not just by the lower schooling quality of relatively backward regions in these regions identification relies on demographic shocks that make some first sons better suited for co-residence than others

The age difference between the oldest child and the oldest son would not

constitute the basis for a valid instrument if households chose the gender of their first child through for example the use of diagnostic methods such as ultrasounds While this is known to occur in many regions of India particularly in North India it is not a common practice in the survey region of this study the Southern state of Karnataka Supporting this the survey data reveal that the proportion of oldest children that are sons is 050

The primary concern with this identification strategy is the possibility of

bias due to the possible correlation of the demographic shock with total number of children and the effect of the latter on schooling outcomes A strictly positive age difference between the first child and the oldest son suggests that the first child is a daughter with the age difference increasing with the number of older daughters in the family Any form of son preference will generate a positive correlation between low birth order daughters (or equivalently the birth order of the oldest son) and the number of children Thus demographic shocks increase family size and hence can also affect schooling through a classic quantity-quality trade-off

A second concern relates to the interpretation of the results Households

that enter into inter-generational familial contracts do so because they are credit constrained Thus any identified effect of the family contract on schooling may be interpreted as a reflection of credit constraints not of the family contract per se Relatedly in addition to their effect on family size the later-than-expected birth of the first son also generally results in family sex ratios that favor girls If girls are costlier for parents perhaps because of expected expenditure on dowries

3

this may represent a negative wealth shock and affect schooling decisions through this avenue

I address the first issue by also conditioning schooling outcomes on the

total number of children treating this variable as endogenous I use data on the gender and ordering of the first two children in the household as instruments for the number of children The identification strategy is fully described in the body of this paper In addition to providing credible identification of both expectations of co-residence and number of children on educational investments it also allows standard over-identification tests of the instruments as well as additional controls for direct demographic effects on outcomes The second concern is addressed by conditioning results on household savings Allowing for the endogeneity of this variable enables regressions that condition on expected income as well as current and expected credit constraints

The empirical analysis uses household data from rural Karnataka state in South India The data set part of a larger study on the determinants of schooling in the region includes a detailed household survey of all parents with children in 3rd grade in 2009-10 in over 720 government schools yielding a sample of approximately 10000 households The data set provides information on expected residential arrangements in old-age of young parents who are currently investing in their childrenrsquos schooling This is invaluable for several reasons First the data provide the ldquocorrectrdquo independent variable of interest it is only expectations of future residential patterns that can affect schooling investments at the time that they are made Second the availability of data at the time when schooling investments are being made provides ldquocorrectrdquo measures of other relevant variables Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school

The drawback of using data on households at the time of investing in their childrenrsquos schooling is that we cannot examine the effect of expectations of co-residence on completed schooling Instead we examine three other outcomes school attendance (the number of days that the child attended school between June to January of the 2009-10 school year) and test scores in language and mathematics Test scores are from tests that were conducted by an independent testing agency on students in 3rd grade The tests provide measures of their skills relative to state norms for students in grade 3 Attendance data are from school administrative records This is important since it removes the need to rely on parent-provided measures of their investment in their children such as reported hours of work or expenditures on private tuitions While parents do report unequal treatment for girls relative to boys (in terms of expectations of years of schooling

4

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

this may represent a negative wealth shock and affect schooling decisions through this avenue

I address the first issue by also conditioning schooling outcomes on the

total number of children treating this variable as endogenous I use data on the gender and ordering of the first two children in the household as instruments for the number of children The identification strategy is fully described in the body of this paper In addition to providing credible identification of both expectations of co-residence and number of children on educational investments it also allows standard over-identification tests of the instruments as well as additional controls for direct demographic effects on outcomes The second concern is addressed by conditioning results on household savings Allowing for the endogeneity of this variable enables regressions that condition on expected income as well as current and expected credit constraints

The empirical analysis uses household data from rural Karnataka state in South India The data set part of a larger study on the determinants of schooling in the region includes a detailed household survey of all parents with children in 3rd grade in 2009-10 in over 720 government schools yielding a sample of approximately 10000 households The data set provides information on expected residential arrangements in old-age of young parents who are currently investing in their childrenrsquos schooling This is invaluable for several reasons First the data provide the ldquocorrectrdquo independent variable of interest it is only expectations of future residential patterns that can affect schooling investments at the time that they are made Second the availability of data at the time when schooling investments are being made provides ldquocorrectrdquo measures of other relevant variables Studies based on data on the current elderly and their adult children generally lack information on savings and school quality at the time that current adults were in school

The drawback of using data on households at the time of investing in their childrenrsquos schooling is that we cannot examine the effect of expectations of co-residence on completed schooling Instead we examine three other outcomes school attendance (the number of days that the child attended school between June to January of the 2009-10 school year) and test scores in language and mathematics Test scores are from tests that were conducted by an independent testing agency on students in 3rd grade The tests provide measures of their skills relative to state norms for students in grade 3 Attendance data are from school administrative records This is important since it removes the need to rely on parent-provided measures of their investment in their children such as reported hours of work or expenditures on private tuitions While parents do report unequal treatment for girls relative to boys (in terms of expectations of years of schooling

4

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

marriage age or hours of work in the household) they are far less likely to admit to unequal treatment of their sons Unwillingness to report differential investments in their sons would make it impossible to assess any such differential based on parent-provided information even should it exist

The analysis of this paper reveals a negative effect of parental dependence on the oldest son on his schooling achievement as measured by test scores The results also suggest that one explanation for lower schooling achievement is the lower school attendance of sons who parents expect to reside with The evidence thus suggests a reduced commitment to the schooling of the oldest son when parents expect to reside with him when elderly The results are robust to controls for total number of children and savings

This paper is related to several literatures most obviously to research on

the economic relationship between parents and children the determinants of parental investment in the schooling of children and old-age support for the elderly and on family and social exchange Beckerrsquos seminal work (1981) on the economic determinants of fertility and investments in children emphasizing the costs and returns to parents generated a rich literature explaining these investments as a consequence of parental need for old-age support (Nugent 1985 Cain 1982 1983) Focusing explicitly on schooling researchers have examined whether parents would invest efficiently in their childrenrsquos schooling particularly in economies where young parents lack access to credit (Baland and Robinson 2000) In the absence of such markets it has been recognized that the inter-generational family unit can serve as an implicit credit market (Kotlikoff and Spivak 1981 Lillard and Willis 1997 Cox 1990 Raut 1990) reducing borrowing constraints of younger generations and serving the savings needs of older ones

While much of the earlier literature neglected concerns about default

justifying this by assuming two-sided altruism recent work acknowledges the probability of default and discusses how exchange amongst overlapping generations of agents can be sustained through social norms that take the form of trigger strategies conditioning future access to the intergenerational contract to current adherence to its terms (Kandori 1992 Lambertini 1998 Azariadis and Lambertini 2003) Rangel (2003) for example shows that even in the absence of parental altruism parents will invest in childrenrsquos schooling (forward intergenerational goods) if old-age support from children (backward intergenerational goods) is conditional on investment in childrenrsquos schooling

Within a similar framework Anderberg and Balestrino (2003) explore the

determinants of parental investments in childrenrsquos schooling when parents can finance these investments either through a family contract or through borrowing

5

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

from formal credit markets at an exogenously specified interest rate They allow schooling to increase incomes in just one (adult) period and compare the rate of return to schooling across the two contracts Because the probability of default generates borrowing constraints within the family contract they show that in equilibrium the rate of return to schooling in this contract exceeds that obtained when parents borrow from formal markets suggesting that family contracts are characterized by lower levels of schooling In contrast by allowing schooling to affect incomes at different stages of the life cycle I show that the return parents get from childrenrsquos schooling within the system of family exchange is ambiguous and is determined by how schooling affects life cycle income profiles

The empirical literature on the topic has primarily focused on transfers

from non-resident children to their parents examining whether they increase with childrenrsquos schooling in regressions that also control for (adult) childrenrsquos incomes (Lillard and Willis 1997 Raut and Tran 2005) 1 Raut and Tran (2005) also examine the reverse relationship regressing completed schooling on transfers from non-resident (adult) children to their parents These studies generally take childrenrsquos schooling (or transfers when examining the effect of transfers on schooling) as exogenous ignoring the possibility that schooling investments and expectations of old-age support are jointly determined If schooling is determined keeping expectations of old-age support in mind then unobservable determinants of levels of support will directly influence schooling generating biased coefficients

A related empirical literature examines the determinants of family residential arrangements and structures (Edmonds Mammen and Miller 2004 Manacorda and Moretti 2006 Foster (1993) Edlund and Rahman (2005)) and considers the effect of co-residence on a variety of outcomes such as the labor supply of the (adult) son and daughter-in-law the parents reside with (Sasaki 2002) Much of this literature instruments inter-generational co-residence by the birth order of the adult son in question utilizing the prevailing norm of residence with the oldest son that prevails in many cultures However as previously noted birth order is known to be a significant determinant of an individualrsquos education and health and hence is also likely to be correlated with unobserved individual ability and preferences As such a fatherrsquos birth order may directly influence outcomes for his children and his wife invalidating its use as an instrument

1 While such transfers play an important role in many economies particularly the East Asian economies they are less important in the Indian context where support for the elderly primarily takes the form of coresidential arrangements with

6

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

A final contribution of this paper is to the literature on social networks Many have argued that membership in social networks including the family provides a substitute for absent or imperfectly functioning credit and insurance markets and that they may also enable more efficient exchange (Nugent 1990 Ben Porath 1980) In Asia it is widely believed that social norms which sustain family exchange reduce the need for the development of annuities markets and others which provide for life cycle consumption smoothing While it is also recognized that participation in such networks may come at a cost there are few studies that investigate what these costs are or their magnitude The analysis of this paper provides evidence on this issue

The remainder of this paper is structured as follows Section 2 describes the theoretical framework and derives implications for the effect of schooling on the profitability of the intergenerational contract The data and setting are described in section 3 which also discusses summary statistics Section 4 outlines the empirical framework and the identification strategy Section 5 discusses results and the last section concludes

2 Theoretical Framework

The primary objective of this section is to provide a framework to interpret the results of the empirical analysis I assume that households lack access to formal financial instruments that enable consumption smoothing over the life cycle However consumption smoothing is possible through loan contracts amongst units of different overlapping generations The starting point of this analysis is the assumption that commitment to the intergenerational contract is not possible children do not always provide for their elderly parents I draw heavily on Lambertinirsquos (1998) analysis of loan contracts amongst overlapping generations extending her analysis to the determination of parental investments in childrenrsquos schooling I show that when commitment is not possible the effect of the intergenerational contract on childrenrsquos schooling is ambiguous it depends on the effect of schooling on the profile of life-cycle incomes2

21 Intergenerational exchange and family structures

As has been shown by Lambertini (1998) Azariadis and Lambertini (2003) and others despite the inability to commit to the intergenerational contract perfect

2 In contrast when commitment is not an issue intergenerational exchange will increase childrenrsquos schooling assuming that the primary effect of schooling is to increase incomes in later stages of the life cycle (prime earning years and later) relative to early working years

7

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

information can enable consumption to be smoothed over the life cycle through trades between overlapping generations Following default assume that the debtor cannot lend in the inter-generational market either because of social norms that disallow future trades or because the debtorrsquos assets can be seized following default With perfect information on defaulters lenders can then tailor the terms of the contract so that it is always in the borrowerrsquos interest to voluntarily repay

One feature of this model is that these contracts are most likely to be observed in households with a high demand for consumption smoothing with demand being determined by the nature of life cycle income profiles and by preferences (the intertemporal elasticity of substitution) In particular households with hump-shaped income profiles are likely to value inter-generational contracts more than those with relatively flat profiles

I apply this framework to the context of intergenerational exchange in the Indian economy an economy in which financial instruments that enable life cycle consumption smoothing are still scarce particularly in rural areas The requirement of perfect information suggests that exchange will occur primarily amongst family members I assume that these contracts exist within co-residential intergenerational family units specifically within co-residential stem families an inter-generational family unit featuring just one unit of each generation In India this unit is the dominant residential arrangement for the elderly Surveys reveal that it constitutes approximately 83 of all stem joint and joint-stem families (Caldwell Reddy and Caldwell 1984)3 and that the majority of stem families feature the participation of 3-4 generations (Hashimoto 1991)

The preference for exchange within co-residential units has been explained by one of two factors The first is that the inter-generational contract also enables the smoothing of labor services over the life cycle given imperfect substitutability between family and hired labor with older family members providing child care in return for labor services in old age (Asis Domingo Knodel and Mehta 1995) The lower transaction costs associated with co-residence would make this the preferred mode of exchange While our theoretical framework takes the form of a loan contract between overlapping generations it can easily be adapted to the case where members of different generations trade labor services with the older generation providing support to young adults through supervision of their children with this service being repaid by care provided by the younger generation to elderly parents A second reason for embodying exchange within the co-residential unit is the importance of household

3 A joint family refers to married siblings living together while a joint‐stem family is one in which the parents live with multiple married children and grandchildren

8

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

public goods such as kitchens open space and certain household durables Co-residence may be preferred since it lowers the cost of public goods (Rosenzweig and Wolpin 1993 Kochar 2000) Both these explanations undoubtedly contribute to the prevalence of inter-generational co-residence as the preferred means of exchange Co-residence also provides a natural way to transfer a primary asset the residential house across generations in a way that is conducive to repayment being in the form of care and help for the elderly

22 Inter-generational Loan Contracts without Commitment

Consider a pure exchange overlapping generations economy where individuals live three adult periods young adulthood a period of middle age and old age As soon as children become adults (ie in the first adult period) they make their own independent consumption decisions even though they may continue to reside with their elderly parents Income is low in young adulthood peaks when an individual is middle aged and falls thereafter Consumption requirements are highest in the first period of adulthood when young adults are raising their own children and investing in their childrens human capital Because of the difference between consumption and income profiles individuals would like to borrow in young adulthood and to lend when middle aged so as to smooth consumption over the life cycle

Let c be private consumption β be the subjective discount factor and let qt represent the cost of a unit investment in schooling (h) Rt+1 is defined as the gross yield on loan bt+1 Rt+1=(1+rt+1) where r is the interest rate I use superscripts to index generations and sub-scripts to index the stage of the individuals life cycle Assuming that an individuals utility function is separable in consumption and the schooling of his children a generation t individual (one who reaches adulthood in period t) maximizes the following utility function when young

(1)

Both u(c) and v(h) are strictly increasing concave and differentiable Lifetime utility is maximized subject to the set of one-period constraints

(2)

(3)

(4)

9

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

(5)

where represents the loan taken by generation t individuals repayable in period (t+1) and other loan quantities are similarly defined With hump shaped income the optimal plan calls for an individual in generation t borrowing from his parents in period t the first period of young adulthood repaying this loan in period t+1 and simultaneously making loans to his child These loans are repaid by the child when the parent is old in period (t+2)

As previously discussed default implies the cessation of exchange with future generations Since the inter-generational contract provides the only means of smoothing consumption across periods borrowing and lending decisions (for individuals in families which have previously maintained the inter-generational contract) are therefore subject to the individual rationality constraints (IRCs)

(6)

(7)

Let μ1 be the Lagrange multiplier on constraint (6) and μ2 be the multiplier on (7) Then the first order condition for and are respectively

(8)

(9)

With hump incomes that peak when the individual is middle-aged the budget constraints (3-5) reveal that constraint (6) will be binding but constraint (7) will not That is in (8) and (9) μ1gt0 but μ2=0 With this the first order condition for

is given by (8) so that IRCs reduce the demand for loans by young adults from their middle-age parents However middle-aged parentsrsquo decisions regarding the amount of loan to supply to their children are unaffected by IRCs The first order condition for (equation 9) reduces to the standard first order condition that obtains when commitment is not an issue

(10)

Interest rates in any period are endogenously determined by an equilibrium condition that equates the demand for loans (within the family unit) with the supply Thus Rt+2 solves the equation

10

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

(11)

where and This yields interest rates for each period that vary with the life cycle incomes of the contracting parties but also of all past and previous generations

Assuming that income is a monotonically increasing function of human capital the interest rate function is

(12)

23 Schooling investments

Parents make schooling investments strategically taking into account the effect of schooling on loan interest rates That is optimal investment in schooling is solved for sequentially by first determining the interest rate schedule (12) that specifies the interest rate at any given level of schooling and then working backwards to determine the optimal investment in a childrsquos human capital taking into account the effect of schooling on interest rates The first order condition for investments in a childrsquos human capital is given by

(13)

The last term on the right hand side of (13) indicates that the inter-generational loan and the probability of default affects the rate of return to investment in

childrenrsquos schooling If is positive parents will strategically over-invest in their childrens education relative to a pure consumption model that would be applicable in the absence of the inter-generational contract that is if In this latter case parental investments in childrenrsquos schooling would be given by the familiar condition and would reflect preferences schooling costs and parental income

PROPOSITION 1 If the IRCs bind the sign of is ambiguous Schooling-induced increases in second stage income increase first period loan demands and hence the interest rate Conversely schooling-induced increases in third stage

11

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

income reduce first period loan demands and hence interest rates The net effect depends on whether the value of the family contract relative to autarky (as reflected in the difference in the marginal utility of consumption under these two contracts) is greater in old age than in prime age and on the schooling gradient in these two periods4 If as seems likely the family contract is particularly valued for its effect on old-age welfare we would expect parental dependence on children for old age support would reduce their investment in childrenrsquos schooling Eventually however the sign of this effect is an empirical issue

24 Multiple children and strategic investments

This framework suggests that the rate of return to the family contract can be enhanced if parents invest strategically in their childrenrsquos schooling While this framework assumes just one child strategic investments in families with multiple sons require parents to identify the child they expect to reside with at an early age

The prevailing norm in most economies that feature inter-generational co-residence including India is for parents to reside with the oldest child (Asis Domingo Knodel and Mehta 1995) While this may be the consequence of a social norm it can also be justified on the grounds of economic profitability The value of the contract between a father and a son is summarized in the rate of return to the contract Rt+2 Since this interest rate is determined by equating the supply of credit (from the father) to the demand from his son it is a function of the difference in their incomes at any given life cycle period and hence the difference in their age Too small or too large an age difference will adversely affect the value of the contract Similarly low life expectancies may reduce the profitability of contracting with younger children

This suggests that the demand for the inter-generational loan will influence the time to the birth of their first child parents will choose this so as to ensure an optimal age difference with their oldest child However ldquodemographic shocksrdquo in the form of the birth of a daughter or a series of daughters may result in the age difference between parents and their oldest son being less than optimal reducing the value of the inter-generational contract with the oldest son and correspondingly parental gains from strategic under-investment in his education In such cases parents may delay the decision of which of their sons to reside with to a later date basing this in part on preferences and the revealed ability and circumstances of their (adult) children This may result in co-residence with sons other than the oldest son or even in parents living alone if adherence to the contract cannot be guaranteed

4 See Appendix for proof

12

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

3 Data and Setting

31 Survey

The data I use for this study comes from a survey of approximately 10000 households in rural areas of the southern state of Karnataka The study was designed to understand the determinants of schooling The unit of administration for school planning purposes in the state is a cluster a unit above the village with each cluster covering an average of 15 villages For the purposes of this study 240 clusters were randomly chosen from across the study area (11 districts of the state) Within each cluster an average of 15 village governments or gram panchayats were randomly selected (2 Gram panchayats in larger clusters and one in smaller) and within each Gram Panchayat two schools were surveyed (the largest and a randomly selected school) In each school parents of all third grade children were interviewed In addition to conventional information on household demographics and economic outcomes such as consumption income and hours of work the household module also provides detailed information on parental expectations of residential arrangements in old age Finally the household survey collected detailed data on the family background of each parent including information on their siblings and the residential arrangements for their parents

The household survey was supplemented by a school survey that provides information on the school attended by the child including school enrollments and numbers of teachers It also provides detailed school records on the monthly attendance of each child in 3rd grade between June 2009 and January 2010 the date of our survey Additionally all children in grade 3 were tested in language and mathematics through tests designed by an independent agency and implemented by the survey team The tests were designed to assess student learning relative to the state-specific standards for children in grade 3

32 Education

Table 1 summarizes data on fathersrsquo years of education by the primary occupation of the household Households are predominantly involved in agricultural occupations with 35 of households earning income primarily from their own farm operations and 28 earning most of their income as agricultural laborers A further 21 of households are engaged in unskilled non-agricultural work The proportions of households in salaried occupations and in business and trade are small (4 of households in each of these occupations) These occupations are however characterized by much higher education levels 9 and 7 years respectively relative to agricultural labor and unskilled non-agricultural

13

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

labor (3 years) Life cycle income from physical labor is likely to be strongly hump-shaped peaking when an individual is at his physical peak and declining sharply with age thereafter Households engaged in these occupations are therefore most likely to value opportunities for life cycle consumption smoothing and hence the intergenerational contract Occupations which require more education and are less dependent on physical labor are likely to be characterized by income profiles that do not fall off so sharply with age If so increased education because it offers entry into these occupations will lower the demand for inter-generational contracts Offering an incentive compatible contract for households characterized by higher levels of education may therefore not be profitable

India has witnessed a considerable increase in education levels in the past two decades This is clearly evident from table 2 in which I report parentsrsquo responses to questions regarding the minimum years of schooling that were considered necessary for boys and girls when they were growing up and for the current generation of children This minimum has increased from 9 to 14 years for boys Household responses suggest a 2 year gender gap that has remained the same across generations with the minimum necessary schooling level for girls reported as 7 years for the previous generations and 12 years for the current one

Table 3 documents parental opinions of the minimum years of schooling required for different occupations Salaried occupations are thought to require at least 12 years of schooling (with the mean response being 13 years) while agricultural occupations are perceived as requiring only a primary education (5 years) or less Clearly schooling of 12 years or more is likely to result in an occupational shift from agricultural to salaried professions Completion of 10 years of schooling (high school) is also believed to provide entry into business and trade

33 Residential arrangements and expectations

Table 4 provides information on the residential arrangements of the grandparents of children currently in school (including arrangements that prevailed for those no longer living) by expectations of old-age residence for parents Though 32 of the elderly resided or reside by themselves the dominant arrangement is residence with the oldest son (35 of the elderly) However a significant percentage of the elderly also report residence with a son other than the oldest son (31) Residence with a daughter is rare accounting for only 13 of residential arrangements

There is a strong correlation between residential arrangements of grandparents and those expected by the current generation of parents Thus in

14

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

households with grandparents who resided alone parents also predominantly expect to reside alone (35 of such households) And of families where the elderly parent resided (or resides) with a son 48 report an expectation that they too will reside with a son However a norm of co-residence with the oldest son is clearly prevalent not just amongst households in which grandparents resided with the oldest son but across all household types For example amongst households where grandparents resided with a son other than the oldest son the predominant expectation is that parents will reside with the oldest son (33) with the percentage of households expecting this arrangement being statistically indistinguishable from the corresponding percentage in households where grandparents did reside with the oldest son (32) Similarly 26 of parents whose own parents resided alone expect to reside with their oldest son These data suggest that deviations from the norm may reflect the inability of the oldest son to provide for his parents rather than willful default on his part and hence do not constitute an abrogation of the norm This conforms to the theoretical framework of section 2 that suggests that the ability to offer a self-enforcing contract limits willful default

34 Summary statistics

Summary statistics for the sample as a whole as well as by parentsrsquo expected residential arrangements when old are in table 5 Parents who expect to reside alone have higher levels of education and are less likely to be agricultural laborers The other groups of households display little difference in these socio-economic outcomes The total number of children is also lower for parents that expect to reside alone (27 children) followed closely by households in which parents expect to reside with the oldest son (28) The data at the bottom of the table provide information on the birth order of the oldest son across family types I delay a discussion of this until the discussion of the empirical methodology of this paper in the next section

Table 6 provides summary data on the main outcomes we consider total days of attendance in schools and language and mathematics test scores As in other parts of rural India mean attendance is relatively low at 82 of the total school days (174) from the start of the school year to our survey date (June 2009 to January 2010) Attendance is marginally higher for girls relative to boys and in households where parents expect to reside alone Mirroring this test scores are also marginally higher for girls and for children in households in which parents do not expect to co-reside with their children in old age If anything schooling outcomes appear to be marginally better for older sons when parents expect to reside with him relative to outcomes for oldest sons in households in which parents state that they expect to co-reside with another child However the

15

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

marginally better outcomes for these older sons and for children in households where parents expect to reside alone may well reflect the differences in socio-economic indicators revealed in table 5 including the lower number of children in households in which parents expect to reside with the oldest son relative to households in which they expect to reside with another son

16

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

4 Empirical Methodology

The sensitivity of the theoretical results to the set of maintained assumptions suggests that the effect of the inter-generational contract on schooling can only be empirically established This section takes up that task

41 Framework

The primary objective of the empirical analysis of this paper is to examine whether and how the schooling of the oldest son is affected by his parentrsquos expectation of co-residence with him Let δi be an indicator variable which equals 1 if parents expect to enter into a loan contract with their oldest son 0 otherwise From the analysis of the previous section

(14) δ = 1 if Rt+2 gt= )

0 Otherwise

Allowing for the null hypothesis that intergenerational exchange has no effect on schooling the first order condition for schooling investments (equation 13) can be rewritten as

(15)

Taking a linear approximation the estimating equation for years of schooling (hi) is

(16) hi = αo + α1iδi + Xi´ α2 + ui

Where and Xi represents wealth and observed preference shifters that determine schooling This is a standard random coefficient model with an endogenous regressor δi

Let α1i = Then (16)

can be written as

(17)

17

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

As noted by Heckman and Robb (1985) identification using instrumental variables would not be possible if the error term in (17) has a zero mean However as they note since δi reflects the expectation of co-residence at the time when parents are investing in their childrenrsquos schooling εi is likely unknown at the time these investments are being made This suggests that

justifying identification through instrumental variables

42 Regression error term and bias in OLS regressions

The bias in OLS estimates of the effect of expected co-residence on schooling attainment is clear from equations (14) and (12) From (14) the probability of co-residence reflects the interest rate on the inter-generational loan account Equation (12) shows that this interest rate will in turn reflect the schooling attainment of all generations including expectations of the schooling of the current generation of children That is expectations of co-residence and schooling investments in children are jointly determined OLS estimates will suffer from reverse causation It may well be that expectations of completed schooling determine the probability of co-residence with the oldest son instead of expectations of co-residence causing strategic investments in childrenrsquos schooling If parents can infer their childrenrsquos ability at a young age as is very likely this ability unobserved by the econometrician will be a component of the regression error term It will also be correlated with expectations of co-residence Thus any estimated effect of co-residence on schooling may merely reflect the correlation between the two variables and cannot be taken as indicative of a causal effect of co-residence on schooling attainment

OLS estimates may also suffer from an omitted variables bias For example social norms that dictate a special role for the oldest son in the family may well result in norms that favor the oldest sons in the allocation of goods and hence in schooling investments including parental time spent on the child5 These norms may well be specific to families As suggested by the theoretical framework of this paper they may exist in families that have maintained the norm from one generation to the next but not in others If so they will be a component of the regression error term and will also be correlated with expectations of co-residence In this case the bias introduced will be positive Including an indicator variable that takes the value 1 if the child in question is the oldest son amongst the regressors will not remove this bias if social norms favoring the oldest son exist only in some households

5 In addition to norms that favor the oldest son in co‐residential arrangements the oldest son frequently also has a special role in the marriage of daughters in subsequent relationships with daughtersrsquo children and family and in funeral customs for parents

18

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Finally biased coefficients may also result not because of an omitted social norm that favors oldest sons but because of omitted parental abilities If expectations of co-residence do determine the schooling of children then this will also be true of previous generations That is parental abilities both observed and unobserved will differ across families that have previously supported co-residential arrangements and those that have not Thus expectations of co-residence within the current generation of parents will be correlated with unobserved parental ability a direct determinant of schooling outcomes for children

43 Identification of expectations of inter-generational co-residence

As previously noted the profitability of the inter-generational contract depends on the difference in incomes between the father and the son and hence on the age difference between the two While this age difference is partly endogenous being chosen by parents it also includes an exogenous component in the form of demographic ldquoshocksrdquo due to the birth of a daughter (or a number of daughters) rather than a son Such shocks reduce the profitability of the inter-generational contract but are unlikely to be correlated with preferences for the oldest son social norms or unobserved ability (of the son or of the parent) As such they constitute valid instruments to identify the effect of co-residence on childrenrsquos schooling attainment

I measure the demographic shock by the age difference between the oldest child and the oldest son The last four rows of table 5 provide strong support of the effect of demographic shocks on expectations of co-residence In 68 of the households where parents expect to reside with the oldest son the oldest son is the oldest child This percentage is only 41 in households where parents expect to reside with a younger son Similarly the mean age difference between the oldest child and the oldest son is only 134 years in households that expect to co-reside with the oldest son but as much as 267 when parents state that they expect to co-reside with a younger son The data thus suggest that co-residence with the oldest son is the preferred option only when the son is of relatively low birth order

The demographic shock will however affect co-residence only in families with a demand for co-residence It is widely believed that one of the primary determinants of the secular decline in the economic value of the family and specifically in inter-generational co-residence is increasing state investment in schooling (Caldwell Reddy and Caldwell 1982 Becker 1981) With rising state investments social norms regarding acceptable levels of schooling are revised upwards as indicated in our survey data Social pressures to educate children to

19

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

acceptable levels may constrain the ability of the household to choose optimal schooling levels and hence affect the probability of co-residence When these constraints bind demographic shocks will have less effect on the probability of co-residence

State Governmentrsquos investment in schooling in India has primarily taken the form of increased number of teachers and hence reductions in the student-teacher ratio In the state of Karnataka the student-teacher ratio in primary schools fell from 50 in 1990-91 to 35 in 2003-046 However there is considerable variation in student-teacher ratios across the state a variation that aids the empirical analysis of this paper First the decline in the student-teacher ratio varies across districts with the more backward northern region witnessing smaller declines For example consider Bidar district in the North and Shimoga and Tumkur districts in the South all districts with a student-teacher ratio of 47 in 1990-91 By 2003 the student teacher ratio had fallen to 27 in Shimoga and 26 in Tumkur but remained a high 40 in Bidar In our survey states the northern states recorded a slight increase in the student-teacher ratio between 1998-99 and 2003-04 from 398 to 413 In comparison the student-teacher ratio in the southern states declined in this same period from 342 to 298

However the variation in student-teacher ratios is not just across districts there is also considerable variation within a district and indeed amongst the schools that fall within the constituency of the village government This is because villages are divided into residential sub-habitations with a large main village site being surrounded by smaller habitations The Governmentrsquos school location policy provides a school to each sub-habitation (with a population in excess of 200) Since the assignment of teachers to schools is based on enrollment cut-offs the variation in habitation size within a village complex generates similar variation in student-teacher ratios In our sample for example the average student teacher ratio in main village schools is 32 while it is lower at 27 in habitation schools It is worth noting that the socio-economic status of households who reside in sub-habitations of the main village is generally significantly lower than those of households in the main village complex since sub-habitations are primarily populated by households of lower castes Thus the variation in student-teacher ratios is not correlated with average village wealth or socio-economic status poorer habitation schools feature lower student-teacher ratios and have witnessed greater declines in this ratio over time

6 These data are from the State Human Development Reports Government of Karnataka (2005 and 1999)

20

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Utilizing this variation the identifying variables for expectations of co-residence are interactions between the demographic shock and the student-teacher ratio in the government school attended by the child Rather than use the ratio of enrollments to teachers I used a predicted student-teacher ratio based on the rules that determine the number of teachers as a non-linear function of enrollments7 Because identification comes from the interaction variable it is possible to allow for direct effects on schooling of a number of demographic indicators including the birth order of the oldest son

44 Birth order of oldest sons and fertility

The primary concern with this identification strategy is that the interaction between demographic shocks and school quality may also affect the householdrsquos fertility and hence schooling through a classic quality-quantity trade-off (Becker and Lewis 1973) This is because the age difference between the oldest child and the oldest son will be large if the first child (and perhaps even the first few children) is a daughter If parents exhibit a preference for sons this is likely to generate ldquoson preferring differential stopping behaviorrdquo with parents continuing to have children until the targeted number of sons is born Such behavior will increase the number or children in the family (Das 1987) and suggests that the gender of the first child and equivalently the birth order of the first son is likely to be a determinant of family size (Jensen 2003) To the extent that school quality affects the opportunity cost of children the interaction of the demographic shock with school quality will also affect fertility choices

Data from the 2005-06 National Health and Fertility Survey (NFHS) confirm a preference for sons in the state though to a lesser degree than in other states particularly those in North India The percentage of women and men wanting more sons than daughters was 116 and 127 respectively while the percentage of women who want more daughters than sons is only 46 The corresponding percentage of men who want more daughters than sons is 27 Households in the state however also demonstrate a demand for at least one daughter a characteristic common to most of the Indian economy (National Family and Health Survey 2005-06)8 At the national level 74 of women and 65 of men want at least one daughter (77 of women and 70 of men want at least one son)

7 Specifically I predict the number of teachers by the following function (max(2 ceil(Enr30)) This reflects the governmentrsquos norm of ensuring a student‐teacher ratio of 30 with the provision that each primary school have at least two teachers 8 This is generally ascribed to the Hindu religious obligation of Kanyadan or the giving of a daughter in marriage considered to be a sacred duty of all Hindus

21

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

If the preference for sons exists only because of the demand for old-age insurance the demographic shock is still a valid instrument It will affect total number of children only through the expectation of co-residence with the oldest son However a preference for sons may also exist for other reasons to help reduce intra-temporal credit constraints in the first adult period through the labor of sons or to increase the profitability of family enterprises including the family farm through the use of family labor

Since the bias stems from the omission of total number of children from the regression the solution is to include this variable allowing for its endogeneity This in turn requires that the number of instruments be sufficient to ensure that the rank conditions for identification are satisfied I base identification on the recognition that while expectations of co-residence with the oldest son are based on his characteristics specifically the years until his birth the total number of children is not determined by the time-to-birth of the first son but by the gender of the child in each pregnancy Obviously utilizing information on just the first birth does not aid identification If the first child is a girl it will reduce the expectation of old-age residence and also increase family size due to son preferring differential stopping behavior Instead following Angrist and Evans (1998) I utilize information on the gender composition and order of births after two children Ranking the four possible combinations ((son-son) (son-daughter) (daughter-son) (daughter-daughter)) in terms of their implications for the total number of children produces a different ranking from that which would emerge if pairs were ranked by the probability of old-age residence with the oldest son thus generating a variable that is independent of the demographic shock that determines the latter This in turn means that rank conditions for identification are satisfied

Specifically after two births householdsrsquo decisions regarding fertility are not dependent on the gender ordering of children but on the total number of sons or daughters That is the implications for total fertility are the same for households who have a son and a daughter regardless of whether the son was born first (son-daughter) or the daughter (daughter-son) The expectation of co-residence does vary across these combinations since it depends on the timing of the birth of the first son However since the regressions control for the expectation of co-residence with the oldest son any identified effect of fertility only reflects the value of sons due to other factors Other commonly offered explanations for a preference for son -- such as the value of the son in farm operations or in earning income or to inherit the family business -- will not generate a difference in the ranking of these two pairs

22

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

This is confirmed in table 7 that summarizes survey data on the probability that the couple has a third child and expectations of co-residence with the oldest son for the four pairings The dependence of old-age residence with the oldest son on the demographic shock and hence on the birth order of the oldest son implies that households with a daughter-daughter pairing will be associated with the lowest expectation of old-age residence with the oldest son Supporting the theory that the birth order of the first son matters for expectations of old-age residence households with a daughter-son pairing report a lower expectation of residence with their oldest son relative to those with a son-daughter pairing That is restricting attention to households with one son and one daughter there is a clear preference ranking of the two possible pairings (son-daughter daughter-son) Finally parents will be indifferent between the two pairings (son-daughter) and (son-son) if pairings are valued only for their implications for this expectation The table lists preferences in this order (daughter-daughter daughter-son son-daughter son-son) and confirms that the daughter-daughter pairing is associated with the lowest percentage of households expecting co-residence with the oldest son (15) followed by the daughter-son pairing (26) The percentage of sons expecting co-residence with the oldest son is higher again for the son-daughter and son-son pairings though there is a difference between these two pairings

The table also confirms that these same pairings would not produce an equivalent ranking if they were ranked on the basis of their implications for fertility With son preference the (daughter-daughter) ranking is associated with the highest proportion of households having at least one more child (079) Conversely there is no significant difference between the remaining three pairings As previously discussed in Section 2 the relatively high effect of the son-son pairing on the probability of a third child is indicative of the demand for at least one daughter The data also support the hypothesis that in households with at least one daughter and one son the ordering of births by gender does not matter for fertility choices The probability of a third birth is identical for the son-daughter and the daughter-son pairing (058)

The table therefore provides the basis for a viable identification strategy a variable that ranks the pairings in terms of their implications for the number of children would be linearly independent of the birth order of the first son and hence the age difference between the oldest child and the oldest son so that using these two variables would satisfy the rank conditions for identification treating both expectations of old-age residence with the oldest son and the couplesrsquo total number of children as endogenous variables

As in Angrist and Evans (1998) more mileage can be achieved by decomposing this ranking into the individual pairs and using the indicator

23

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

variables generated by each pairing as separate instruments This makes it possible to separately include an indicator for the gender of the first child as a regressor and hence allows for alternative ways in which the gender composition of children can affect socio-economic outcomes Specifically it allows for the possibility that households in which a daughter is the first-born may be better off perhaps because this lowers parental labor constraints in investing in their children (Parish and Willis 1994 Garg and Morduch 1998) With the inclusion of an indicator variable in the regression that takes the value 1 if the first child is a son and with the regression constant the two variables used as instruments for family size are indicator variables for the daughter-daughter and the son-son pairing The coefficients on these regressors in first stage regression reflect their value to households over the daughter-son pairing (included in the regression constant) but the coefficients in the first stage regressions are not easily interpretable since they also include the age difference between the oldest child and the oldest son and interactions of this variable with others

Breaking up the rankings into individual pairings also allows standard over-identification tests for these instruments separately including each of the pairings as a regressor allowing identification to come from just the remaining pairing This also provides more evidence on any possible direct effect of the gender composition of siblings on educational attainment Garg and Morduch (1998) for example argue that it is the number of older sisters that matters While we cannot fully address this concern (the number of older sisters is highly correlated with the total number of children) it is possible to test whether having the first two births be daughters (or sons) directly affects educational attainment allowing for the effect of total number of children

A limitation of this approach as in Angrist and Evans (1998) is that I am only able to estimate fertility for households with two or more children Correspondingly since identification comes from the gender composition of the first two children the regression sample is restricted to the 84 of sample households that have at least two children It also implies that the results may only apply to households with two or more children This qualification must be kept in mind in interpreting results

45 Allowing for credit constraints

A final concern relates to interpreting the estimated coefficient on the expectation of co-residence A significant coefficient need not suggest that it is the family contract that induces strategic investment in childrenrsquos education Households that enter into these contracts do so because they are credit constrained And a theoretical literature argues that credit constraints can

24

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

themselves induce an unequal treatment of children (Dasgupta 1993) Thus a significant effect of expectations of old-age residence with the oldest son on parental investments in his schooling relative to other children may merely reflect credit constraints

Equation (15) suggests that the predictive power of the family contract model of strategic investments comes from the fact that the family contract affects the rate of return to a sonrsquos education Thus expectations of co-residence will remain a significant determinant of schooling outcomes even in regressions that control for expected life cycle incomes and credit constraints

To do this I condition regressions on household savings following MaCurdy (1983) and Blundell and Walker (1986) Household savings incorporate expectations of future income as well as current and future credit constraints and hence control for all out-of period variables which may affect schooling investments Conditioning on savings removes any effect of expectations of co-residence on schooling through wealth or credit constraints leaving expectations to affect schooling choices only through preferences or through the net returns to schooling It also controls for many birth order effects on schooling since most of these are assumed to operate through their effect on credit constraints and household wealth This approach however requires a treatment of the endogeneity of savings Assets are a natural instrument and I accordingly predict household savings with the value of assets held by the household at the start of the current period Since agricultural land may directly affect the value of child labor agricultural land ownership and the value of agricultural land are included in the regressor set with identification coming from the value of other households assets

46 Estimating equation

Our final estimating equation for the educational outcome of child i in household j and village k is

In this equation educ is the schooling outcome being considered (attendance days language and mathematics test scores) E(Res_os) is an indicator variable that takes the value 1 if parents state that they expect to reside with their oldest son 0 otherwise This variable is entered independently but also with an interaction with an indicator for whether the child is the oldest son (oldestson) so

25

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

as to test whether expectations of old-age residence differentially affect investments in the schooling of the oldest son The regression equation also conditions on total number of children tchild and on household savings S Expectations of co-residence with the oldest son total number of children and household savings are all treated as endogenous So too is the interaction of expectations of old-age residence with the indicator of whether the child is the oldest son This is done by expanding the instrument set to include interactions of the indicator for oldest son with other instruments for old-age residence

As previously noted the regression includes a number of demographic characteristics of the individual and of the household Amongst child-level regressors (X) in addition to the childrsquos age gender and caste I also include dummy indicators for whether the child is the oldest son the oldest daughter or the oldest child At the household level demographic indicators include a dummy variable for whether the first child is a son as well as the ldquodemographic shockrdquo the difference in age between the oldest child and the oldest son and this difference squared

Additional parental and household characteristics (Z) include the age and squared age of both parents years of education of both parents indicators for the literacy of the fatherrsquos father and the motherrsquos father an indicator for ownership of agricultural land and the value of agricultural land School and village level variables (T) are the predicted student-teacher ratio in the school (based on prevailing norms which assign teachers to schools on the basis of the school population) a quadratic in school population the proportion of students in the school that are from scheduled castes and tribes and the village agricultural wage for men and women

47 Regression sample

As previously noted the sample is restricted to the 84 of households with at least two children Additionally I trim the data removing outliers (falling in the top 1 percentile) Finally the regressions are limited to children who attend school for at least 100 days (out of a total of 175 school days between June and January of the school year) This is because a number of students enroll in the early months and subsequently never attend school or because of long-term seasonal migration which also severely restricts attendance The 100 day cut-off eliminates the bottom 5 of the distribution (by attendance) The final regression sample is approximately 7350 households

26

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

5 Results

51 OLS regressions

Table 8 provides OLS estimates of the effect of expected co-residence with the oldest son on schooling outcomes of all children in our sample with an interaction with the indicator for the oldest son enabling a test for a differential effect on this child

The regressions reported in this table suggest that expected co-residence with the oldest son has little significant effect on schooling outcomes with the exception of a negative effect on attendance of children in such households There is no significant effect on test scores either of the variable itself or of its interaction with the indicator for the oldest son The total number of children however reduces all schooling outcomes with the coefficient being statistically significant for attendance and language test scores Similarly an increase in savings implies a reduction in schooling outcomes with a statistically significant effect (at conventional levels) on test scores

52 First Stage and Instrumental Variable Regressions

To produce causal evidence of the effect of expectations of old-age residence on schooling investments I turn to IV regressions based on the set of instruments previously described Table 9 provides first-stage regressions on the endogenous variables Expectations of co-residence with the oldest son the interaction of this variable with an indicator variable for whether the child is an oldest son the total number of children in the household and household savings

The first regression confirms that an increase in the age difference between the first child and the first son reduces expectations of old-age residence with the oldest son Allowing for the interaction with the student teacher ratio the marginal effect of the age difference on this expectation evaluated at mean levels of the relevant variables is -004 And as expected growing state investment in schools and school quality as reflected in the student-teacher ratio in schools reduces the effect of this demographic shock As norms about minimum levels of schooling are revised upwards the probability of residing with children in old age is reduced constraining the ability of parents to make this choice Turning to fertility regressions (column 3) the coefficients on the son-son and daughter-daughter pairing are positive and statistically significant at conventional levels These results confirm that the gender composition of the first two children affect fertility choices They also are suggestive of household demand in this state for at least one son and one daughter

27

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Table 10 provides results from IV regressions based on the first stage regressions from table 9 The first column reveals a negative effect of the expectation of residence with the oldest son on the number of days that he attends school an effect that is statistically significant at the 10 level The next two columns reveal that test scores are also lower for oldest sons in households in which parents expect to reside with him For test scores the coefficients are statistically significant at the 5 level Thus the results from this table suggest that expectations of residing with the oldest son when elderly do result in lower schooling outcomes for this son The negative effect on days of attendance suggests a possible pathway parents may be more likely to rely on the oldest son for work in the house or in income-earning occupations thereby lowering his participation in school and hence lowering his scholastic achievement

The next table table 11 reports results implementing some of the exclusion restrictions suggested by the regressions in table 10 Specifically I omit the dummy indicator for whether the first child in the household is a son from the regression Additionally I include the age difference between the oldest child and the oldest son and the squared difference amongst the instruments allowing them to affect outcomes only through the set of endogenous variables Doing so does not significantly alter results The coefficient on the interaction between the indicator for oldest son and parentrsquos expectation of residence with him is negative and statistically significant for all schooling outcomes (attendance and test scores)

In contrast the expectation of co-residence in old age does not significantly affect the schooling of children other than the oldest son though the coefficient on the variable (parents expect to co-reside with the oldest son) is positive it is not statistically significant and is of relatively low magnitude This is not surprising The regression conditions on household savings and hence on current or expected credit constraints one avenue through which expectations of old-age residence may affect other children For oldest sons the expectation of co-residence is still expected to determine his schooling since it affects the returns to schooling (equation 13) It is unlikely to significantly affect the returns to schooling of other children in the household

The negative effect of expectations of co-residence on the schooling achievement of the oldest son is not just an ldquooldest sonrdquo or an ldquooldest childrdquo effect the regression separately includes controls indicators for whether the child in question is an oldest son or the oldest child Being the oldest son in fact significantly increases attendance and correspondingly test scores Thus in households in which parents do not expect to reside with the oldest son oldest sons are characterized by higher schooling attainment relative to other children In

28

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

households where parents do expect to reside with their oldest son the overall coefficient on his schooling attainment is negative even allowing for the direct positive effect of being the oldest son

These results contrast with OLS estimates that suggest a negative but insignificant effect of expected co-residence on the schooling attainment of the oldest son As previously discussed the positive bias introduced in OLS regressions may be a consequence of differential preferences for children across households stemming from norms that favor the oldest son in the allocations of goods and perhaps parental time

Turning to other results the regressions reveal that oldest daughters generally do poorly relative to other children The coefficient on attendance is negative and statistically significant while test scores are also lower though not significantly so Confirming results from other studies that have examined the effect of fertility on schooling outcomes the total number of children has a negative and significant effect on attendance and language test scores The effect of fertility on mathematics scores is negative but not significantly so In contrast to the OLS regressions increases in savings increase attendance and test scores though the estimates are statistically significant only in the case of language test scores The results imply that reductions in savings or equivalently a reduction in income reduce childrenrsquos attendance in school and hence test scores

I use the regression estimates from table 11 to infer the magnitude of the effect of expectations of old age residence on schooling outcomes As estimated at the mean values of the relevant variables a 10 increase in the expectation of residence with the oldest son reduces his days of attendance by 04 This is comparable to the effect of the number of children on participation a 10 increase in the number of children reduces days of attendance by 03 Estimated magnitudes for test scores are higher A 10 increase in the expectation of co-residence with the oldest son reduces language test scores by 17 and mathematics test scores by 19 A similar increase in the number of children reduces language and math test scores by 1

53 Over-identification tests

The last table table 12 reports results from over-identification tests for the instruments for fertility separately including first the dummy indicator for the son-son pairing and then the indicator for the daughter-daughter pairing amongst the regressors Due to space constraints I report results only for attendance and language test scores Identical results are obtained from regressions on

29

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

mathematics test scores9 The regressions validate identification both of these indicators have an insignificant direct effect on outcomes

6 Conclusion

The question of how familial systems of support endure and their effect on family outcomes has long been of interest to researchers This paper examines one such system the dependence of elderly parents on their oldest son and specifically the expectation that they will reside with him in old age It has long been assumed that this is one factor explaining son preference in countries such as India and hence observed high fertility rates And it widely hypothesized that such dependence would affect parental investments in childrenrsquos schooling

This paper first develops a theoretical framework that suggests that parental dependence on children for old age support has an ambiguous effect on their schooling it depends on how schooling affects life cycle income profiles The empirical analysis explores the effect of parental dependence on schooling outcomes basing identification on a combination of demographic shocks and measures of state investment in schooling Through regressions that also condition on the total number of children and household savings treating both as endogenous I find that the expectation of co-residence with the oldest son reduces his attendance in school and schooling achievement

9 For regressions on mathematics test scores the coefficient on son‐son is ‐031 (standard error of 126) The coefficient on daughter‐daughter is 003 (standard error of 095)

30

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

References

Anderberg Dan and Alessandro Balestrino 2003 ldquoSelf-enforcing Intergenerational Transfers and the Provision of Educationrdquo Economica 7055-71 Angrist Joshua D and William N Evans 1998 ldquoChildren and Their Parentsrsquo Labor Supply Evidence from Exogenous Variation in Family Sizerdquo The American Economic Review 88(3) 450-477 Asis Maruja Milagros B Lita Domingo John Knodel and Kalyani Mehta 1995 ldquoLiving Arrangements in Four Asian Countries A Comparative Perspectiverdquo Journal of Cross-cultural Gerontology 10145-162 Azariadis Costas and Luisa Lambertini 2003 ldquoEndogenous Debt Constraints in Lifecycle Economiesrdquo The Review of Economic Studies 70(3)461-487 Baland Jean-Marie and James A Robinson 2000 ldquoIs Child Labor Inefficientrdquo Journal of Political Economy 108(4)663-679 Becker Gary S (1981) A Treatise on the Family Becker Gary S and H Gregg Lewis 1973 ldquoOn the Interaction between the Quantity and Quality of Childrenrdquo The Journal of Political Economy 81(2)S279-S288 Becker Gary S and Kevin M Murphy 1988 ldquoThe Family and the State Journal of Law and Economics 31(1) 1-18 Behrman JR and P Taubman 1986 ldquoBirth Order Schooling and Earningsrdquo Journal of Labor Economics 4S121-S145 Ben Porath Y 1980 ldquoThe F connection Families Friends and Firms and the Organization of Exchangerdquo Population and Development Review 61-30 Blundell Richard and Ian Walker 1986 ldquoA Life-Cycle Consistent Empirical Model of Family Labor Supply Using Cross-section Datardquo Review of Economic Studies LIII 539-558

31

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Caldwell John C P H Reddy and Pat Caldwell 1982 ldquoThe Causes of Demographic Change in Rural South India A Micro Approachrdquo Population and Development Review 8(4)689-727 Caldwell John C PH Reddy and Pat Caldwell 1984 ldquoThe Determinants of Family Structure in Rural South Indiardquo Journal of Marriage and Family 46(1)215-229 Cox Donald ldquoIntergenerational Transfers and Liquidity Constraintsrdquo The Quarterly Journal of Economics 105(10 187-217 Das Narayan 1987 ldquoSex Preference and Fertility Behavior A Study of Recent Indian Datardquo Demography 2495-108 Dasgupta Partha 1993 An Inquiry into Well-Being and Destitution New York Oxford University Press Edlund Lena and Aminur Rahman 2005 ldquoHousehold Structure and Child Outcomes Nuclear vs Extended Families ndash Evidence from Bangladeshrdquo Columbia University Manuscript Edmonds Eric V Kristin Mammen Douglas L Miller ldquoRearranging the Family Income Support and Elderly Living Arrangements in a Low-Income Countryrdquo The Journal of Human Resources XL(1) 186-206 Ejrnaeligs Mette and Claus C Poumlrtner 2004 ldquoBirth Order and the Intrahousehold Allocation of Time and Educationrdquo The Review of Economics and Statistics 86(4)1008-1019 Foster Andrew 1993 ldquoHousehold Partition in Rural Bangladeshrdquo Population Studies 4797-114 Garg Ashish and Jonathan Morduch 1998 ldquoSibling Rivalry and the Gender Gap Evidence from Health Outcomes in Ghanardquo Journal of Population Economics 11471-493 Government of Karnataka 1999 Human Development in Karnataka ndash 1999 Government of Karnataka 2005 Karnataka Human Development Report 2005

32

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Greif A 1997 ldquoContracting Enforcement and Efficiency Economics Beyond the Lawrdquo Michael Bruno and Boris Pleskovic eds Annual World Bank Conference on Development Economics Washington DC The World Bank Jensen Robert 2003 ldquoEqual Treatment Unequal outcomes Generating Sex Inequality through Fertility Behaviorrdquo Harvard University Manuscript Kandori Michihiro 1992 ldquoSocial Norms and Community Enforcementrdquo The Review of Economic Studies 59(1) 63-80 Kochar Anjini 2000 ldquoParental Benefits from Intergenerational Co-residence Empirical Evidence from Rural Pakistanrdquo Journal of Political Economy 108(6)1184-1289 Kotlikoff Laurence J amp Spivak Avia 1981 ldquoThe Family as an Incomplete Annuities Marketrdquo Journal of Political Economy 89(2)372-91 Lambertini L 1998 ldquoBorrowing and Lending without Commitment and with Finite Liferdquo Manuscript Lillard Lee A and Robert J Willis 1997 ldquoMotives for Intergenerational Transfers Evidence from Malaysiardquo Demography 34(1) 115-134 MaCurdy Thomas E 1983 ldquoA Simple Scheme for Estimating an Intertemporal Model of Labor Supply and Consumption in the Presence of Taxes and Uncertaintyrdquo International Economic Review 24(2) 265-289 Manacorda Marco and Enrico Moretti 2006 ldquoWhy do Most Italian Youths Live with their Parents Intergenerational Transfers and Household Structurerdquo Journal of the European Economic Association 4(4)800-829 Nugent Jeffrey B 1985 ldquoThe Old-Age Security Motive for Fertilityrdquo Population and Development Review 11(1) 75-97 Nugent Jeffrey B 1990 ldquoOld Age Security and the Defense of Social Normsrdquo Journal of Cross-Cultural Gerontology 5 243-254 Parish W and R Willis (1994) ldquoDaughters Education and Family Budgets Taiwan Experiencesrdquo Journal of Human Resources 28(4)1126-1166

33

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

34

Rajan S Irudaya 2010 ldquoAssessing the Economic Well-being of Elderly Persons in South Asiardquo Manuscript Rangel Antonio 2003 ldquoForward and Backward Intergenerational Goods Why is Social Security Good for the Environmentrdquo American Economic Review 93(3)813-834 Raut Lakshmi and Lien H Tran 2005 ldquoParental Human Capital Investment and Old-Age Transfers from Children Is it a Loan Contract or Reciprocity for Indonesian Familiesrdquo Journal of Development Economics 77389-414 Rosenzweig Mark R and Kenneth I Wolpin 1993 ldquoIntergenerational Support and the Life-Cycle Incomes of Young Men and Their Parents Human Capital Investments Coresidence and Intergenerational Family Transfersrdquo Journal of Labor Economics 11(1) part 1 84-112 Sasaki Masaru 2002 ldquoThe Causal Effect of Family Structure on Labor Force Participation among Japanese Married Womenrdquo The Journal of Human Resources 37(2)429-440

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Table 1 Fatherrsquos education years by occupation

Primary source of income Fatherrsquos education in years

Number of households

Own farm 511 (482)

4113 (035)

Agricultural labor 281 (411)

3204 (028)

Non-agricultural labor ndash unskilled

349 (378)

2463 (021)

Non-ag labour - skilled 544 (451)

854 (007)

Salary 946 (536)

454 (004)

Business or trade 668 (465)

504 (004)

Source Survey data Figures in parentheses are standard deviations for education years and proportion of total households for number of households

Table 2 Parentrsquos expectations of minimum levels of education required for boys and girls

Minimum years of schooling thought necessary For parentsrsquo generation For current generation of children

Boys 920 (491)

1426 (371)

Girls 715 (521)

1215 (307)

Source Survey data Standard deviations in parentheses

Table 3 Householdsrsquo views on minimum years of education required by occupation

Primary source of income Minimum required years of education (mean)

Own farm 434 (358) Agricultural labor 416 (348) Non-agricultural labor - unskilled 509 (373) Non-ag labour - skilled 674 (361) Salary 1366 (321) Business or trade 952 (323)

Source Survey response to question ldquoWhat do you believe is the minimum years of schooling required for each occupationrdquo Standard deviations in parentheses

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

36

Table 4 Current parentrsquos expected old age residence by fatherrsquos parentsrsquo old age residence

Fatherrsquos parentsrsquo old age residence Parentrsquos expected residence in old age (row ) (column )

Alone With oldest son

With other son

With daughter

Other Total

Alone 1205 4093 3525

965 3278 2589

725 2463 2186

44 149 3143

5 017 4167

2944 10000 2773

With oldest son

876 2716 2563

1188 3684 3187

1108 3436 3340

51 158 3643

2 006 1667

3225 10000 3038

With other son

517 3131 1513

562 3404 1508

551 3337 1661

17 103 1214

4 024 3333

1651 10000 1555

With daughter 158

2638 462

225 3756 604

202 3372 609

14 234 1000

0 00 00

599 10000 564

Other (includes canrsquot say)

662 3015 1927

788 3588 2114

731 3329 2204

14 064 1000

1 005 833

2196 10000 2069

Total 3418

3220 10000

3728 3512 10000

3317 3125 10000

140 132

10000

12 011

10000

10615 10000 10000

Note Based on data from sample surveys

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

37

Table 5 Summary Statistics

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Fatherrsquos education (years)

440 (467)

450 (469)

401 (461)

465 (463)

431 (485)

Motherrsquos education 332 (397)

332 (399)

300 (411)

382 (402)

302 (407)

Total number of children

285 (125)

282 (124)

337 (115)

267 (117)

334 (118)

Number of sons 169 (085)

167 (083)

169 (082)

162 (081)

175 (090)

Number of daughters 178 (099)

164 (088)

185 (098)

176 (099)

188 (104)

Scheduled caste or tribe

035 (048)

034 (047)

036 (048)

033 (047)

037 (048)

Household savings (Rs)

2723429 (2893144)

2901159 (2982262)

3395238 (3025017)

1990191 (2489781)

2766507 (2840827)

Land owned (acres) 244 (538)

248 (532)

258 (539)

211 (507)

259 (562)

Proportion of households with main income own ag

035 (048)

036 (048)

035 (048)

032 (047)

040 (049)

Proportion of households with main income from ag lab

028 (045)

029 (045)

028 (045)

022 (042)

033 (047)

Student-teacher ratio in government school

2698 (367)

270 (361)

272 (336)

267 (381)

271 (373)

Proportion of oldest sons who are oldest child

059 (049)

068 (046)

041 (049)

059 (049)

058 (049)

Birth order of oldest son

165 (095)

147 (081)

198 (107)

161 (089)

168 (097)

Age difference between oldest son and oldest child

180 (287)

134 (267)

267 (311)

166 (271)

188 (286)

Number of households 9718 3080 1534 2297 1765

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

38

Table 6 Attendance and Test scores by birth order and gender and parentrsquos expectation of old age residence

Parentrsquos expected residential arrangements when old Variable Full sample With oldest

son With other

son Alone Canrsquot say

Attendance (days) Oldest son

14586 (1231_

14522 (1247)

14414 (1307)

14730 (1128)

14653 (1217)

Other sons (mean)

14409 (1301)

14325 (1260)

14338 (1321)

14567 (1283)

14436 (1360)

Daughters (mean) 14614 (1220)

14512 (1239)

14485 (1262)

14696 (1150)

14691 (1220)

Language test scores Oldest son 5462

(1907) 5498

(1890) 5286

(1931) 5776

(1846) 5175

(1942) Other sons (mean) 5222

(1956) 5274

(1889) 5099

(1965) 5421

(2030) 5079

(1959) Daughters (mean) 5572

(1941) 5556

(1921) 5531

(1946) 5922

(1843) 5353

(1978) Mathematics test scores

Oldest son 4681 (1641)

4748 (1640)

4542 (1592)

4972 (1582)

4325 (1685)

Other sons (mean) 4550 (1574)

4532 (1541)

4443 (1553)

4811 (1542)

4427 (1668)

Daughters (mean) 4738 (1629)

4748 (1665)

4647 (1588)

5023 (1574)

4527 (1628)

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

39

Table 7 Fertility and Expectations of Old-age residence with oldest son by pairings of first two births

Pairings Number of households

Proportion with three or more children

Expectations of residence with oldest

son Daughter-daughter 2612

(027) 079

(041) 015

(036) Daughter-son 2258

(023) 058

(049) 026

(044) Son-daughter 2332

(024) 058

(049) 040

(049) Son-son 2457

(025) 056

(050) 035

(048)

Note Figures in parentheses under number of households is proportion to total households For remaining two columns standard deviations in parentheses

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Table 8 OLS regressions

Attendance (days) Language test score Mathematics test score Parents expect to reside with oldest son

-098+

(053) 067

(072) 052

(062) Oldest sonparents expect to reside with oldest son

-031 (068)

-018 (098)

066 (087)

Total children (log) -291

(067) -190

(097) -068 (093)

Savings (Rs lsquo000) -0006 (001)

-004

(001) -004

(001) STR -021

(010) -012 (013)

-012 (013)

Age difference (oldest child amp oldest son)

017 (021)

018 (030)

045+

(024) Age difference square -002

(002) -001 (003)

-004+

(002) Oldest son 055

(051) 036

(079) -040 (072)

Oldest daughter -091+

(051) 137+

(079) 105+

(065) Oldest child -082

(042) 049

(061) 072

(052) First child is son

002 (043)

-056

(065) -009 (057)

Age 015 (022)

-098

(040) -073+

(039) Son -187

(061) -165+

(092) -027 (079)

Scheduled caste -168

(052) -156

(069) -091 (061)

Scheduled tribe -135

(070) -332

(090) -274

(085) Father education years 015

(003) 036

(006) 027

(005) Mother education years 027

(005) 076

(007) 050

(006) Regression F (Prob gt F)

905 (000)

1925 (000)

1370 (000)

Notes Additional regressors included in all regressions are father and motherrsquos ages and ages squared indicator for literacy of mother and father dummy indicator for ownership of agricultural land value of agricultural land school enrollment and enrollment square proportion of students in school from scheduled castes and tribes village male and female agricultural wages Sample size is 7351 Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Table 9 First Stage Regressions

Parents expect to reside with oldest

son

Oldest son parents expect to reside with oldest

son

Number of children (log)

Savings

Instruments STRage diff -0004

(0002) -0001 (0001)

-0002

(0001) 004

(008) STRage diff sq 0001

(00002) 00001

(00001) 00002+

(00001) -0002 (001)

Oldest sonSTRage diff

-00004 (0001)

-0001

(00004) 0001

(00004) 001

(004) Oldest sonSTRage diff sq

000003 (000006)

00001

(000005) -000004 (000004)

-0002 (0004)

Son-son -007

(002) -001 (001)

021

(001) 069

(111) Daughter - daughter -003

(002) -0003 (001)

021

(001) -041 (121)

Value of assets (Rs lsquo000)

00002

(00001) 00001

(000004) 00001+

(000004) 003

(001) Assets age difference

-00001

(000002) -96 e-6

(000001) 54 e-6

(000001) 0004

(0002) Assets age difference square

39 e-6

(26 e-6) 56 e-7

(00001) -66 e-7 (13 e-6)

-00005

(00002) Age difference (oldest child and oldest son)

010

(004) 002

(003) 015

(002) -120 (206)

Age difference square

-001

(001) -0004 (0003)

-001

(0003) 013

(027) STR -0003

(0002) -0002 (0002)

-00015 (00014)

-044

(012) Father education 0001

(0001) 0001

(0001) -0001

(00008) 029

(008) Mother education -00026

(0002) -00003 (0001)

-0009

(0001) -014

(009) Regression F (Prob gt F)

833 (000)

4235 (000)

19662 (000)

3425 (000)

Notes Additional regressors include those listed in table 8 as well as in the note to the same table Standard errors (in parentheses) are clustered at village level Significant at 5 level + Significant at 10 level

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

42

Table 10 2SLS regressions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

009 (006)

308 (1240)

1230 (938)

Oldest sonparents expect to reside with oldest son

-2174+

(1257) -3641

(1780) -3145

(1574) Number of children (log) -572

(259) -61

(446) -150 (338)

Savings (Rs lsquo000) 010+

(006) 017+

(010) 008

(009) Other regressors STR -023+

(011) -016 (018)

-011 (015)

Age difference (oldest child amp oldest son)

035 (036)

021 (058)

051 (045)

Age difference square -003 (003)

-002 (005)

-004 (004)

Oldest son 639+

(374) 1077

(541) 900+

(476) Oldest daughter -243

(112) -107 (185)

-031 (150)

Oldest child 077 (106)

330

(156) 322 (137)

First child is son

116 (115)

120 (207)

019 (154)

Age 002 (031)

-117

(048) -095

(046) Son -211

(068) -235

(109) -059 (095)

Scheduled caste -134

(061) -073

(092) -030 (077)

Scheduled tribe -108 (076)

-290

(113) -235

(100) Fatherrsquos education 012

(005) 030

(007) 024

(006) Motherrsquos education 025

(006) 075

(010) 052

(008) Wald χ2

(Prob gt χ2) 25299 (000)

46527 (000)

39574 (000)

Note All regressions are IV regressions Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

43

Table 11 2SLS regression ndash With exclusion restrictions

Attendance (days) Language test scores

Mathematics test scores

Endogenous variables Parents expect to reside with oldest son

259 (522)

483 (824)

573 (681)

Oldest sonparents expect to reside with oldest son

-2042+

(1201) -3439

(1718) -3317

(1571) Number of children -500

(173) -514

(270) -216 (221)

Savings (Rs lsquo000) 008

(006) 016+

(009) 010

(008) Other regressors STR -023

(011) -014 (016)

-015 (015)

Oldest son 633+

(364) 1045

(526) 984

(478) Oldest daughter -192

(075) -052 (120)

-046 (103)

Oldest child 051 (101)

301

(157) 336 (140)

Age 002 (029)

-120

(045) -084

(043) Son -225

(066) -243

(098) -099 (088)

Scheduled caste -137

(060) -075

(089) -038 (079)

Scheduled tribe -110 (075)

-292

(111) -232

(100) Fatherrsquos education years 013

(005) 030

(007) 024

(006) Motherrsquos education years 025

(006) 075

(009) 051

(008) Wald χ2

(Prob gt χ2) 25518 (000)

48615 (000)

37180 (000)

Note All regressions are IV regressions Regressions omit age difference (between oldest child and oldest son and age difference square as well as indicator variable for whether first child is a son Additional regressors are listed in the note to table 8

Significant at 5 level + Significant at 10 level Standard errors are clustered at the village level

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

44

Table 12 Over-identification tests for instruments for number of children

Attendance (days) Language test scores

(1) (2) (3) (4)

Endogenous variables Parents expect to reside with oldest son

341 (543)

342 (527)

559 (877)

464 (861)

Oldest sonparents expect to reside with oldest son

-2133+

(1211) -1877

(1253) -3516

(1730) -3475

(1812) Number of children -533

(194) -396

(258) -543+

(287) -537

(436) Savings (Rs lsquo000) 008

(006) 007

(006) 016+

(009) 016+

(009) Other regressors Daughter-daughter 028

(072) -- 026

(111) --

Son-son -- -048 (092)

-- 011 (143)

STR -023

(011) -022

(011) -014 (016)

-015 (017)

Oldest son 650+

(366) 594

(373) 1059

(527) 1054

(543) Oldest daughter -197

(075) -157

(106) -057 (119)

-060 (171)

Oldest child 053 (101)

049 (101)

303

(157) 301

(157) Age

0002 (029)

-0001 (028)

-121 (046)

-119 (046)

Son

-223

(067) -202

(082) -242

(099) -249

(127) Scheduled caste

-134

(061) -140

(059) -073 (090)

-074 (091)

Scheduled tribe

-108 (075)

-115 (076)

-290

(111) -291

(113) Fatherrsquos education years

012

(005) 013

(005) 030

(007) 030

(007) Motherrsquos education years

025

(006) 026

(006) 075

(009) 075

(010) Wald χ2

(Prob gt χ2) 25408 (000)

25902 (000)

48758 (000)

48354 (000)

Note All regressions are IV regressions Additional regressors include those in table 8 as well as in the accompanying note Standard errors (in parentheses) are clustered at the village level

Significant at 5 level + Significant at 10 level

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

APPENDIX A I ignore any effect of schooling on first stage income10 First consider the case when schooling only increases second stage income (yt+2) Under the assumption that incomes increase

monotonically with schooling the sign of is therefore determined by that of in turn given by the equilibrium condition (11) Differentiating (11)

(A1) Equation (A1) results because the sons peak earnings ) do not directly influence the fathers loan supply decision ( ) Thus the numerator on the right hand side of (14) comprises only the effect of the sons income on the loan he demands from his father when he is young ( ) Under standard regularity conditions the denominator of (A1) is positive

Therefore the sign of and hence will be positive if the sons demand for loans increases with his income when middle-aged Suppressing the super-script for generation t for notational simplicity (so that the effect of incomes on loan demands and hence the effect of human capital investments on the interest rate on the inter-generational contract is given by

(A2) where is autarkic consumption and |A|lt011

Since μ2=0 u(ct+2) gt u(yt+2) This inequality in conjunction with μ1 gt 0 implies that u(ct+1) lt u(yt+1) because (6) is now a strict inequality Consequently

which in turn implies that Thus schooling increases the interest rate on loans between (adult) children and their parents 10 Even if schooling did increase first stage income due to the likelihood of default changes in first stage income have no effect on young adultsrsquo demand for loans from their parents Intuitively the inability to enforce the contract implies binding credit constraints on first period loan demands Conversely changes in second period income (and consumption) affect the probability of default and hence the constraint itself 11

45

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46

Now allow schooling to also increase third-stage income With this

(A3) =

In turn and once again ignoring generational subscripts

(A4)

As before is autarkic consumption in old age Since μ2=0 u(ct+2) gt u(yt+2) and

which in turn implies that Thus while schooling induced increases in second stage income increase interest rates similar increases in third stage incomes lower interest rates Allowing for schooling to increase both second and third stage incomes the overall effect on interest rates is given by

(A5)

Where

Thus the sign of depends on whether the value of the intergenerational contract relative to autarky is greater in the second or third stage of the life cycle and on the schooling gradients in these two stages

46