ENGEL CURVE METHOD FOR MEASURING POVERTY

By

T. Krishna Kumar, Jayarama Holla, and Puja Guha

January 8, 2008

P.V. Sukhatme Memorial Lecture by T. Krishna Kumar at the Annual Conference of the Indian Society of Probability and Statistics, Nagpur, India,

January 10, 2008

Economics and Social Science Area

Indian Institute of Management

Bannerghatta Road

Bangalore-560076. INDIA -

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ENGEL CURVE METHOD FOR MEASURING POVERTY1

By

T. Krishna Kumar2, Jayarama Holla3, and Puja Guha3

I INTRODUCTION

1.1 Professor Sukhatme, as the Head of Statistics Division of the Food and Agricultural Organization of the United Nations, emphasized the importance of augmenting world food production, and improving its distribution so as to reach the deprived sections of human community across the world. He also brought that experience to address the hunger situation in India. It is in this connection that he made his pioneering contribution to the statistical measurement of the extent of hunger (or under-nutrition) and malnutrition (or protein deficiency) (Sukhatme (1961, 1965, 1974)). He stressed the importance of examining the total food requirements on the one hand and its requirements at the individual level distinguished by age, sex, and physical activity on the other. He went deeper into the nutrition science to argue that calorie deficiency is much more important than protein deficiency, as utilization of proteins requires a minimum quantity of calories. His measure of incidence of hunger was based on the integration of the joint distribution of the requirements and availability over the set where the availability at the individual level is less than what is required. Parts of this method were borrowed, with due acknowledgements to Sukhatme, by Dandekar and Rath (1971) in providing a scientific basis for defining a poverty line. Indian literature on measurement of poverty has set the trends in poverty measurement elsewhere in the world. Thus Professor Sukhatme’s contributions to estimation of hunger have a lasting impact on measurement of poverty and its alleviation.

1.2 Around 1991 Sitaramam showed the first author the draft of a paper he and Anil Gore, wrote. That was the first draft of an entirely new approach to the measurement of poverty without a poverty-line, and it was based on cereal consumption deprivation. While discussing

1 P.V. Sukhatme Memorial Lecture by the first author at the Annual Conference of the Indian Society of Probability and Statistics, Nagpur, January 10, 2008.

2 Guest Faculty, Indian Institute of Management, Bangalore and Retired Professor, Economic Analysis Unit, Indian Statistical Institute, Bangalore. The work reported here is based on the work the first author did with V. Sitaramam and Anil Gore in the early nineties. The authors thank N. Krishnaji, Federico Perali, and S. Subramanian for discussions and comments on a working draft of this paper. The authors thank NSSO for providing the data on CDs with excellent documentation.

3 Doctoral students, Indian Institute of Management, Bangalore

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that draft Sitaramam explained to him the work he and his colleagues were doing on “Enzymology” or “Catalysis”. It was then that he saw a similarity between the saturation curves they were using in catalysis (as well as in his draft paper with Anil Gore) and the Engel curves for necessities (or essential commodities) of economic analysis4. He joined them in revising that draft to provide the economic content (Kumar, Gore and Sitaramam (1996))5. An empirical application of those ideas were provided by establishing a hierarchy of needs using National Sample Survey Organization (NSSO) data and using cereals, the first in that hierarchy, as the commodity to measure the commodity-specific consumption deprivation (Sitaramam, Kumar, Gore, Paranjpe, and Sastry (1996)). That study used grouped data of NSSO for various earlier rounds (16th to 46th rounds covering the period 1960-1990) and estimated saturating Engel curves for cereals using per capita monthly expenditure on cereals as a function of monthly per capita total expenditure.

1.3 In recent years many researchers studying poverty in India had access to ungrouped data at the household level provided by NSSO. The earlier work of Sitaramam et. al. (1996) was extended recently using this household level data for the three large surveys of 1987-88, 1993-94, and 1999-2000, and by introducing household size as an additional variable affecting the Engel curve (Kumar, Mallick, and Holla (2008)). That study observed that there could have been a substitution of cereals by some other food items and that in some states cereal substitutes, such as tapioca, are used in place of cereals. In order to take these aspects into account we extend that work further in this paper by considering deprivation in food (all food items, instead of limiting to cereals). The earlier work did not make any adjustments to different household compositions within a given household size and treated adults and children, and males and females, alike. The literature in consumer demand and living standards studies suggest that households of different compositions must be converted to comparable adult equivalent scales.6 In this paper we replace per capita consumption by per adult male equivalent consumption, and household size by number of adult equivalent units. In the previous analysis each sampled household was given equal weight ignoring the sample design that gave more opportunities for certain households to get selected. In this paper we make the necessary correction by multiplying the sample observations by a multiplier provided by NSSO to correct for this.

4 Engel curve for a specific commodity is the relation between the consumption expenditure on that commodity as a function of income (total expenditure).

5 This was perhaps one of the first instances of defining an inclusive measure of poverty, and the first without any poverty line. The first draft of the paper written by Sitaramam and Gore was privately circulated for comments in 1991. The revised paper by Kumar, Gore and Sitaramam was submitted for publication in February 1993 and presented at a conference on poverty and income inequality in March 1994 held in Bangalore.

6 We thank an anonymous referee of Journal of Development Studies who emphasized the need for such adjustment while reviewing our earlier work for that journal.

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II DIFFERENT DIMENTIONS OF HUMAN DEPRIVATION AND TRADITIONAL MEASURES OF POVERTY

2.1 Hunger and malnutrition are the basic forms of human deprivation. Other dimensions of deprivation could be due to lack of access to basic health services, housing, primary education, drinking water, sanitation, etc. Economists label all of them together as essential goods and services and define poverty as a condition of not having adequate personal income to procure these essential services. Noting that food is the most essential of all these essential commodities, they defined poverty as not having enough personal resources to acquire adequate food, such as two square meals a day. When economists were vague about what constitute the basic food requirement such as two square meals a day Dandekar and Rath (1971) used the ideas contained in Sukhatme’s work and defined minimum calorie requirement for a reference individual and adjusted it to capture the average calorie requirements at All-India level for rural and urban sectors depending on the demographic and occupational distribution of the population. Dandekar and Rath determined, using the National Sample Survey data, at what total expenditure the households meet this average calorie requirement and called it the poverty line. The official poverty line is based primarily on this methodology developed by Dandekar and Rath, which was itself based on Sukhatme’s pioneering contribution on measuring hunger.

2.2 V.K.R.V. Rao criticized this method stating that what it measures is under-nutrition and not poverty. Sukhatme was also critical of this approach for using the average requirement. He was of the view that the capacity of a person to perform work is not limited by his current calorie intake but by the efficiency with which he converts the calorie intake into metabolisable energy over his homeostatic range of intake.TP

7PT More specifically, he stated that over a long enough period

to cover intra-individual variations that adjust storage and utilization of calories, if calorie intake is x and calorie requirement (that depends on age, sex, occupation and activity) is y and their joint distribution is f(x, y) then the extent of under-nutrition in the aggregate is given by:

1.2....................................................................),(∫∫<

=yx

dxdyyxfu

In recent years there has been a considerable debate on the way poverty estimates are made in India. An excellent discussion is found in the work of Deaton and Kozel (2005). That entire

TP

7PT Although P.V. Sukhatme was a member of the Expert Group on estimation of proportion and number of poor set

up by the Government in 1989, he expressed his dissent and reiterated his point of criticism by submitting a supplementary note as Annexure 1 to the Report of the Expert Group (1993). Krishnaji (1981), however, was critical of the suggestion made by Sukhatme. He pointed out that the estimation of intra-individual variation for the same age-sex-occupation specific group of households, required for Sukhatme’s procedure, cannot be derived from non-experimental data of NSSO.

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debate is based on accepting the basic methodology of Dandekar and Rath and focuses on several empirical shortcomings of data used and the dogma associated with it.

2.4 There are some other major directions in which the poverty research has been commented upon recently. It is noted that the calorie norm itself is inappropriate. Behrman and Deolalikar (1987) found that the poor substitute, even at low levels of income, luxury food items for food items with higher calories when their income rises, implying that the poor’s preferred need is not necessarily that of meeting the calorie requirement. Rath (1996) and Rath (2003) and Sen (2005) demonstrate that the actual calorie intake has gone down below the norm over the years even at moderate levels of income. Meenakshi and Viswanathan (2003) demonstrate that while poverty line-based poverty has decreased the calorie deprivation has increased. The main theme of most of these papers is that the poverty line is measured for a reference group for a reference year and it is adjusted for other non-reference groups and non-reference years using price deflators. The changing poverty lines so determined do not conform to the calorie norm used in defining the reference poverty line.

2.5 It is also suggested that instead of the research economist suggesting what should be the poverty line the responding household or individual must answer a minimum income question stating at what level of income he or she would consider that his or her both ends are met-thus going back to the vague definition of poverty line that prevailed before the work of Sukhatme and Dandekar and Rath (Pradhan and Ravallion (2000)). Kumar, Mallick, and Holla (2008) show that cereal consumption deprivation, a major component of poverty in India, has little correlation with the various traditional measures of poverty, thus questioning the practical relevance of the traditional measures of poverty if consumption deprivation of essential commodities is the focus of any study on poverty. Lipton (1997) picks a few holes in the prevailing traditional methodology of poverty measurement. In particular he comments that the severity of poverty measured by traditional Foster-Greer, Thorbecke (1984) type of measure lacks intuitive economic meaning. Atkinson commented, nearly two decades ago, that there is a need to bring about a vertical integration between poverty measurement and welfare economics based on consumption (Atkinson (1987)).

2.5 Some of the essential goods and services, such as food, are private goods supplied mostly through market mechanism, while some others such as primary health services, drinking water, and sanitation are public goods provided by the government. A few other essential goods and services, such as education and non-primary health services, are quasi-public goods provided by non-governmental organizations. The economic access to these basic goods and services is determined not only by the resources at the command of each individual or individual household, but also by the quantity and quality of public and quasi-public goods provided by the

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government and non-governmental organizations.8 Thus personal income is not the major determinant of poverty. Poverty is associated with unemployment or irregular employment thereby making measured or observed income being very volatile. In fact it is that volatile low income that is a major characteristic feature of poverty. Thus, the identification of the poor by a volatile measure seems to be inappropriate. The traditional methods of poverty measurement based on income or total expenditure and its distribution thus seem to be only an indirect way to study poverty. In view of all these deficiencies of the traditional measures of poverty direct measures of poverty, based on consumption deprivation of essential commodities, will be much more useful.

III A NEW MEASURE OF POVERTY BASED ON THE ENGEL CURVE

3.1 The expert group (Government of India, 1993) observed various limitations of the traditional method of estimating the proportion and the number of the poor. Some of them are worth reporting here:

(i) One must note that poverty concept and poverty line are not absolute but relative, and in fact it is the relative poverty that determines the absolute poverty at any income level

(ii) Poverty line determined from consumption pattern does not take into account items of social consumption provided by the government

(iii) The poverty line combines normative and behavioral elements as while the calorie requirement is determined normatively for an essential item food, the requirements for non-food items are set as determined by the observed relation between the food consumption and non-food consumption

(iv) The head-count measure does not measure the severity of poverty

3.2 We follow the route taken by Atkinson and try to integrate poverty measurement with basic microeconomic analysis of demand for an essential commodity. Our approach can be explained easily by identifying two different ways of viewing poverty. One may view poverty at an individual level and then aggregating it over the set of all those who are poor in a given community. This requires associating poverty with the condition of the poor, thus necessitating the definition and identification of the poor9. There is an alternative view where one can consider an individual as a member of a community and it is the situation of the individual within the

8 For a fuller discussion of some of these issues one may see Section II of Kale Memorial lecture of Vaidyanathan (Vaidyanathan (2001)).

9 It is this aspect that gave the poverty line a central role in measurement of poverty. Once the poverty line is so defined the attention was unwittingly shifted to income and income distribution rather than to consumption and consumption distribution and consumption deprivation.

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community that determines what the necessities are for that community. This is the relative nature of poverty that the expert group noted above. It is this interaction of an individual with other members of his community that determines his priorities in consumption, and what his requirements are. It is the distribution of the consumption expenditure on essential commodities relative to the norm determined by the community that provides us information on consumption deprivation. It is the consumption deprivation of an entire community with respect to all essential commodities that constitutes poverty of that community. This is the approach Kumar et. al. (1996), and Sitaramam et.al. (1996) took. In the latter work a hierarchy of needs was established, while in the former the most essential of those needs, cereals, was taken and cereal consumption deprivation was used as a poverty measure.

3.2 Engel curve provides a wealth of information on the community’s consumption behavior at various levels of total expenditure and for different family compositions. Dandekar and Rath (1971), Rao (1981), and Deaton and Tarrozi (2000) came very close to taking a full view of the Engel curve but confined to look only at the poverty line portion of the Engel curve. In determining the total expenditure at which the minimum calorie requirements are met Dandekar and Rath used the observed empirical relation between food expenditure and the total expenditure. Dandekar and Rath looked at the Engel curve based on the National Sample Survey data to determine the total expenditure that would permit an expenditure on food which would meet the calorie requirements. They used the Engel curve only for that purpose. Bhanoji Rao used the typical properties of an Engel curve of a necessity to suggest that the proportion of food expenditure increases, reaches a maximum and then declines. He suggested that the point where this proportion reaches a maximum could be taken as the threshold for acute poverty and suggested that one and half times that level can be taken as the poverty line. Again he left Engel curve behind after deriving a poverty line from it. The Engel curve for a commodity is actually the demand function for that commodity, keeping the prices constant. As such it depicts the consumption behavior of persons or households with different levels of total expenditure. Deaton, who has done considerable work on consumer behavior and consumer demand functions, also examined poverty issue only from the traditional approach and ignored looking at the entire Engel curve for essential commodities. The Engel curve not only suggests how to fix a poverty threshold it also provides a distribution of mean consumption expenditure on food according to income. Thus the Engel curve summarizes the economic equilibrium consumption expenditure on food.

3.3 Sitaramam suggested using commodity-specific consumption deprivation, such as cereal or food consumption deprivation, as a measure of poverty. Kumar, Gore, and Sitaramam (1996) demonstrated that this new measure satisfies various properties that a poverty measure should satisfy, except that it has no poverty line for identifying who the poor are. They even suggested that there is no need to have a poverty line to measure poverty. Ideally an Engel curve for an essential commodity must saturate at a finite level of expenditure on that commodity. They

suggested using that saturation level of commodity-specific consumption of an essential commodity as a norm set by the community. Any shortfall from that level may be taken as the commodity-specific consumption deprivation. They showed that a standardized cumulative commodity-specific consumption deprivation index falls within the class of deprivation functions Atkinson suggested for a class of poverty indices.

3.4 Figure 3.1 below depicts the typical forms Engel curves could take

Total Expenditure

Expe

nditu

re o

n a

spec

ific

com

mod

ity

Figure 3.1Different Types of Engel Curves

Luxuries

Necessities

Taking an essential commodity for which the Engel curve is concave they postulated that the Engel curve would admit a saturation level of expenditure. As the normally used Engel curves in economics do not admit a finite asymptote they used a functional form that does admit such a finite asymptote, a form suggested by the saturation curves used in catalysis10. The deprivation function derived from the saturating Engel curve and the associated deprivation or poverty index are depicted in Figure 3.2 below:

10 They compared the new specification with some of the commonly used Engel curve specifications and found that the new specification was to be preferred on the basis of least error sum of squares and randomness and Normality of the estimated errors (Sitaramam et. al. (1996).

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9

Total Expenditure

Expe

nditu

re o

n a

spec

ific

com

mod

ityFigure 3.2

Consumption Deprivation

Engel Curve for Necessities

Consumption Deprivationcurve

Deprivation or Poverty

Taking an essential commodity such as cereals we get the following commodity-specific consumption deprivation index (poverty index):

1.3)()(

0*

*

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−⎟⎟⎠

⎞⎜⎜⎝

⎛ −= ∫

∞

dyyfC

yCCD

Where C* is the maximum value of consumption expenditure, and C(y) denotes the actual mean consumption at a given level of total expenditure y, and f(y) is the probability density function of the total expenditure. As the deprivation function is a monotonic decreasing function in y the above infinite integral converges and has a finite value.

3.5 We may list here some important aspects of this new measure of deprivation. While the poverty line is subjectively chosen by researchers the norm used in our deprivation index is determined by the socioeconomic setting in which a household is situated. It is objectively derived empirically from the observed Engel curve. To the extent that this is estimated from an estimated Engel curve it is subject to probabilistic errors. Kumar, Gore, and Sitaramam (1996) suggest several interesting statistical problems that arise as a result. This index is based on economic considerations and not on nutritional and other normative considerations. The index shares one feature that was inherent in Sukhatme’s approach to measuring hunger. This measure is crucially dependent on the distribution of “actual consumption deprivation” of an essential commodity in the community relative to the community-specific saturation norm (assumed to be

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the same for all individuals in the community).11 The traditional measures of poverty are related to the consumption deprivation only through an indirect and weak link between income and or total expenditure and consumption deprivation. The index is such that if there are more persons or households with greater consumption deprivation greater is the contribution of that group to poverty. Thus this deprivation index measures severity of deprivation. We thus notice that the Engel curve based measure of deprivation takes care of all the problems of the traditional poverty indexes cited by the Expert Group and the criticism Lipton had leveled against them.

IV EMPIRICAL COMPUTATION OF POVERTY INDEX BASED ON ENGEL CURVE

4.1 We use the data on consumer expenditure at the household level provided by the National Sample Survey Organization (NSSO) for the 43rd, 5oth and 55th rounds covering 1987-88, 1993-94, and 1999-2000.12 We illustrated the proposed methodology in detail in a recent work (Kumar, Mallick, and Holla (2008)). The present work is an extension of that work. We examine the household level data in 15 major states of India, and also at All-India level, both in rural and urban settings. For completeness, and to make the presentation self-contained, we repeat some of the salient features of our empirical approach to the measurement of consumption deprivation. We also notice that the NSSO’s sample design is such that relatively richer households were oversampled. As the sample design is a multi-stage stratified sampling the data do not represent the population unless we take due note of the underlying sample design and use the corresponding multipliers.

4.2 The earlier study was undertaken with per capita monthly expenditure on cereals and per capita total monthly expenditure. As different households have different household compositions such per capita figures do not reflect comparable expenditures between households. This aspect again was not considered in our earlier study, although the Engel curve specification used allowed for shifts in the Engel curve due to changes in household size. It was mentioned in the earlier study that the food consumption pattern is different for different states and that there seems to be a substitution of cereals by some other food items. That study also did not include cereal substitutes which constitute the staple food for some poorer households in some states. In this study we take cereal substitutes also into account and include all food items in calculating food deprivation index as a poverty measure. We also convert the expenditure into adult equivalent scales.

11 The traditional measures of poverty use instead the distribution of income or total expenditure below the norm of a poverty line.

12 There are other data sources that one can use for estimating the extent of poverty. The data collected by National Nutrition Monitoring Bureau is one. The panel data collected for a few villages by ICRISAT is another. One may see Vaidyanathan (2001) for a discussion of relative merits of such different data sources.

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4.3 Engel curves depict the consumption expenditure of a household against the total expenditure of the household. Different households have different household composition. There seems to be a priori reasons to suspect that the actual and normative levels of consumption vary by age and sex. Combining them by a simple addition does not reflect the underlying distribution of expenditure by age and sex. In most household surveys it is the total household consumption expenditure that is obtained and not individual expenditure by each member of the household. The issue of adult equivalent scale arises for two reasons. First, an adult male’s consumption living alone is different from his consumption when he is a member of a two-person household after marriage. This issue is referred to as economies of scale within a household. The other issue is simply that one cannot compare the per capita consumption of a four member household with two children with the per capita consumption of a four member households with all four being adults. Sabatese et.al. (2001) find statistical evidence for significant differences in consumption per person by age, by sex, and by country.

4.4 To address this issue we provide adult equivalent scales that are specific to India where the consumption expenditure of an adult male is taken as the reference and the food expenditures of adult females, male and female children are expressed as a multiple (fraction) of the food expenditure of an adult male. Usually some sophisticated theoretical justification is often given and theory is called upon to determine a methodology of deriving the adult equivalent scales. This justification is based on welfare comparisons between individuals and between households. What we compare is not the utility of consumption of food of one person with that of another person. Such interpersonal comparison of utilities cannot be done in general. We compare, instead, the consumption deprivation in terms of a shortfall in expenditure on food at constant prices. While we admit that such shortfalls have different disutilities at different income or total expenditure levels and hence cannot be added, we also view that in the absence of any known law of variable marginal utility of income we assume it to be constant justifying the addition of such nominal values of food consumption deprivation.

4.5 Two major considerations for choosing the adult equivalent scale are: (i) they must be stable so that comparisons can be made according to those scales across time and space, (ii) they must be specific to the country. There are several studies that examined the effect of using different adult equivalent scales on the poverty estimates and many poverty studies use adult equivalent scales. Rarely do we find any justification for the scales used. As there is ambiguity of what scales one should use, quite often researchers resort to only performing a sensitivity analysis of poverty measures to different adult equivalent scales. The most popular among these is the OECD scale that assigns the first adult a weight of 1, the second and subsequent adults a weight of 0.7, a child a weight of 0.5. There is no reason to assume that these widely used scales are applicable to India.

4.6 Sen and Sengupta (1983), in their study of malnutrition of rural children in West Bengal, observe possible sex bias as reflected in greater malnutrition of girl child compared to a male

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child. In order to find scales that are suitable to Indian conditions we estimated a regression equation of household expenditure on food with the independent variables being total expenditure, the number of male and female adults, and male and female children, and household size square. Using the estimated regression line additional food consumption is calculated for adult male, adult female, male child, and female child. The adult equivalent scales are derived from these estimates. These are presented below:

The Adult Equivalent Scales for Food Expenditure in India (based on NSSO data)

1987-88-Rural 1 0.7591317 0.5215729 0.47118906

Urban 1 0.87164084 0.38990162 0.44167062

1993-94

Rural 1 0.80906785 0.55370166 0.47533897

Urban 1 0.88298132 0.52116718 0.37658138

1999-00 Rural 1 1.0373348 0.97217663 0.74000138

Urban 1 0.72746812 0.53903435 0.49041613

These AESs are based on All-India samples. The AES s of 1999-2000 seems to differ from those of the previous years. Using these estimates and the observations made by Sen and Sengupta to guide us we altered slightly the commonly used OECD scales. The AES s we used are: Adult male 1, adult female 0.8, male child 0.5 and female child 0.4. We used these adult equivalent weights in our analysis for determining food consumption expenditure per adult male equivalent and for replacing the household size by the number of adult male units in the household.

4.6 There is an issue of contamination of reported data in the 55th round of NSSO. This was

because two reference periods were used and the normally used 30 day reference period data

may have been adjusted by the respondent to correspond with the 7 day period response. The

effect of that on the estimates, and comparability of the estimates between the rounds was

examined by Deaton and Dreze (2002), Sundaram and Tendulkar (2003), Sen and Himanshu

(2004), and Deaton and Kozel (2005). In order to address this issue and make the results

comparable between the rounds for the 55th round data we used the correction factor for food

given in table 5 of Sen and Himanshu (2004).

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4.7 We need price deflators to convert the expenditures between the rural and urban sectors,

between states, and between different rounds. Deaton and Tarozzi (2000), Deaton and Dreze

(2002), and Deaton (2003) discuss in detail regarding this issue. We employ the price indices

derived from NSSO data given by Deaton (2003) to deflate the estimates of cereal consumption

for comparison purposes between years, between states, and between rural and urban sectors.

The price deflators derived from Deaton (2003) are presented in Table 1 with All India Rural for

1993-94 as the base (100).

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Table 1: The Price Deflators Used in the study (Derived from Deaton (2003)

With 1993-94 All India Rural=100

43rd Round 50th Round 55th Round

1987-88 1993-94 1999-2000 Rural Urban Rural Urban Rural Urban All India 55.96 78.79 100 136.7 159.1 220.6 Andhra Pradesh 44.67 73.79 79.2 135.1 127.7 222.1 Assam 61.89 61.45 112.7 103.1 177.5 167 Bihar 58.48 73.02 103.1 115.9 161.9 184.5 Gujarat 55.89 84.18 98.2 144.5 155 230.5 Haryana 59.73 69.62 113.6 125.5 176.3 204.2 Karnataka 50.76 59.01 90.7 104.4 150.5 176.3 Kerala 63.47 113.26 118.5 194.6 182.1 331 Maharashtra 56.17 83.8 94.7 145.6 154.8 239.1 Madhya Pradesh 51.97 88.89 93.8 158.1 151.2 240.1 Orissa 59.01 56.75 94.3 102.3 157.4 162.3 Punjab 59.73 84.5 113.6 147.8 176.2 226.3 Rajasthan 57.1 93.22 104.9 158.3 167.2 262.6 Tamil Nadu 57.46 64.81 95.5 115.9 149.5 185.8 Uttar Pradesh 55.68 69.14 103.5 116 163.7 186.7 West Bengal 62.76 72.79 107.2 120.2 170 198.6

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4.8 Data do not come the way the theory conceptualizes it. While we expected food to be an

essential commodity that would saturate at a finite level of total expenditure, it is not confirmed

by the data. Adult equivalent monthly food expenditure plotted against adult equivalent monthly

total expenditure shows that at higher levels of total expenditure the proportion spent on food

increases. This is because the food expenditure includes food products purchased, and the rich do

spend a lot on purchased sweets and food preparations in restaurants. In addition, this could be

due to such affluent households spending more on food for guests and for family and religious

festivals.

4.9 In order to take care of this situation one must determine a cut-off point in total

expenditure where the Engel curve would turn from concave to convex. Using the notion that

any curve can be approximated by a polynomial of sufficient degree and that a cubic allows for

the curve to be both concave and convex in different segments, we estimated a third degree

polynomial between adult male equivalent food and total expenditure. We then determined a cut-

off point such that below that cut-off point the cubic fit would be concave with an asymptote13.

Subsequently we used households whose monthly per capita total expenditure is less than the

cut-off in further analysis14. The Total expenditure cut-off points so obtained empirically are

presented in Table 2.

13 The procedure was iterative. When we first determined the cut-off and estimated the cubic Engel curve again for the truncated sample it remained convex at higher ranges of total expenditure. Hence we repeated this process until we obtained an Engel curve that is entirely concave up to the cut-off level of total expenditure.

14 This procedure is equivalent to our treating this cut-off point as a poverty line. This is analogous to, but different from the suggestion of Rao (1981). Thus while Kumar et al. (1996) dispense with the focus axiom we bring it back here, as the data do not conform to the theoretical specification.

Table 2: Total Expenditure Cut-off Points Obtained from a Cubic Engel Curve Fitted for the Entire Sample

In Rs Per Adult Male Unit Per Month in 1993-94 Prices

Rural Urban Rural Urban Rural UrbanAll India 848.25 1012.25 1053.22 784.72 1366.63 876.83Andhra Pradesh 1024.57 1261.24 1050.81 541.32 834.18 531.63Assam 741.31 1213.18 842.48 830.82 801.48 1172.54Bihar 1104.13 1615.69 989.48 2591.46 1269.41 904.16Gujarat 842.73 1057.46 823.09 1952.53 1278.40 1332.04Haryana 968.86 1015.59 1129.73 1164.23 775.00 834.94Karnataka 1857.09 1714.32 1552.44 1005.31 836.22 1894.39Kerala 1426.21 637.27 1996.81 1680.28 2235.22 836.80Maharashtra 556.80 1213.72 1490.09 918.10 1424.24 1037.81Madhya Pradesh 1152.72 685.79 971.88 2520.23 1371.99 505.94Orissa 471.39 936.44 536.29 1328.20 810.93 1194.78Punjab 2178.69 635.32 801.76 1155.16 1176.34 717.67Rajasthan 836.81 690.68 1176.70 502.72 947.63 680.86Tamil Nadu 1248.12 1000.72 968.68 873.32 1286.05 1138.14Uttar Pradesh 576.71 1478.93 1031.43 584.42 1206.41 1310.37West Bengal 562.50 1246.97 1062.78 908.18 1475.02 735.97

43rd Round 50th Round 55th Round 1987-88 1993-94 1999-2000

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4.10 For obtaining a smoother Engel curve we considered group means of these variables for a

fine grid of total expenditure classes. We started with more than 30 equally spaced class

intervals, and merged the cells whenever the cell frequencies were less than 5. We ended up with

much larger number of class intervals than 12 class intervals used by NSSO published summary

reports. Let us assume that qBi B is the expenditure in real terms or constant prices on food, let z Bi B

denote the household characteristics, and here it is the number of adult male equivalent units in

the household, and yBi B denote the total expenditure in real terms. The following specifications are

normally in use for Engel curves (Lewbel (2006), Banks, Blundell, and Lewbel (2006), and

Kumar, Gore, and Sitaramam (1996)):

)(:)(

:)(

)log(:)(kerPr)log(:)()(:)(

:)(

32

i

iii

iiiii

iii

iiii

iiiii

iii

yyzqKGSSitaramamGoreKumar

yyyzqBBLLewbelBlundellBanks

yzqPHHouthacaiseyyzqMWLLWModifiedyloqyyzqWLLeserWorking

yzqABBowleyAllen

+++=−−

++++=−−

++=−+++=−+++=−

++=−

δγβα

εδγβα

γβαδγβαδγβα

γβα

4.11 We estimated all these functional forms. We found that in a majority of cases Banks-

Blundell-Lewbel form is the best fitting in terms of highest RP

2P. However, the saturating

functional form used by Kumar, Gore, and Sitaramam (KGS) (1996) has, in a majority of cases,

the second best RP

2P. Furthermore it is found that these RP

2P s associated with KGS specification are

quite large and the percent shortfall from the RP

2P of best-fitting (Banks-Blundell-Lewbel form is

negligibly small, the maximum percent shortfall being only 1.45%. The RP

2Ps associated with these

Engel curves, along with the maximum RP

2P and the shortfall of KGS specification are presented in

Tables 1a, 1b, and 1c of Appendix. We also found, using Normality tests, that the errors are

distributed as a Normal distribution. Hence we chose KGS specification of the Engel curve.TP

15PT A

TP

15PT Although we used adult equivalent scales the adjusted household size (zBi B) may still appear in the Engel curve as

the adult equivalent scale only corrects for scale in food expenditure and the relation between these two variables (Engel curve) may still be subject to economies of scale. In fact we did observe, in a majority of cases, a statistically significant negative coefficient for the adjusted household size.

typical picture of the type of fits obtained is presented below in Figure 4.1 for the fits obtained

for All India Rural 1993-94. The estimates of the parameters of the saturating KGS Engel curves

are presented in Tables A2a, A2b, and A2c of the Appendix.

Figure 4.1: The Relative Performance of Alternate Engel Curves

The type of fits obtained by the cubic Engel curve (BBL) and the saturating Engel curve of KGS

is depicted for 1993-94 All India Rural in Figure 4.2 below:

Figure 4.2: The Closeness of KGS and BBL Engel curves and the actual data

0

100

200

300

400

500

600

700

Axi

s Ti

tle

Graph of Saturating Engel Curve for 93-94-all-India Rural: Actual Vs Predicted

Actual

KGS

BBL

18

19

V ESTIMATES OF FOOD CONSUMPTION DEPRIVATION BASED ON ENGEL CURVES

5.1 We define poverty index as the food deprivation index of a chosen community (rural or

urban sector of a particular state). We term this food deprivation index a modified Sitaramam

Index, or SI*.

samplekththeinhouseholdiththeofmultipliertheismsamplekththeinhouseholdiththeforendituretotal

isyandsamplekthforfoodforcurveEngeltheisyCsamplestheallovernconsumptiofoodtorefersC

sizesampleitsnsampletoreferskwhere

mC

yCC

mnSI

followsascurveEngelanyforgeneralinwrittenbecanSIIndexSitaramamifiedThe

ki

kik

k

ki

n

i

kikn

ikik

k

k

k

exp,)(

max*,

1.5.....................................*)(100

:*,,mod

1*

*

1

* ∑∑ =

=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

With KGS form of Engel curve the above formula takes the form (Kumar, Mallick, and Holla

(2008)):

2.5..................]})(

)([))((

1001

***

1

* ∑∑ =

=

++++

+++=

n

i i

i

iikin

ikik

k zz

zym

mnSI

k γβαγβα

γβαδγδ

Where the parameter values with an asterisk refer to the Engel curve among all data sets that has

the maximum saturation value for food expenditure.

5.2 The food consumption deprivation index (poverty index) for the three years and for All

India and the 15 major states, given separately for urban and rural, are presented in Table 3.

Table 3: Food Consumption Deprivation Index (Sitaramam Index) as a Measure of Poverty (As

Percentages):

All India and 15 Major States, for Rural and Urban for 1987-88, 1993-94, and 1999-2000

Rural Urban Rural Urban Rural UrbanAll India 44.74 40.70 35.45 33.76 34.08 25.73Andhra Pradesh 22.86 25.85 26.99 18.76 28.42 15.35Assam 31.91 42.50 31.79 35.61 26.43 32.84Bihar 25.55 33.08 29.33 87.41 49.04 30.39Gujarat 38.41 31.59 27.98 31.03 22.33 25.43Haryana 37.21 28.16 28.43 23.03 27.73 21.01Karnataka 38.80 35.11 35.16 41.15 23.76 28.93Kerala 42.55 28.04 28.43 47.57 28.31 17.44Maharashtra 23.76 51.97 19.16 41.94 13.97 19.38Madhya Pradesh 35.26 27.85 20.46 46.78 13.52 16.86Orissa 23.63 32.91 26.39 31.74 25.17 32.10Punjab 31.13 24.89 26.64 18.51 30.53 26.21Rajasthan 33.35 34.68 45.37 19.26 44.88 20.37Tamil Nadu 39.13 31.10 23.70 27.71 28.19 25.71Uttar Pradesh 25.07 42.77 20.04 33.77 19.38 27.27West Bengal 29.01 31.19 18.67 30.65 25.68 25.02

43rd Round 50th Round 55th Round 1987-88 1993-94 1999-2000

20

The trends in these poverty estimates over the three years at the All India level are depicted in

Figure 5.1

Figure 5.1 Trends in Food Deprivation Index in Rural and Urban Sectors-At All India Level

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

87-88 93-94 99-00

SIC

D

Year

Trend in Cereal Consumption Deprivation Index

RuralUrban

It may be noted that the gap between the rural and urban food deprivation has increased after

introducing economic reforms. There has been no significant improvement in the rural food

deprivation after the introduction of economic reforms. The picture is mixed at the state level.

Some states seem to have benefitted more from economic reforms than others. The trends of

food deprivation at the state level are shown in Table 4.

21

Table 4: Trends in Food Deprivation Before and After Economic Reforms:Rural, Urban and Gap Between Rural and Urban

Rural Urban Rural-Urban Gap Rural Urban Rural-Urban Gap

All India Decrease Decrease Decrease Decrease Decrease IncreaseAndhra Pradesh Increase Decrease Increase Increase Decrease IncreaseAssam Decrease Decrease Increase Decrease Decrease DecreaseBihar Increase Increase decrease Increase decrease IncreaseGujarat Decrease Decrease Decrease Decrease Decrease DecreaseHaryana Decrease Decrease Decrease Decrease Decrease IncreaseKarnataka Decrease Increase Decrease Decrease Decrease IncreaseKerala Decrease Increase Decrease Decrease Decrease IncreaseMaharashtra Decrease Decrease Increase Decrease Decrease IncreaseMadhya Pradesh Decrease Increase Decrease Decrease Decrease IncreaseOrissa Increase decrease Increase Decrease Increase DecreasePunjab Decrease Decrease Increase Increase Increase decreaseRajasthan Increase decrease Increase Decrease Increase DecreaseTamil Nadu Decrease Decrease Decrease Decrease Decrease IncreaseUttar Pradesh Decrease Decrease Increase Decrease Decrease IncreaseWest Bengal Decrease Decrease Decrease Increase decrease Increase

Before Reforms 1987-88 to 1993-94 After Reforma 1993-94 to 1999-2000

22

5.3 While it is meaningless to compare different measures of poverty that differ in concept, it

is perhaps useful to examine how the temporal and spatial correlations behave between our food

deprivation index and the traditional poverty estimates. We chose two poverty indices of Deaton

and Dreze (DD), headcount index (HCI) and poverty gap index (PGI). Figure 5.3a and 5.3 b

present the time trends in some of the traditional poverty estimates and the food deprivation

index (SI*) at All India level for rural and urban respectively.

Figure 5.3a Trends in Traditional Poverty Indices and Food Deprivation Index-All India Rural

Figure 5.3b Trends in Traditional Poverty Indices and Food Deprivation Index-All India Urban

23

We arranged the states in the increasing order of headcount index of poverty and plotted together

on one line graph the food consumption deprivation index and the headcount poverty index for

all the states for rural and urban sectors separately. These graphs are provided in Figures 5.3c

and 5.3d below:

Figure 5.3c: Trends in Headcount Poverty Index and Food Consumption Deprivation Index, 15

Major States, 1987-88 Rural (the states arranged in the increasing order of HCI)

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 5 10 15 20

HCI

SI

Figure 5.3d: Trends in Headcount Poverty Index and Food Consumption Deprivation Index, 15

Major States, 1987-88 Urban (The states arranged in the increasing order of HCI)

60

50

40

30 HCI

20

10

00 5 10 15 20

SI*

24

Table 5a and 5b present some of the poverty estimates and their correlations with our food

deprivation index (SI*). From these correlations it is evident that except for the base year 1993-

94 for all other years the spatial correlation between the food deprivation index and the

traditional poverty indices HCI and PGI is very poor. If one considers food deprivation as a

measure of poverty then the traditional poverty measures do not seem to measure it.

Table 5a: Spatial Correlations Between Food Deprivation Index and Poverty Indices of Deaton

and Dreze: Rural

1993-94 1999-2000DD-HCI DD-PGI SI* DD-HCI DD-PGI SI* DD- HCI DD-PGI SI*

All-India 39.00 9.20 44.74 33.00 7.00 35.45 26.30 5.20 34.08AP 35.00 8.00 22.86 29.20 5.80 26.99 26.20 4.80 28.42Assam 36.10 6.50 31.91 35.40 5.70 31.79 35.50 6.10 26.43Bihar 54.60 13.20 25.55 48.60 10.70 29.33 41.10 8.50 49.04Gujarat 39.40 8.40 38.41 32.50 6.80 27.98 20.00 3.80 22.33Haryana 13.60 2.80 37.21 17.00 3.00 28.43 5.70 0.70 27.73Karnataka 40.80 10.50 38.80 37.90 8.60 35.16 30.70 6.10 23.76Kerala 23.80 4.80 42.55 19.50 3.90 28.43 10.00 1.70 28.31Maharashtra 44.30 11.20 23.76 42.90 8.20 19.16 31.30 6.60 13.97MP 43.70 10.80 35.26 36.60 11.20 20.46 31.90 7.60 13.52Orissa 50.40 13.00 23.63 43.50 9.70 26.39 43.00 10.50 25.17Punjab 6.60 1.00 31.13 6.20 1.00 26.64 2.40 0.30 30.53Rajasthan 35.30 9.20 33.35 23.00 4.40 45.37 17.30 3.00 44.88TN 49.00 13.70 39.13 38.50 9.10 23.70 24.30 4.60 28.19UP 34.90 7.50 25.07 28.60 5.80 20.04 21.50 3.90 19.38WB 36.30 7.70 29.01 25.10 4.20 18.67 21.90 3.50 25.68

Correlation -0.2267 -0.1862 1.00 -0.1170 -0.1622 1.00 -0.0358 -0.0888 1.00

1987-88

25

Table 5b: Spatial Correlations Between Food Deprivation Index and Poverty Indices of Deaton

and Dreze-Urban

DD-HCI DD-PGI SI* DD-HCI DD-PGI SI* DD-HCI DD-PGI SI*All-India 22.50 4.80 40.70 17.80 3.70 33.76 12.00 2.30 25.73AP 23.40 4.90 25.85 17.80 3.40 18.76 10.80 1.90 15.35Assam 13.60 2.00 42.50 13.00 2.00 35.61 11.80 1.90 32.84Bihar 38.10 8.20 33.08 26.70 5.60 87.41 24.70 5.00 30.39Gujarat 16.40 2.80 31.59 14.70 2.60 31.03 6.40 1.00 25.43Haryana 11.80 2.30 28.16 10.50 1.90 23.03 4.60 0.70 21.01Karnataka 26.00 5.70 35.11 21.40 4.50 41.15 10.80 2.10 28.93Kerala 21.00 4.50 28.04 13.90 2.70 47.57 9.60 1.70 17.44Maharashtra 20.70 4.10 51.97 18.50 3.50 41.94 13.90 2.60 19.38MP 21.20 5.30 27.85 18.20 4.60 46.78 12.00 2.80 16.86Orissa 20.80 4.20 32.91 15.20 3.00 31.74 15.60 3.00 32.10Punjab 6.60 1.00 24.89 7.80 1.10 18.51 3.40 0.40 26.21Rajasthan 19.80 4.00 34.68 18.30 3.20 19.26 10.80 1.70 20.37TN 26.20 6.20 31.10 20.80 4.50 27.71 11.30 2.00 25.71UP 29.30 6.30 42.77 21.70 4.60 33.77 17.30 3.30 27.27WB 22.30 4.20 31.19 15.50 2.90 30.65 11.30 1.90 25.02

0.00Correlations 0.2019 0.1199 0.00 0.6088 0.6165 1.00 0.3357 0.2806 1.00

1987-88 1993-94 1999-2000

26

27

VI CONCLUDING REMARKS

6.1 Given the recent debate on the traditional poverty estimates in India we find it useful to

revive a decade and half old suggestion of Kumar, Gore, and Sitaramam to measure poverty

using an Engel curve for essential commodities. We used household level data from three recent

large consumer expenditure surveys of NSSO and estimated food consumption deprivation. We

showed that this index has very little spatial correlation with the traditional measures of poverty.

6.2 NSSO data has some limitations but it seems to be the best available data. The imputed

values for home produce and meals eaten outside, the meals served for guests and domestic help

etc. leave sufficient room for subjective judgments, and quite often the field investigator may be

prompting the respondent on what prices to use for such imputations. There is a need to do

alternate pilot surveys and studies to focus on individual questions of this sort.

6.3 One may estimate the Engel curves for some other necessities such as health services,

primary and secondary education, water, fuel and light, etc. and estimate the associated

consumption deprivations. The question then arises as to how to combine them into a single

index of poverty. The study by Nathan, Mishra and Reddy (2008) provides a measure based on

Euclidean distance between the target or norm and actual multidimensional deprivation. Human

development indices and poverty indices can be brought into the manifold of microeconomics of

consumer demand through Engel curve analysis of essential goods and services.

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APPENDIX

Table A1a: 43rd Round-R2s associated with alternate Engel curves and shortfall in R2 of KGS

specification

Filename R2-AB R2-WL R2-MWL R2-PH R2-BBL R2-KGS Max-R2 KGS-Shortfall %Shortfall43rd Round-Rural43_r_allindia.dat 0.987835 0.999322 0.995558 0.972547 0.999604 0.999487 0.999604 0.000116505 0.01165543_r_AP.dat 0.967672 0.998138 0.996218 0.995673 0.998177 0.998123 0.998177 5.3312E-05 0.00534143_r_Asm.dat 0.986319 0.9963 0.995806 0.986415 0.996352 0.996323 0.996352 2.8243E-05 0.00283543_r_Bih.dat 0.964073 0.979929 0.976464 0.964658 0.982685 0.979737 0.982685 0.002947347 0.29992843_r_Guj.dat 0.990657 0.99727 0.996111 0.981153 0.998019 0.997488 0.998019 0.000531291 0.05323543_r_Har.dat 0.975086 0.991883 0.989534 0.965799 0.992603 0.992179 0.992603 0.000423085 0.04262443_r_Kar.dat 0.96586 0.983235 0.983535 0.968511 0.983504 0.982556 0.983535 0.00097942 0.09958243_r_Ker.dat 0.978724 0.981516 0.98031 0.961589 0.984323 0.981907 0.984323 0.002416274 0.24547643_r_Mah.dat 0.988237 0.997587 0.997071 0.993985 0.997616 0.997601 0.997616 1.54288E-05 0.00154743_r_MP.dat 0.973094 0.987316 0.98555 0.971143 0.988065 0.987275 0.988065 0.000790637 0.08001943_r_Ori.dat 0.986039 0.998842 0.998294 0.985552 0.998912 0.998888 0.998912 2.44784E-05 0.00245143_r_Pun.dat 0.92808 0.959717 0.956711 0.953482 0.960203 0.958783 0.960203 0.001419586 0.14784243_r_Raj.dat 0.979184 0.993454 0.990472 0.964239 0.995593 0.993947 0.995593 0.001646103 0.16533943_r_TN.dat 0.964243 0.990357 0.987959 0.961057 0.990732 0.990593 0.990732 0.000138048 0.01393443_r_UP.dat 0.988662 0.994361 0.994618 0.986768 0.994433 0.994241 0.994618 0.000377643 0.03796943_r_WB.dat 0.991649 0.999224 0.998242 0.994258 0.999379 0.999319 0.999379 5.98047E-05 0.00598443rd Round-Urban43_u_allindia.dat 0.984189 0.999568 0.999243 0.972501 0.999601 0.999497 0.999601 0.000103757 0.0103843_u_AP.dat 0.948716 0.992839 0.989355 0.97751 0.992864 0.992654 0.992864 0.000209625 0.02111343_u_Asm.dat 0.985054 0.994091 0.99244 0.985212 0.995673 0.994102 0.995673 0.001570825 0.15776543_u_Bih.dat 0.959537 0.989138 0.98576 0.971071 0.990614 0.989107 0.990614 0.001506597 0.15208743_u_Guj.dat 0.975308 0.991164 0.98964 0.978656 0.992098 0.991222 0.992098 0.000875743 0.08827243_u_Har.dat 0.970069 0.989829 0.988547 0.983188 0.99017 0.989857 0.99017 0.000313194 0.0316343_u_Kar.dat 0.951441 0.994049 0.990589 0.984439 0.994187 0.993897 0.994187 0.000289624 0.02913243_u_Ker.dat 0.970742 0.98218 0.980836 0.954326 0.982601 0.982377 0.982601 0.000223872 0.02278443_u_Mah.dat 0.985019 0.993745 0.993173 0.95936 0.993853 0.993684 0.993853 0.000168983 0.01700343_u_MP.dat 0.980114 0.994244 0.992014 0.965655 0.99575 0.99464 0.99575 0.001109993 0.11147343_u_Ori.dat 0.976415 0.991824 0.991065 0.985302 0.991969 0.99186 0.991969 0.00010958 0.01104743_u_Pun.dat 0.977879 0.99032 0.989683 0.982426 0.990471 0.990358 0.990471 0.000113285 0.01143743_u_Raj.dat 0.979248 0.984842 0.985037 0.966425 0.985784 0.984642 0.985784 0.001141784 0.11582543_u_TN.dat 0.976498 0.993736 0.992342 0.972275 0.994154 0.993742 0.994154 0.000412313 0.04147443_u_UP.dat 0.967253 0.983676 0.983921 0.967668 0.983703 0.983443 0.983921 0.000477811 0.04856243_u_WB.dat 0.954886 0.975904 0.971061 0.962656 0.98223 0.975638 0.98223 0.00659227 0.671153

31

Table A1b: 50th Round-R2s associated with alternate Engel curves and shortfall in R2 of KGS

specification

File name R2-AB R2-WL R2-MWL R2-PH R2-BBL R2-KGS Max-R2 KGS-Shortfall % shortfall50th Round-RuralAll India 0.972764 0.998888 0.996573 0.987044 0.999120 0.998969 0.999120 0.000151 0.015102Andhra Pradesh 0.961153 0.996851 0.995802 0.988971 0.997289 0.996965 0.997289 0.000323 0.032427Assam 0.972762 0.996594 0.995436 0.991392 0.996789 0.996645 0.996789 0.000144 0.014482Bihar 0.966430 0.996468 0.994923 0.987699 0.996799 0.996428 0.996799 0.000371 0.037189Gujarat 0.976972 0.989327 0.987686 0.981710 0.991038 0.989361 0.991038 0.001676 0.169160Haryana 0.960863 0.985148 0.984720 0.978808 0.985817 0.985274 0.985817 0.000543 0.055077Karnataka 0.958302 0.970037 0.971259 0.958329 0.976133 0.970720 0.976133 0.005412 0.554479Kerala 0.973775 0.987084 0.984961 0.979269 0.987805 0.986566 0.987805 0.001239 0.125416Maharashtra 0.984321 0.989165 0.990906 0.979594 0.989720 0.988874 0.990906 0.002031 0.205014Madhya Pradesh 0.962340 0.994102 0.994302 0.990255 0.994488 0.994227 0.994488 0.000261 0.026276Orissa 0.987156 0.996357 0.996318 0.990371 0.996759 0.996321 0.996759 0.000439 0.044017Punjab 0.969815 0.990176 0.988496 0.985251 0.991870 0.989990 0.991870 0.001880 0.189530Rajasthan 0.985199 0.994651 0.994325 0.977568 0.994577 0.994587 0.994651 0.000064 0.006447Tamil Nadu 0.956159 0.995265 0.993055 0.990436 0.995780 0.994918 0.995780 0.000862 0.086539Uttar Pradesh 0.975513 0.994793 0.994886 0.989702 0.994465 0.994748 0.994886 0.000137 0.013817West Bengal 0.974116 0.995272 0.995538 0.994313 0.994856 0.995068 0.995538 0.000470 0.04723850th Round-UrbanAll India 0.984602 0.999288 0.995171 0.948832 0.999683 0.999660 0.999683 0.000024 0.002390Andhra Pradesh 0.978850 0.997279 0.997097 0.987867 0.997336 0.997230 0.997336 0.000106 0.010665Assam 0.981607 0.992353 0.992363 0.986281 0.992542 0.992346 0.992542 0.000195 0.019690Bihar 0.979177 0.996344 0.995676 0.973948 0.996190 0.996242 0.996344 0.000102 0.010226Gujarat 0.951582 0.969249 0.966508 0.959251 0.982629 0.968375 0.982629 0.014254 1.450629Haryana 0.951257 0.987675 0.985968 0.984058 0.987890 0.987379 0.987890 0.000511 0.051701Karnataka 0.978242 0.992733 0.991485 0.972579 0.992964 0.992869 0.992964 0.000095 0.009611Kerala 0.977608 0.989862 0.990902 0.947361 0.990594 0.989053 0.990902 0.001850 0.186652Maharashtra 0.986613 0.993401 0.993151 0.964778 0.993830 0.993301 0.993830 0.000530 0.053280Madhya Pradesh 0.982779 0.988892 0.988830 0.952696 0.988528 0.988599 0.988892 0.000294 0.029682Orissa 0.958985 0.986029 0.983358 0.976285 0.987582 0.985837 0.987582 0.001745 0.176666Punjab 0.930085 0.971931 0.967976 0.967488 0.973959 0.970567 0.973959 0.003392 0.348292Rajasthan 0.986312 0.996598 0.996340 0.991699 0.996589 0.996587 0.996598 0.000011 0.001139Tamil Nadu 0.979746 0.997315 0.992627 0.978496 0.997629 0.997505 0.997629 0.000124 0.012394Uttar Pradesh 0.991231 0.997987 0.997577 0.979881 0.998075 0.998058 0.998075 0.000017 0.001705West Bengal 0.980840 0.997420 0.996641 0.982433 0.997446 0.997394 0.997446 0.000052 0.005185

32

Table A1c: 55th Round-R2s associated with alternate Engel curves and shortfall in R2 of KGS

specification

File name R2-AB R2-WL R2-MWL R2-PH R2-BBL R2-KGS Max-R2 KGS-Shortfall % shortfall55th Round-RuralAll India 0.988044 0.998639 0.998019 0.976653 0.998733 0.998700 0.998733 0.000033 0.003323Andhra Pradesh 0.984819 0.998433 0.997545 0.986329 0.998584 0.998513 0.998584 0.000070 0.007028Assam 0.980841 0.993025 0.990943 0.980996 0.994747 0.993212 0.994747 0.001536 0.154392Bihar 0.986383 0.990113 0.989532 0.956322 0.990372 0.990256 0.990372 0.000116 0.011758Gujarat 0.974022 0.984437 0.983943 0.974915 0.984406 0.984426 0.984437 0.000011 0.001108Haryana 0.976241 0.982399 0.982375 0.972992 0.982787 0.982381 0.982787 0.000406 0.041266Karnataka 0.990417 0.996332 0.995787 0.983290 0.996453 0.996406 0.996453 0.000047 0.004672Kerala 0.965799 0.991090 0.990799 0.976562 0.990801 0.990971 0.991090 0.000119 0.012029Maharashtra 0.932792 0.992778 0.989459 0.988515 0.993633 0.992572 0.993633 0.001062 0.106837Madhya Pradesh 0.958534 0.983709 0.982340 0.981248 0.983679 0.983466 0.983709 0.000244 0.024755Orissa 0.983873 0.994444 0.993997 0.977693 0.994447 0.994455 0.994455 0.000000 0.000000Punjab 0.985644 0.993564 0.992838 0.983100 0.993947 0.993664 0.993947 0.000283 0.028457Rajasthan 0.991609 0.997769 0.997814 0.983260 0.998172 0.997679 0.998172 0.000493 0.049378Tamil Nadu 0.958724 0.992326 0.987597 0.967222 0.993387 0.992786 0.993387 0.000601 0.060530Uttar Pradesh 0.963828 0.993969 0.992905 0.989195 0.994243 0.993964 0.994243 0.000278 0.027980West Bengal 0.981483 0.994474 0.993248 0.979022 0.994749 0.994576 0.994749 0.000173 0.01737655th Round-UrbanAll India 0.981676 0.999737 0.999327 0.987171 0.999733 0.999733 0.999737 0.000005 0.000483Andhra Pradesh 0.985040 0.995887 0.995254 0.988491 0.996133 0.995946 0.996133 0.000187 0.018769Assam 0.986169 0.992672 0.991676 0.986069 0.992931 0.992801 0.992931 0.000130 0.013068Bihar 0.975359 0.986781 0.986398 0.969232 0.986721 0.986757 0.986781 0.000024 0.002434Gujarat 0.970295 0.987869 0.986622 0.974658 0.988189 0.987833 0.988189 0.000356 0.036071Haryana 0.974008 0.986541 0.984900 0.976400 0.988073 0.986683 0.988073 0.001390 0.140657Karnataka 0.951515 0.983210 0.981659 0.971290 0.983222 0.983160 0.983222 0.000062 0.006301Kerala 0.969973 0.992297 0.990505 0.975519 0.992222 0.992264 0.992297 0.000033 0.003338Maharashtra 0.981343 0.996699 0.996148 0.982762 0.997064 0.996743 0.997064 0.000321 0.032163Madhya Pradesh 0.987713 0.997680 0.997272 0.983061 0.997716 0.997712 0.997716 0.000004 0.000430Orissa 0.975509 0.991390 0.990569 0.975473 0.991400 0.991420 0.991420 0.000000 0.000000Punjab 0.981829 0.987915 0.987961 0.979066 0.987951 0.987872 0.987961 0.000089 0.009056Rajasthan 0.978593 0.989360 0.989198 0.979753 0.989330 0.989338 0.989360 0.000022 0.002219Tamil Nadu 0.975398 0.997366 0.997090 0.982074 0.997946 0.997334 0.997946 0.000612 0.061291Uttar Pradesh 0.961528 0.990058 0.986940 0.972058 0.991650 0.990050 0.991650 0.001600 0.161316West Bengal 0.984493 0.996874 0.996914 0.989094 0.996771 0.996814 0.996914 0.000100 0.009989

33

Table A2a: Results of Maximum Likelihood Estimation of Nonlinear Saturating Engel Curve (KGS) All India and 15 Major States :1987-88 RuralFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India -6.001252 0.000133 -0.000514 2.53544E-08 1497.254 0.001204 1407.752 0.001618 0.999487Andhra Pradesh -17.94559 0.000414 -0.007182 1.41559E-07 1014.289 0.001933 641.7766 0.003475 0.998123Assam 2.692551 0.002259 -0.008217 2.59841E-07 1157.718 0.003745 884.1446 0.009383 0.996323Bihar 155.0988 0.000525 -0.021578 6.55979E-08 933.1999 0.001383 871.1377 0.002719 0.979737Gujarat 53.18122 0.002067 -0.009171 1.29585E-07 1360.222 0.005681 1185.124 0.012932 0.997488Haryana -14.83766 0.000812 -0.001351 3.68756E-08 1383.287 0.008258 1202.301 0.015197 0.992179Karnataka 262.5899 0.000691 -0.035397 7.58785E-08 1316.006 0.001425 1533.497 0.003814 0.982556Kerala 345.8102 0.001058 -0.049001 1.39771E-07 1341.85 0.003052 2336.658 0.009938 0.981907Maharashtra 31.90077 0.001725 -0.008393 3.31498E-07 904.1179 0.00834 727.8382 0.011104 0.997601Madhya Pradesh 0.091283 0.040531 -0.002429 4.71813E-06 1245.693 0.018275 1094.751 0.057664 0.987275Orissa -4.211871 0.000234 -0.002732 3.09329E-08 876.9458 0.001101 657.5223 0.001701 0.998888Punjab 10.13786 0.002288 -0.01083 2.04883E-07 1234.49 0.001238 1010.016 0.007266 0.958783Rajasthan 48.30307 0.001491 -0.008519 1.34175E-07 1202.897 0.005478 1082.143 0.01076 0.993947Tamil Nadu -25.72011 0.000273 0.001736 3.84005E-08 1343.351 0.001191 1208.444 0.002193 0.990593Uttar Pradesh 148.8155 0.002187 -0.016847 2.329E-07 901.0743 0.004446 952.3556 0.004254 0.994241West Bengal -6.46341 0.000397 -0.002879 7.74615E-08 1065.894 0.002957 815.3533 0.003663 0.999319

SE stands for standard error

Table A2.b: Results of Maximum Likelihood Estimation of Nonlinear Engel Curve All India and 15 Major States :1987-88 UrbanFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India -1.29932 0.000875 -1.3E-05 2.1E-07 1348.805 0.001072 1409.32 0.001648 0.999497Andhra Pradesh 5.094769 0.000164 -0.00423 6.21E-08 952.4178 0.000694 903.2599 0.001436 0.992654Assam 10.70959 0.000713 -0.02141 3.15E-07 1501.684 0.001371 1343.15 0.00346 0.994102Bihar 107.9325 0.000401 -0.02184 1.12E-07 1114.887 0.002093 1267.266 0.004189 0.989107Gujarat 67.95869 0.000764 -0.01654 1.01E-07 1097.214 0.00357 1127.563 0.008477 0.991222Haryana -8.2365 0.000934 -0.005 6.58E-08 1097.211 0.003113 928.1257 0.0076 0.989857Karnataka -17.8658 0.000194 -0.0035 5.6E-08 1322.611 0.000739 1127.849 0.001266 0.993897Kerala 33.40024 0.000184 -0.01305 6.89E-08 915.1474 0.001818 950.5985 0.003131 0.982377Maharashtra 20.90798 0.001257 -0.00261 2.14E-07 1652.186 0.008878 1977.45 0.019011 0.993684Madhya Pradesh 17.77421 0.000205 -0.00263 2.12E-08 939.9236 0.002642 1008.848 0.005493 0.99464Orissa 18.80708 0.001274 -0.0164 3.3E-07 1237.386 0.00834 1008.712 0.01628 0.99186Punjab -17.0776 0.000237 0.000336 1.51E-07 922.1123 0.002284 826.3092 0.003709 0.990358Rajasthan 73.60762 0.00088 -0.01135 1.95E-07 1103.39 0.012233 1449.999 0.023355 0.984642Tamil Nadu 36.95188 0.000106 -0.01345 3.95E-08 1128.007 0.000764 1046.023 0.001493 0.993742Uttar Pradesh 140.2167 0.000407 -0.03206 6.58E-08 1387.107 0.001863 1681.728 0.00488 0.983443West Bengal 48.5954 0.000719 -0.01451 1.19E-07 1134.924 0.000793 1049.34 0.001991 0.975638

34

Table A2.c: Results of Maximum Likelihood Estimation of Nonlinear Engel Curve All India and 15 Major States :1993-94 RuralFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India 0.594540 0.001059 -0.002269 0.000000 1269.240307 0.003139 1125.139329 0.003457 0.998969Andhra Pradesh -70.445722 0.000415 0.001247 0.000000 1141.358441 0.000947 773.081585 0.001914 0.996965Assam -99.100998 0.001137 0.007730 0.000000 1181.074082 0.004615 768.700386 0.004880 0.996645Bihar -3.034727 0.000477 -0.003162 0.000000 1060.842990 0.002599 844.038600 0.004037 0.996428Gujarat 75.647814 0.002488 -0.008899 0.000000 1111.299119 0.006977 900.108302 0.016864 0.989361Haryana -9.398071 0.000314 -0.003399 0.000000 1152.534460 0.001369 901.328539 0.002622 0.985274Karnataka -163.732711 0.000519 0.008503 0.000000 1379.324648 0.001118 936.134789 0.001760 0.970720Kerala 151.780872 0.000360 -0.021152 0.000000 1053.964272 0.000715 1126.842909 0.001531 0.986566Maharashtra 350.176147 0.004797 -0.033241 0.000000 706.748231 0.003884 1063.604059 0.021037 0.988874Madhya Pradesh 93.952264 0.000961 -0.015978 0.000000 843.394382 0.001777 648.402055 0.002952 0.994227Orissa -9.745515 0.000590 -0.001471 0.000000 976.725933 0.008569 758.948258 0.012383 0.996321Punjab -86.782595 0.001848 0.001744 0.000000 1118.998913 0.004433 738.226316 0.009880 0.989990Rajasthan -16.073940 0.002382 -0.000175 0.000000 1578.113539 0.005831 1448.965810 0.013505 0.994587Tamil Nadu -18.261492 0.000242 -0.004300 0.000000 991.082848 0.001281 667.640890 0.001984 0.994918Uttar Pradesh 157.021442 0.001212 -0.015997 0.000000 803.705785 0.002053 756.445189 0.005466 0.994748West Bengal 139.065866 0.001914 -0.014979 0.000000 777.939253 0.003910 659.298575 0.005896 0.995068

Table A2d: Results of Maximum Likelihood Estimation of Nonlinear Engel Curve All India and 15 Major States :1993-94 UrbanFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India 0.594540 0.001059 -0.002269 0.000000 1269.240307 0.003139 1125.139329 0.003457 0.998969Andhra Pra -70.445722 0.000415 0.001247 0.000000 1141.358441 0.000947 773.081585 0.001914 0.996965Assam -99.100998 0.001137 0.007730 0.000000 1181.074082 0.004615 768.700386 0.004880 0.996645Bihar -3.034727 0.000477 -0.003162 0.000000 1060.842990 0.002599 844.038600 0.004037 0.996428Gujarat 75.647814 0.002488 -0.008899 0.000000 1111.299119 0.006977 900.108302 0.016864 0.989361Haryana -9.398071 0.000314 -0.003399 0.000000 1152.534460 0.001369 901.328539 0.002622 0.985274Karnataka -163.732711 0.000519 0.008503 0.000000 1379.324648 0.001118 936.134789 0.001760 0.970720Kerala 151.780872 0.000360 -0.021152 0.000000 1053.964272 0.000715 1126.842909 0.001531 0.986566Maharashtr 350.176147 0.004797 -0.033241 0.000000 706.748231 0.003884 1063.604059 0.021037 0.988874Madhya Pr 93.952264 0.000961 -0.015978 0.000000 843.394382 0.001777 648.402055 0.002952 0.994227Orissa -9.745515 0.000590 -0.001471 0.000000 976.725933 0.008569 758.948258 0.012383 0.996321Punjab -86.782595 0.001848 0.001744 0.000000 1118.998913 0.004433 738.226316 0.009880 0.989990Rajasthan -16.073940 0.002382 -0.000175 0.000000 1578.113539 0.005831 1448.965810 0.013505 0.994587Tamil Nadu -18.261492 0.000242 -0.004300 0.000000 991.082848 0.001281 667.640890 0.001984 0.994918Uttar Prade 157.021442 0.001212 -0.015997 0.000000 803.705785 0.002053 756.445189 0.005466 0.994748West Beng 139.065866 0.001914 -0.014979 0.000000 777.939253 0.003910 659.298575 0.005896 0.995068

35

Table A2e: Results of Maximum Likelihood Estimation of Nonlinear Engel Curve All India and 15 Major States :1999-2000 RuralFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India -18.977327 0.001436 0.000020 0.000000 1563.421081 0.002054 1597.268719 0.004576 0.998700Andhra Pradesh -80.463694 0.000212 0.000365 0.000000 1466.213968 0.001404 1209.586105 0.001718 0.998513Assam -21.549157 0.002485 -0.000443 0.000000 1175.422963 0.007181 929.291477 0.014139 0.993212Bihar -0.830838 0.000000 0.000030 0.000000 2095.223205 0.000000 2405.661030 0.000000 0.990256Gujarat 93.034786 0.007361 -0.001147 0.000000 1221.573726 0.016377 1226.118822 0.052354 0.984426Haryana -27.266947 0.014077 -0.000109 0.000000 1435.329195 0.093303 1388.469127 0.184553 0.982381Karnataka 12.722781 0.001898 -0.000388 0.000000 1290.691315 0.002377 1261.272768 0.006685 0.996406Kerala 24.324581 0.001647 -0.000350 0.000000 1350.790383 0.007444 1601.063088 0.019753 0.990971Maharashtra -91.072562 0.002134 0.000134 0.000000 939.444889 0.001054 640.346627 0.004928 0.992572Madhya Pradesh 139.269882 0.004121 -0.001919 0.000000 784.830769 0.008039 752.960248 0.016746 0.983466Orissa 5.160771 0.001601 -0.000279 0.000000 1164.290792 0.004332 1123.236852 0.010774 0.994455Punjab 41.428590 0.003611 -0.000780 0.000000 1393.069501 0.014361 1608.283862 0.039800 0.993664Rajasthan -39.654323 0.000000 0.000189 0.000000 2091.773950 0.000000 2207.502759 0.000000 0.997679Tamil Nadu -115.381221 0.000763 0.000927 0.000000 1399.223548 0.005738 1186.988843 0.010453 0.992786Uttar Pradesh -6.827257 0.001549 -0.000352 0.000000 1097.290405 0.008061 990.903184 0.014258 0.993964West Bengal -12.331441 0.002260 -0.000142 0.000000 1323.650813 0.005386 1192.192431 0.012787 0.994576

Table A2f: Results of Maximum Likelihood Estimation of Nonlinear Engel Curve All India and 15 Major States :1999-2000 UrbanFile A SE(A) B B(SE) C C(SE) D D(SE) R2

All India -35.261129 0.000004 0.000533 0.000000 1098.628847 0.000075 1153.699319 0.000125 0.999733Andhra Pradesh -8.484444 0.000469 -0.000071 0.000000 738.001368 0.002932 710.884733 0.006788 0.995946Assam 35.473488 0.005328 -0.001018 0.000000 1316.937651 0.016947 1437.501799 0.051020 0.992801Bihar -11.683412 0.002330 0.000190 0.000000 1254.670851 0.017304 1323.768128 0.036895 0.986757Gujarat 10.725661 0.002742 -0.000175 0.000000 1091.070340 0.007687 1291.202251 0.025869 0.987833Haryana -27.515548 0.011037 -0.000057 0.000000 1052.097799 0.026708 1027.847329 0.081724 0.986683Karnataka -2.328090 0.001659 -0.000189 0.000000 1302.636003 0.010290 1489.797414 0.026022 0.983160Kerala -47.915759 0.001412 0.000871 0.000000 772.475946 0.002045 734.944095 0.006724 0.992264Maharashtra 44.685563 0.000812 -0.000909 0.000000 919.520934 0.001847 1089.061120 0.006396 0.996743Madhya Pradesh 6.614409 0.000118 -0.000384 0.000000 751.261629 0.000954 799.014654 0.002065 0.997712Orissa 1.375900 0.002985 -0.000182 0.000000 1400.550320 0.012389 1439.954595 0.027271 0.991420Punjab 1.442144 0.009329 -0.000138 0.000000 1072.975306 0.042269 1235.000639 0.111062 0.987872Rajasthan -27.180296 0.003101 0.000569 0.000000 878.021588 0.019291 972.951732 0.047122 0.989338Tamil Nadu -31.079311 0.000326 0.000122 0.000000 1156.008284 0.002111 1194.976017 0.005406 0.997334Uttar Pradesh -43.756143 0.001440 0.000416 0.000000 1238.388068 0.005198 1252.679878 0.014503 0.990050West Bengal -33.789837 0.000588 0.000166 0.000000 1105.722298 0.005696 1009.892201 0.010954 0.996814

36