child labor participation, human capital accumulation, and economic development

Available online at www.sciencedirect.com

Journal of Macroeconomics 30 (2008) 499–512

www.elsevier.com/locate/jmacro

Child labor participation, human capitalaccumulation, and economic development

Salvador Contreras *

McNeese State University, Department of Accounting, Finance, & Economics, 4205 Ryan Street,

Lake Charles, LA 70609, United States

Received 24 May 2006; accepted 10 January 2007Available online 10 May 2007

Abstract

This paper presents a household theoretical model that explains child labor as a function ofhousehold resources, wages, and child work time allocation. The analysis is based on the interplaybetween household educational investment choices and adult–child wage differentials. The theorydynamics reveal that child labor participation is increasing in wage equality and as the wage gapdecreases it reduces the distance by where the households is able to escape the cycle of poverty byinvesting beyond the dynamically attracting poverty level of inefficient human capital investment.The model dynamics also present the conditions by where poor households use child labor as a devel-opment strategy, as a means of accumulating physical assets at the expense of child human capitalinvestment, in the early stages of development. The policy implications of this work are that childlabor bans increase the wage differentials between child and adult earners while simultaneouslydecreasing the household incentive to invest in child education. The impact, of such policies, hasa double negative effect on poor households. Furthermore, policies that reduce wage distortions,between adult and child labor, increase adult human capital, and provide universal access to educa-tional will have long-run developmental growth effects. These policies, in the long-run, are shown toproduce household substitution away from child labor and toward the acquisition of schooling basededucation.� 2007 Elsevier Inc. All rights reserved.

JEL classification: H31; J22; J24; O12

Keywords: Human capital; Child labor; Wage distortion; Development

0164-0704/$ - see front matter � 2007 Elsevier Inc. All rights reserved.

doi:10.1016/j.jmacro.2007.01.005

* Tel.: +1 337 475 5522.E-mail address: [email protected]

mailto:[email protected]

500 S. Contreras / Journal of Macroeconomics 30 (2008) 499–512

1. Introduction

Child labor has played itself out in the political, public, and academic, forum with amixed set of policies and remedies. The problem that economists face in addressing thetopic of child labor lies on how one interprets the expected welfare utility experience ofindividual households if child labor is, or is not, eliminated. According to Fan (2004)and Basu and Van (1998) an increase in child labor policy restrictions leads to a positive,negative, welfare effect depending on the structure of the assumed labor market. That is,the imposition of a ban on child labor will shift the supply curve of labor to the left, this, inturn, leads to an increase in the wage rate for adults; yet, the increase in wages raises, low-ers, household utility depending on which effect dominates the change, substitution orincome effect. The income effect would dominate a substitution effect in the case wherechild labor is not substituted from one industry to another.1 In this case, the rise in theadult wage caused by a reduction in the labor supplied will have a positive income effectthat could potentially compensate the household for the loss income from its young notbeing able to participate in the labor market. On the other hand, if child labor is only dis-placed from one sector and reallocated in another, say from export to domestic produc-tion, the substitution of one labor group for another will have zero to negative neteffects on household welfare. That is, the child labor entering the domestic productionmarket will displace adult labor lowering overall wages for all participants of the domesticproduction market. The wages in the primary, export production, market may have over-all zero net impact on adult wages due to the influx of adults entering the export produc-tion market because of higher wages relative to those earned in the domestic productionmarket. If the substitution of one labor sector to another dominates the income effect, thatwould in tern depress child wages, and possibly expose children to more hazardous workenvironments, and have a mixed effect on adult wages. On the other side of the economicdebate exits a moral and ethical consumer behavior problem, is the consumption of knownchild labor produced goods acceptable? Basu and Van (1998), Fan (2004), Edmonds(2005), Edmonds and Pavcnik (2005), among others, argue that child labor while sociallywrong, may serve as an economic good. Under some assumptions, and conditions, theyargue that child labor bans could have negative welfare effects.

This paper presents a general equilibrium model that addresses the effects of child laboron household outcomes. Of interest is the notion that child labor bans will depress house-hold resources by reducing household income. While work by Baland and Robinson(2000) state that child labor is an equilibrium outcome and that under certain conditionschild labor bans may lead to child welfare improving outcomes; this paper, along withBasu and Van (1998), find that child labor bans are not efficient outcomes. The reasonfor this result lies on the effect that wage distortions have on the incentives of childrento participate in the labor market. The dynamics of the model show that child labor par-ticipation is a decreasing function of wage inequality between adults and child laborers.The paper sets to uncover the impact of child labor participation as a dynamic approachto household decisions of child educational choices given that a household begins the pro-cess of development from a poverty stricken beginning.

1 Doepke and Zilibotti (2005) work provide the case of a successful child labor regulation that makes regulationimplementation dependent on the will of the majority and assures policy success by household self-enforcement.

S. Contreras / Journal of Macroeconomics 30 (2008) 499–512 501

Hazan and Berdugo (2002) finds that in the early stages of development child labor par-ticipation is prevalent. In this paper, Hazan and Berdugo (2002) view is supported underthe condition that child labor wages are not distorted. That is, in this paper the use of insti-tutional wage regimes alters household choices and distorts individual incentives creatingthe conditions by where perpetual poverty traps exist. While, Baland and Robinson (2000)call this a capital market imperfection, this paper treats markets as competitive and effi-cient. Thus, any wage distortions must come exogenously to both households and goodproducers. Therefore, wage distortions in this paper come from institutional inefficiencies.Where, wage distortions between adult and child earners are derived in two modes. Weakinstitutions that prevent the state from properly allocating resources where social players,household choices, have created socially inadequate allocation of resources.2 Secondly,exogenous market distortions in the name of labor bans, on export goods, will force thestate to alter the wage structure to dissuade child labor participants from entering thisemployment sector as a way of complying with the ban.3

The innovative elements of this work lie on institutional effects on household outcomesand household investment decision on human capital development. The evolution ofhuman capital is shown to be independent of household resources which stand in contrastwith the prevailing view that household income is a major determinant of child labor par-ticipation (Hazan and Berdugo, 2002). This result comes from child labor time allocationthat is found to be dependent on parameters and the relative adult–child wage but is notdependent on household resources. Moav (2005) finds that educational investment is inde-pendent of physical capital growth. While, this work finds educational investment depen-dent on household physical capital resources (Moav, 2005) construction of human capitaldevelopment is strictly increasing and concave in educational investment. Hence, in Moav(2005) work, the evolution of educational investment is synonymous with the evolution ofhuman capital. In this regard, Moav (2005) derived evolution of human capital is consis-tent with this papers finding that human capital evolves independent of physical capitaldevelopment. This paper shows that the distortions found in the adult–child wage areindicative of human capital development poverty trap in the short-run. This finding is dif-ferent from that found in Baland and Robinson (2000), Hazan and Berdugo (2002) andFan (2004). In the early stages of development the most crucial variable is not liquidityconstraints, or household resources, but wage distortions. Furthermore, an importantimplication, of this work, is found in the effect that adult–child wage differentials haveon the threshold distance faced by the household to escape the poverty trap. Dynamically,this paper finds that as adult–child wages converge, in the early stages of development,child labor rises, in the short-run, but in the long-run it is shown that child labor isabandoned.

The paper is broken into four sections. The first section introduces the child labor the-ory. Section 2 builds the human capital accumulation equation, defines the labor market,produces the household budget constraint, and sets up the good market. A standard two-period heterogeneous agent OLG model is employed to extract the dynamical interpreta-tion of the theory. Section 3 presents the major theoretical implications of the model and

2 This implies that in poor stricken societies household choices may run counter to social optimal resourceallocations. Thus, institutional intervention is needed to reallocate social misallocations.

3 As implied by the statement, this assumes that a state has the capacity to implement an export market laborban.


derives the dynamic evolution of the economy. This section also looks at the householdimpact from varying parameter assumptions and the implications of these changes tohousehold outcomes. Finally, Section 4 concludes the paper.

2. Model

This paper assumes that households operate in a small open economy under an over-lapping-generations framework. Each period the household chooses the amount of laborhours to supply in the production of a single good. Household agents live for three peri-ods. In the first period agents are children, in the second period agents are adults, in thethird period the agent retires, and thereafter the agent expires.

2.1. Human capital

In the first period the household decide the amount of educational investment to givetheir one offspring. The household simultaneously decides on the amount of effort, frac-tion of time, to give toward the acquisition of human capital through schooling. Humancapital follows a Cobb–Douglas production function. Where human capital is a functionof the amount the household spends on the child, et, and parental human capital, ht,i.

htþ1;i ¼ ðet;ið1� lt;iÞÞ/h1�/t;i ð1Þ

where / is the share of educational investment effect on human capital production. ht,i isthe parent type i’s human capital, l is the share of child time devoted to the labor market,where 0 6 l 6 1, and e is the investment in child education. Eq. (1) is consistent with theconstant returns to human capital literature (Lucas, 1988; Moav, 2005). Following thework of Galor and Moav (2004) and Moav (2005) it is assume that h(0) = 1. Furthermore,the model assumes that human capital is bound to lime!0h0ðeÞ ¼ c <1, lime!1h 0(e) = 0,h1 > 0, h11 < 0, h2 > 0, and h22 < 0.

2.2. The household

The household has two, possible, income streams, wage income by parent, of type i,wtht,i, and child income wtHt,ilt,i, where Ht;i 2 Rþ.4 To simplify the analysis it is assumedthat H = wh, where 0 6 w 6 1. This assumption claims that the effective child labor wageis some fraction of parental human capital, where extending w, to include institutional,environmental, and, or, random shocks can be easily applied to understand the effect ofexternal factors on the child labor market.5 The household operates under the followingconstraint:

wtht;i þ wtHt;ilt;i P ct;i þ et;i þ st;i ð2Þ

4 In this model, H, as c in Basu and Van (1998) and Fan (2004), scales child wages to reflect adult equivalentincome wages.

5 The interpretation of w continues to be the human capital filter that measure the relative adult–child wage(Basu and Van, 1998).


Eq. (2) states that household income is equal to, or greater than, household consumption,c, plus child investment, e, and household savings, s. Eq. (2) is consistent with the set-up ofFan (2004) and Doepke and Zilibotti (2005).6

To simplify the analysis, it is assumed that there is a finite number of households of typei agents, where i 2 I, and I represents the type vector of all households. It is assumed thatthere is zero population growth, each household is composed of one parent and one child.7

The household maximizes utility with respect to investment choices, e, s and labor partic-ipation, l:

Maxct;i ;ctþ1;i ;htþ1;i

U ¼ b lnðct;iÞ þ ð1� b� cÞ lnðctþ1;iÞ þ c lnðhtþ1;iÞ ð3Þ

Subject to ct;i ¼ wtðht;i þHt;ilt;iÞ � et;i � st;i

ctþ1;i ¼ Rtþ1st;i ð4Þhtþ1;i ¼ ðet;ið1� lt;iÞÞ/h1�/

t;i

The utility function, Eq. (3), is similar to that used by Emerson and Souza (2003), Fan(2004) and Moav (2005) in adding human capital to the utility function. This model ex-tends their work to include physical capital through second period parental retirement.8

The utility function follows constant returns to scale assumptions, such that, parents con-sumption preferences in period t, b, and parent preference of child human capital, c, aregreater than zero but less than one. Thus, a household headed by parent of type i, in per-iod t maximizes utility by choosing household consumption in period t, her own retirementconsumption at period t + 1, and child human capital. Children in period t is assumed toform its own households in period t + 1. Household utility is subject to the standard con-straints, Eqs. (2), (4), and (1). It is assumed that labor wages, wt, and capital wages, Rt+1,are determined in a, one good, competitive market.

From Eqs. (3), (2), (4) and (1) the following optimality conditions are derived:

e�t;i ¼c/wtht;iðð1þ BÞ þ wiDÞ

1� cð1� /Þ ð5Þ

s�t;i ¼ð1� b� cÞwtht;iðð1þ BÞ þ wiDÞ

1� cð1� /Þ ð6Þ

l�t;i ¼Bwi

þ D ð7Þ

where

B ¼ c/ðcð/� 1Þ � bÞbð1� cð1� 2/ÞÞ ; D ¼ 1

1� cð1� 2/Þ

Eq. (5), states that household allocation to child investment is increasing in wages,parental human capital, and effective child wage scaling. Note, that Eq. (5) is consistentwith Fan (2004), furthermore, Eq. (5) satisfies, Fan (2004) Lemma 1 part (1).9 Eq. (6),

6 However, Fan (2004) and Doepke and Zilibotti (2005) did not factor in household savings.7 These assumptions are consistent with the work of Moav (2005) and Emerson and Souza (2003).8 Moav (2005) includes a capital market in his analysis assuming that the agent always works.9 See Appendix for proof.


states that household savings, are increasing in wages, parental human capital, and childwage scaling. Lastly, Eq. (7), states that the lower the adult–child wage distortion thehigher the degree of child labor participation.10

The corner solution, e = 0, is reached in two ways. If / = 0, or, if parents, either, derive,or are given, a value of the share of educational investment to be zero, where no householdwill have a positive investment in education. That is, a subsistence constraint will alwayslead to a corner solution, "ct,i P wtht,i(1 + wt,ilt,i) � st,i,et,i = 0 (Fan, 2004; Basu and Van,1998). Note, the assumption implies that st,i > 0, must be sufficiently large for the parent tobe able to consume in period t + 1. From the assumptions placed on et,i, a unique et,i > 0 isfound when the household consumption requirements are less than household incomeminus retirement savings, ct,i < wtht,i(1 + wl) � st,i, where / > 0. Otherwise, et,i = 0, andthe economy crashes to a poverty trap.11

2.3. Good market

Consider an economy composed of a finite number of firms producing of a singlehomogenous good (Galor and Weil, 2000). Firm’s employ three inputs, adult labor, childlabor, and physical capital in their production plan. Each firm operates under constantreturn-to-scale, Cobb–Douglas technology. Where, output is a function of physical capitaland effective labor:

yt ¼ f ðkÞ ¼ kat ; kt �

KLahþ LcHl

ð8Þ

Similarly to the technique employed by Hanushek et al. (2003), the marginal productiv-ities of labor are derived from Eq. (8):

wt;a ¼ ð1� aÞht;ikat ð9Þ

wt;c ¼ ð1� aÞHlkat ð10Þ

Finally, the returns to physical capital, rt ¼ aka�1t , is similarly derived from Eq. (8).

Consistent with the assumption of perfect labor substitutability (Fan, 2004; Basu andVan, 1998), it is assumed that firms are indifferent between hiring child and adult labor,all else equal.

2.4. Labor market

The labor market is composed of I number of type i agents. Where, as stated previously,each household, type i, is composed of one parent one child. Such that, the total worldpopulation, N, is the sum of all adult labor, La, plus all possible child labor, Lc. For sim-plicity, it is assumed that at equilibrium, total labor demand is equal to total adult laborsupply, point O in Fig. 1. Consistent with Basu and Van (1998), it is assumed that W rep-resents every point along the firm’s output expansion path curve, where input wages,

10 See Appendix for proof.11 For a formal proof, see Moav (2005) Lemma 1 proof on page 97. The poverty trap dynamics are set in the

next section.

Fig. 1. Adult–child labor market dynamics.


wa = wc, are quasi-market determined.12 That is, the portion that is not market deter-mined, w, is assumed known to the firm.13 From Fig. 1(a), three cases arise, each one cor-responding to the equality wa ¼ ð1� aÞHlka

t , where each W trajectory is derived as afunction of w. The first case, where w < 1, l > 0, is the basis of analysis for Basu andVan (1998).14 Case two states that w = 1, l > 0, such that child labor and adult laborare identical in every respect. Lastly, case three states that child labor is more productivethan adult labor, by assuming that w > 1. There are several reasons why child labor maybe preferred to adult labor, such as, easier to train, more energetic, less likely to rebel.

When child labor does not exist, the economy operates under point O, where adultlabor supply equals labor demand. In this case, adult labor commands the optimal wage,w0a. When introducing child labor into the model, the labor supply curve shifts to theright.15 When the child population enters the labor force point P 0 becomes the correspond-ing labor supply at the current wage, w0a. As shown by Fig. 1(b), given the new labor sup-ply curve, the wage drops to w00a. Operating under the assumption that w < 1, it is easy tosee that the income effect dominates the substitution effect, that is, the distance betweenw0a � w00a > w0c � w00c has a higher impact on adult wages. The impact of a drop in the effec-tive wage has a larger impact on adults, thus, the value of displaced adult wages has netnegative impact on household welfare.

When w = 1, case W 0, child and adult labor are equal substitutes. The distance O � P 0,unemployment is equally bored by the children and adults resulting in an ambiguousimpact to household income. Lastly, when, w > 1, case W00, child labor commands higherwages than adult labor. In this case the distance, O–P 0 is mostly a net negative income

12 Note that W, W0, and W00 represents different values of child wages corresponding to a fixed adult wage forchanging values of w.13 Allowing the labor market to clear.14 It should be noted that Fig. 1(b), differs from the assumptions of Basu and Van (1998), where Basu and Van

(1998) assumes that the adult labor supply is perfectly inelastic, for expositional reasons this assumption isrelaxed.15 For expositional purposes, it is assumed that the entire child population entered the labor market, but this

could be easily converted into the analysis of a fraction of the child population entering the market.


effect on child labor. In all three cases, the slope of La is the most important element of thisanalysis. Basu and Van (1998) assumes that labor is supplied inelastically to the labor mar-ket. If this is the case, then, the unemployment created by the introduction of child laborcontinues to be the distance OP 0 but it would be difficult to sort out who is largely dis-placed by the increase in labor. If firms employ the cheapest inputs then, child labor willdisplace all adult labor for all w < 1. Thus, if the labor market is assumed to have somepositive slope, then, it can be inferred that even the cheapest of child labor will have a res-ervation wage. Based on this theory, we set in the next section the conditions by wherechild labor participation is a function of relative wages.

3. Dynamics and implications

To derive the dynamic evolution of the economy, this section uses lemmas and propo-sitions to show the behavior of household choices in child investment and the implicationof those choices on their development.

3.1. Educational investment

Proposition 1. For a sufficiently poor household, in resources, wh, there exists a mapping of

educational investment that is characterized as increasing and concave for all e 2 ð0;~eÞ.Furthermore, for all e > ~e there exists a linear increasing relationship of household

educational investment in household resources; such that, the household education investment

is characterized by multiple steady states.

Proof. The proof follows from Eq. (5), the assumptions placed on human capital develop-ment Eq. (1), and is illustrated in Fig. 2. The second part of Proposition 1 states thathousehold educational investment in children is linear in household resources. This is

Fig. 2. Dynamic evolution of household investment, on child education, e.


easily seen by setting household resources, wh, be equaled to C. By taking derivative of Eq.(5) with respect to C the second part of the proposition is derived.16

Under the assumptions of human capital accumulation, Eq. (1), human capital isassumed to have the relationship h(0) = 1, such that educational investment eh > 0 "t,i.17

These two assumptions imply that for low levels of household educational investmentthere exists a set of human capital values that maintains human capital development at afixed point h( Æ ) = 1. Thus, for all e0 < e < ~e that satisfies h( Æ ) = 1, there exists anincreasing concave portion of e that satisfies the relationship ek > 0, ek,k < 0 8e < ~e andh( Æ ) = 1. Fig. 2 represents these relationships. At low levels of initial physical and humancapital there exists a higher incentive for households to hold on to physical capital assetsbecause the returns to human capital are zero (Galor and Moav, 2004). Above some pointe > ~e, household investment in education grows at a constant rate. Proposition 1 statesthat there are at least two steady states, (e0,e0) and ð~e;~eÞ, where the first is the economypoverty trap and the later is the inefficient steady state. h

3.2. Economy

From Eqs. (5), (6), (7), (9), and (10), the following systems are derived:

khh ¼ 1� cð1� /Þð1� aÞc/ð1þ Bþ wDÞð1� B=w� DÞ

� �1=a

ð11Þ

kkk ¼ ð1� aÞð1þ Bþ wDÞð1� b� cÞh1� cð1� /Þ

� � 11�a

ð12Þ

Eq. (11) is the evolution of human capital at steady state. Eq. (12) is the evolution ofphysical capital at steady state.

Lemma 1. Human capital development is independent of physical capital development,@khh

@k ¼ 0.

Proof. The proof to Lemma 1 is in the lemma itself. That is, the partial of the evolution ofhuman capital, at steady state, with respect to k is zero. This result is similar to the resultderived by Moav (2005). h

Lemma 2. Physical capital is convexly growing in human capital and initial capital is greaterthan zero.

Proof. The proof of Lemma 2 lies on Eq. (12). Taking first- and second-order partial withrespect to human capital produces a increasing convex curve, @kkk

@h > 0 and @00kkk

@h00 > 0. Thesecond part to Lemma 2 is derived through assumption, h0 > 0. h

16 @e@C ¼

c/ðð1þBÞþwDÞ1�cð1�/Þ > 0 and @00e

@C00 ¼ 0.17 The corner solution outcomes were considered in the previous section.


Proposition 2. Let Proposition 1, Lemmas 1 and 2 hold. Then, there exits a dynamic map-

ping, kk and hh, based on Eqs. (11) and (12), such that the dynamic evolution is characterized

by multiple steady states.

Proof. The proof of Proposition 2 is in Proposition 1, Lemmas 1 and 2, and illustrated inFig. 3. Lemma 1 states that human capital grows independent of physical capital develop-ment. Proposition 1 states that there exits at least two household investment decisionsteady states. Hence, at the poverty trap steady state e0 < ~e there exits a unique humancapital value h = 1. Steady state household education level ~e generates hð~eÞ > 1. Thedynamic mapping of physical capital is derived from Lemma 2. The dynamic evolutionof physical capital is attracting toward the kkk curve from above and below of the curve.18

While, human capital is repealing from right and left of the khh curve. h

As shown by Fig. 3, to the left of hð~eÞ level, the economy is attracting toward the pov-erty trap steady state. In this model, there is no (0,0) steady state.19 Thus, point A repre-sents the economies poverty trap. For poor households, it implies that incremental levelsof household investment in child education produces no higher levels of human capitalattainment for all e 2 ð0;~eÞ. According to Eq. (11), as the adult–child wage scale goesdown, the higher the wage inequality, the larger the distance between hð~eÞ � hðe0Þ. Thisimplies that as the adult–child wage inequality grows, the lower the likelihood of a utilitymaximizing household to invest on children education. Yet, Eq. (7) states that as theadult–child wage scale goes down, the child supplies lower levels of time to the labor mar-ket. To reconcile both results it is important to note that e is not an argument in Eq. (7). Apoor household that operates under an institutional regime that forces w! 0 is an econ-omy that is outside the scope of this theoretical analysis.20

On the other hand, as the value of adult–child wage scale goes up, wage inequality isreduced, the distance hð~eÞ � hðe0Þ narrows. According to Eq. (7), child labor increasesits share of labor time allocation.21 At the same time the unproductive child investmentspace is reduced. This result is complement to the argument put forward by Galor andMoav (2004) that states that in the early stages of development the household underinvests in human capital and over invests in physical capital accumulation. The dynamicinterpretation of the model supports such an argument. The household continues to viewinvestment in children human capital accumulation as an unproductive investment if all

18 From the above of the steady state curve physical capital is decreasing, kt < k. Similarly, physical capital isincreasing from the below of kkk when kt > k.19 This result is due to the assumption that h P 1 "t,i. This assumption also implies that the corner solution

e = 0 does not produce a (0,0) steady state.20 The implications of this result are nonetheless extremely important. The household is devoid of relative value

to holding on to the child. The child has no incentive to work and there is no household incentive to invest in it.This may explain conditions by where relatively poor families sell of their children as indenture servitude aspayment on outstanding debt as a means of extracting value.21 Levy (1985) finds that increases in children wages leads to an increase child labor participation in farming and

decreases school enrollment. While his work does not look into the effects of wage differentials between adults andchildren, the coefficients of his elasticity analysis shows that an increase of 10% in child wages leads to a increaseof 9.6% in labor participation of children between 6 and 11. The impact of male adult wages, for the same increaseon the same group, leads to an increase of 5%. Yet, in the next cohort group, children 12–14 year of age, the same10% increase in wages has a lower impact on child labor participation of 3.8% for child wages and 5.3% for adultmale wages. That is, as the wage differentials increase the net impact on child labor participation decreases.

Fig. 3. Dynamic evolution of physical and human capital.


they have is small amounts of resources. Yet, the household is better off because the childis contributing to household resources. That is there are greater household, short-term,returns to having the child participate in the labor market vis-a-vis child education invest-ment. This implies that for relatively high levels of w, within a number of generations,household can find conditions by where investing in child education is an optimal alloca-tion of investing resources. At some point, households can overcome the distancehð~eÞ � hðe0Þ by investing enough resources in human capital accumulation to put thehousehold beyond point B, Fig. 3. Once the economy enters the dynamic growth path,holding all else constant, the household will enter a period of self-sustained growth wherethe returns of household child education investment is greater than child job market par-ticipation. Stated differently, economic growth, at the household level, is followed by adecline in child labor participation (Edmonds, 2005).

3.3. Wage distortion effects

This section is used to further illustrate the effects of adult–child wage distortions onhousehold behavior. To tests these behaviors the paper employs simulated graphs builtusing standard parameter assumptions. The parameters values used are presented in Table1. The values in Table 1 are used to deriving Fig. 4. The first three columns in Table 1 askshow do wage distortions affect the development of the household economy. As seen fromFig. 4(a), as the value of w goes down, as wage inequality increases, the quantity of physical

Table 1Parameter values

(1) (2) (3) (4) (5)

b 0.3 0.3 0.3 0.3 0.3a 0.3 0.3 0.3 0.3 0.3c 0.35 0.35 0.35 0.35 0.35w 0.1 0.5 1.0 0.5 0.5/ 0.5 0.5 0.5 0.25 0.5

Fig. 4. Impact on capital equilibrium dynamics with changing values of w and /.


capital resources needed to reach the equilibrium point also increase. This finding is consis-tent with the dynamics found from both Propositions 1 and 2 and illustrated by Fig. 3.

Fig. 4(b) assumes parameter values column (4) and (5) in Table 1. Fig. 4 shows that asthe educational investment share on human capital accumulation goes down, the lower thehousehold threshold distance to reach steady state, all else equal. This is an importantimplication for poor households. It states that in the early stages of development as theeducational investment allocation has a higher impact on the accumulation of human cap-ital the worse of the household becomes. The derivation is consistent with the theory pre-sented in this paper in that having a greater incentive to invest in children creates theconditions by where poor households invest in a myopic investment instrument at theexpense of long-run development. The household has little incentive to invest on childhuman capital. Thus, in the short-run, the household invests relatively little in the child’seducation, while, utilizing its labor capacity to increase household resources. According toFigs. 3 and 4(b), having the household concentrate in the accumulation of physical assetssimultaneously lowers the level of resources needed to overcome the investment trap. Pro-duces a result similar to Galor and Weil (2000) in that household development beyondpoint (B) in Fig. 3 has the effect of having both human capital and physical capital growingat a constant growth rate.

4. Conclusion

This paper built a general equilibrium model that analyzes the implications of childlabor participation on household development. The model allowed the household to


choose the amount of educational investment resources to furnish their offspring as well asthe amount of child labor participation. The theory and dynamics showed that child laborparticipation is an efficient outcome under regimes that have little to no wage discrimina-tion. A non-wage discriminating regimes was found to have short-run dynamic child laborparticipation properties. However, in the long-run, these properties were shown to disap-pear. The implication of this analysis is an argument against labor bans that focus at dis-torting the adult–child wage.

Under wage distorting regimes, the dynamics showed that child labor participation isdeclining as the distortions increase. Yet, these properties were also shown to have theeffect of lowering the household’s incentive to invest in the child’s education. This impliesthat for a child labor ban policy to have a positive child welfare effect, lower child laborparticipation and increasing human capital acquisition, then, the policy must have astrong element of child educational investment. But as shown by the poverty dynamicsof the model, the educational investment must be higher than the lost income due tothe ban. Otherwise, as suggestive by the model, the household’s relative value of holdingon to the child decreases. This condition may lead to a worse overall outcome to thechild.

The implications of this work indicate that institutional markets should be used to cor-rect wage distortions, increase parental human capital, and provide universal access toeducation. By decreasing the adult–child wage distortion the household is best able toextract the appropriate child value. Increasing parental human capital through adult liter-acy programs, vocational training, etc. will have positive spillover on child human capitaldevelopment. Lastly, making universal access to education will lower the overall house-hold expense to educate a child, will create an alternative to labor participation, and it willincrease the level of human capital.

Acknowledgements

I thank Arthur Denzau, Yi Feng, Simon Lamar, Amit Ghosh, and an anonymous ref-eree for their valuable feedback and comments. Also, I’m indebted to Claremont GraduateUniversity, California State University Long Beach, and the University of Redlands. Allremaining errors are my own.

Appendix

Proof of Fan (2004) Lemma 1: part (1) of lemma is easily derived by taking derivative ofEq. (5) with respect to wi.

@e@wi

:c/wtht;ilt;i

1� cð1� /Þ > 0 ð13Þ

Similarly, part (2), of Lemma 1, is found by taking Eq. (7) and taking derivative withrespect to wi. First, Eq. (7) is set to (1 � l):

1� l ¼ 1� Bwi

� D


Thus,

@ð1� lÞ@wi

:B

w2i

< 0

B ¼ c/ðcð/� 1Þ � bÞbð1� cð1� 2/ÞÞ < 0

D ¼ 1

1� cð1� 2/Þ > 0

The numerator in B is clearly negative, while the denominator is positive. Making B

negative. D is a positive function of parameters.

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child labor participation, human capital accumulation, and economic development

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