For example, the International Labour Office (1996) estimates that, worldwide, 120 million children between the ages of 5 and 14 work full-time.

Transcription

1 Is Child Labor Ineffiient? Jean-Marie Baland University of Namur James A. Robinson University of California at Berkeley We build a model of hild labor and study its impliations for welfare. We assume that there is a trade-off between hild labor and the aumulation of human apital. Even if parents are altruisti and hild labor is soially ineffiient, it may arise in equilibrium beause parents fail to fully internalize its negative effets. This ours when bequests are zero or when apital markets are imperfet. We also study the effets of a simple ban on hild labor and derive onditions under whih it may be Pareto improving in general equilibrium. We show that the impliations of hild labor for fertility are ambiguous. I. Introdution Although hild labor is an age-old phenomenon and of enormous importane in the ontemporary world, 1 there has been little formal analysis of this issue. While the existene of hild labor is frequently ondemned as odious and immoral, the real issue is to better understand We would like to thank Sam Bowles, seminar partiipants at the University of Oslo, the Tinbergen Institute (Amsterdam), the University of Toulouse, the University of Melbourne, the International Eonomi Assoiation XII Congress in Buenos Aires, two anonymous referees, and an editor for their insightful omments on former drafts of this paper. Baland would like to thank the MaArthur Foundation Researh Network on Inequality and Eonomi Performane for support, and Robinson would like to thank the Southern California Studies Center at the University of Southern California for finanial assistane. 1 For example, the International Labour Offie (1996) estimates that, worldwide, 120 million hildren between the ages of 5 and 14 work full-time. [Journal of Politial Eonomy, 2000, vol. 108, no. 4] 2000 by The University of Chiago. All rights reserved /2000/ $

2 664 journal of politial eonomy the determinants of hild labor so as to evaluate its welfare impliations. In this paper we show that, even when parents are fully altruisti toward their hildren, hild labor an be Pareto ineffiient. Central to our analysis is the impat of labor on a hild s future earning ability as an adult. Child labor is soially ineffiient when it has a suffiiently adverse effet on suh ability, but it may nevertheless persist either when parents leave their hildren no bequests or when apital markets are imperfet. Both of these irumstanes imply that parents fail to internalize the soially effiient trade-off between hild labor and earning ability. We first show that hild labor is ineffiient when the family is so poor that parents do not leave bequests to their hildren. When bequests are positive, parents ompletely internalize the adverse impat of hild labor on the future inome of their hildren sine, by reduing bequests aordingly, they an ompensate themselves for the urrent inome they lose when not making their hildren work. Seond, even if bequests are interior, hild labor may be ineffiiently high beause parents fae apital market imperfetions, whih stop their transferring the future redution in bequest into the present. Sine the ineffiieny of hild labor partly stems from the nonnegativity onstraint on bequests, one might onjeture 2 that introduing reverse altruism, with transfers from hildren to parents, would restore the effiieny of resoure alloation. We show in an extension to our basi model that this is indeed the ase when parents fae perfet apital markets. However, the ineffiieny of hild labor stemming from imperfet apital markets is unaltered by the presene of reverse altruism. 3 Turning to poliy impliations, we show that if the general equilibrium effets are well behaved, a small ban on hild labor may onstitute an atual Pareto improvement even though it does not diretly ompensate parents. The reason is that endogenous hanges in wages indued by a redution in hild labor may make parents and firms better off. 4 The observation that a nonnegativity onstraint on bequests an lead to ineffiient resoure alloation in the family is originally due to Beker and Murphy (1988) and Nerlove, Razin, and Sadka (1988). We show that this has important impliations for the effiieny of hild labor. The intuition behind our results is related to the Rotten Kid theorem of Beker (1974) as formalized by Bergstrom (1989). Bergstrom derived the general onditions under whih, if intrafamily transfers are interior, 2 We are grateful to the editor for bringing this point to our attention. 3 While our basi model is the altruisti model of Beker (1991), the extension of our results to the ase of two-sided altruism with imperfet apital markets shows that hild labor would be ineffiiently high in the onventional old-age seurity model of fertility (see, e.g., Nugent 1985). 4 This result ontrasts with that of Basu and Van (1998), who find that a ban on hild labor is not Pareto improving.

3 hild labor 665 family members independently hoose ations that benefit the whole family, that is, maximize joint family inome. However, in a one-good model, whih is equivalent to the one we study when saving is positive, interiority of transfers is itself suffiient to establish effiieny. This is what interior bequests ahieve. However, when saving is at a orner, our model effetively has two dated goods and the Rotten Kid theorem does not hold in general. Thus positive transfers are not suffiient to guarantee effiieny in this ase. 5 The importane of the nonnegativity onstraints on both bequests and savings arises from apital market imperfetions. In the ase of bequests, if hildren ould borrow when they were young, they ould transfer resoures to their parents and ompensate them for redued hild labor, even if parents subsequently planned to leave no bequests. 6 Alternatively, hildren ould enter into a ontrat with their parents involving a transfer of future inome in exhange for a urrent redution in hild labor. However, suh ontrats are in general neither self-enforing nor legally enforeable. Our analysis adds to the literature on hild labor in a number of ways. As in Eswaran (1996) and Basu and Van (1998), we find that hild labor is a faet of poverty. 7 However, in neither of their papers is there a lear-ut welfare argument that suggests that hild labor is ineffiient. 8 Grootaert and Kanbur (1995) suggest that if there is a trade-off between hild labor and eduation, then hild labor an be ineffiient if there are positive externalities to human apital aumulation. In our view, even when the soial return to human apital is ignored, the nature of intrafamily resoure alloation may stop even the private return from being aptured, and we present two new arguments as to why this might be so. The idea that the amount that parents indue their hildren to work may be ineffiient an be traed to John Stuart Mill sine he regarded hild labor as a ase par exellene, in whih it would be highly for the advantage of everybody, if everybody were to at in a ertain manner, but in whih it is not the interest of any individual to 5 In the spirit of Bergstrom s results, we ould in fat show that, with more than one good and without transferable utility, hild labor ould be ineffiient even when bequests and savings were interior. Nevertheless, we feel that the simpler model we develop in this paper haraterizes intuitively the irumstanes under whih hild labor is ineffiient. 6 Loury (1981) developed a related model with heterogeneous agents in whih investment in eduation is the only way to transfer resoures between generations. Capital market imperfetions generally imply that the marginal return to eduation will not be equalized aross families so that investment in human apital is ineffiient. 7 The onnetion between poverty and hild labor is well established in the empirial literature (e.g., Rosenzweig 1981; Labenne 1997). 8 For example, Basu and Van (1998) onstrut a model of the labor market in whih there are multiple stable equilibria. In one there is a high wage that allows adults not to send their hildren to work, and in the other there is a low wage and hild labor. These equilibria are not Pareto ranked sine in the equilibrium without hild labor firm profits are lower.

4 666 journal of politial eonomy adopt the rule for the guidane of his own ondut, unless he has some seurity that others will do so too (1965, p. 699) (see the disussion in Hollander [1985, p. 749]). Later, Mill notes that it is right that hildren should be proteted from being overworked. Labouring for too many hours in the day, or on work beyond their strength, should not be permitted to them, for if permitted it may always be ompelled. Freedom of ontrat, in the ase of hildren, is but another word for freedom of oerion. Eduation also, the best whih irumstanes admit of their reeiving, is not a thing whih parents or relatives should have it in their power to withhold. [1965, p. 952] The opportunity to put hildren to work has been laimed to distort fertility deisions upward. For example, Dasgupta (1995, p. 1895) argues that in poor ountries hildren are also useful as inome-earning assets. This provides households with another motive for proreation. Similarly, Weiner (1991, p. 186) laims that many governments have not been deterred from making eduation ompulsory by the presene of widespread poverty and by the argument that the poor need the inome of their hildren. Government offiials have reasoned that parents ought not to be allowed to use hildren to inrease their own inome. Suh a poliy is an induement to a high fertility rate. By establishing poliies that deny parents the inome of their hildren, hildren ease to be regarded as eonomi assets and there is less inentive to inrease their numbers. Eswaran (1996) proposes a formal model to support this idea (see also Basu and Van 1998). He shows that when hildren are needed to provide old-age seurity, allowing parents to put their hildren to work may indue parents to substitute away from small, more eduated to large, less eduated families. 9 We study the effets of hild labor on fertility in Setion IV. The impat of a redution in hild labor on fertility deisions ruially depends on the former s impat on parental inome (suh as a rise in parental wages). Our model is onsistent with rather general interpretations both of hild labor and of the nature of future earnings ability. For example, hild labor inludes not just salaried oupations outside the household 9 Rosenzweig and Evenson (1977) find a positive relation between fertility and hild wage rates using distrit data from India; see also Cain and Mozumder (1981).

5 hild labor 667 but also domesti tasks imposed on hildren. The impliations of suh labor on future earnings inlude not just the loss of formal eduation and human apital but also the lak of soial and ognitive skills 10 or inreased health hazards. There is some ontroversy in the empirial literature about the effets of hild labor on the eduational attainment of hildren (see Grootaert and Kanbur 1995). Some studies have found that hild labor does not have a signifiantly adverse effet. Yet it seems hard to believe that in general the human apital aumulation of hildren is not impaired by having to work. In a reent study of Ghana, Canagarajah and Coulombe (1997, p. 42) onlude that poverty is signifiantly orrelated with the deision to send hildren to shool, and there is a signifiant negative relationship between going to shool and working (see also the evidene in Psaharopoulos [1997] and Jensen and Nielsen [1997]). In support of our model, Weiner (1991, p. 195) reports that in India the proprietors of large businesses have not opposed hild-labor laws. One of the omplaints of managers of large firms is that their labor fore is not suffiiently eduated, that too many workers are unable to read manuals or follow the simple instrutions written on mahines. The paper proeeds as follows. In Setion II, we develop the basi model of family hoie with exogenous fertility and embed this within a simple market framework to study the equilibrium amount of hild labor. We then extend the model to analyze first the impliations of reverse altruism (in Se. III) and seond the effets of hild labor on fertility (Se. IV). Setion V disusses the poliy impliations of our analysis, and Setion VI presents a onlusion. II. The Basi Model: One-Sided Altruism and Exogenous Fertility The model onsists of two periods, t p 1, 2, and there is no disounting of the future by any agent. At the beginning of the first period there are L p parents alive, who live for both periods. At the beginning of the first period they deide how many hildren to have, with eah set of idential parents having n hildren. Children also live for both periods. The other agents in the eonomy run firms and use labor to produe the numeraire good. For simpliity we onsider a single suh agent (a representative firm ), who lives for both periods and has no hildren. In the first period parents deide how to alloate their hildren s unit time endowment between hild labor and human apital aumulation. Parents work and supply labor inelastially, and we assume that eah 10 For example, Ennew (1982, p. 560) notes that when relatively young hildren are fored to are for even younger siblings the older hild loses eduational opportunity at shool, but in addition the younger hild may be prevented from developing suffiient verbal and oneptual skills to benefit from formal eduation.

6 668 journal of politial eonomy parent has A effiieny units of labor in eah period. In t p 1, parental labor supply is ALp and the supply of hild labor is nlpl, where l [0, 1] is the fration of a hild s time that is alloated to work. In t p 1, parents ontrol all inome, inluding that earned by hildren. In t p 2, hildren, now alled adults, work. Their total labor supply at this date is nlph(1 l ), where h(1 l ) are the additional units of human apital possessed by an adult who worked for a fration l of his time endowment when a hild. The funtion h is twie ontinuously differentiable, stritly inreasing, and stritly onave with h(0) p 1 (so that a hild who spent all his time working in the first period still has a single effiieny unit of labor as an adult). In t p 2, adults ontrol their own inome. We assume that the markets for young and old parental, hild, and adult labor are all ompetitive with respetive wage rates w p1, w p2, w 1, and w2 (all wage rates are per unit of human apital). In this setion we shall assume that firms have a linear tehnology so that profits are zero and let all wages be idential and be set equal to one. We assume that parents are endowed with a joint utility funtion defined over their own onsumption of a single onsumption good (whih is the numeraire in the eonomy with prie normalized to unity), t denoted p, for t p 1, 2; the number of hildren that they have, n; and the utility of their hildren (all of whom have idential preferenes and are treated identially by parents). Parental utility is denoted 1 2 W p( p, p, n, W( )), where W( ) is the utility funtion of a hild, whih depends only on hild onsumption, (hild onsumption takes plae only in t p 2). We follow Beker (1991) in assuming that W p is separable (though nothing hinges on this) so that W p( p, p, n, W( )) { U( p) U( p) ndw( ), (1) where U and W are both twie ontinuously differentiable, stritly inreasing, and stritly onave. Here 1 1 d 1 0 is a parameter measuring the extent to whih parents are altruisti. In the paper, n is treated as exogenous exept in Setion IV, where we speifially examine fertility deisions. For simpliity we therefore set n p 1 everywhere exept in that setion. Apart from hoosing the time alloation of hildren, l, parents an also deide to give them transfers of inome in t p 2, whih we all bequests and denote by b 0. They an also transfer inome between periods by saving, denoted by s. We assume that apital markets are imperfet, so that parents annot borrow. Therefore, saving is restrited to be nonnegative, s 0. Parents therefore fae the budget onstraints 1 p p A l s, (2)

7 hild labor 669 and 2 p p A b s, (3) p h(1 l ) b. (4) The three first-order onditions with respet to b, l, and s are, respetively, 2 U ( p) p dw ( ) and b 1 0 or 2 U ( p) 1 dw ( ) and b p 0, (5) and 1 U ( p) p dw ( )h (1 l ), (6) 1 2 U ( p) p U ( p) ands 1 0 or 1 2 U ( p) 1 U ( p) ands p 0. (7) We assume that there exists an interior optimum level of hild labor denoted by l, whih satisfies (6). To see that the level of hild labor l that maximizes (1) may be ineffiiently high, notie that hild labor is effiient when the marginal return to eduation in terms of inome is equal to its opportunity ost 11 in terms of lower hild labor, that is, when h (1 l ) p 1. Child labor is therefore ineffiiently high when h (1 l ) 1 1 with l 1 0. We first define the onditions under whih the level of hild labor deided by parents is effiient. Proposition 1. If bequests and savings are interior, then the laissezfaire level of hild labor is effiient. To see proposition 1, notie that from the first-order onditions above, 2 if b 1 0, then U ( p) p dw ( ) (from eq. [5]). Equation (7) then implies 1 that U ( p) p dw ( ), and substituting this into (6) shows that h (1 l ) p 1. From this proof, one an immediately see that when parental 2 bequest is at a orner, so that U ( p) 1 dw ( ), h (1 l ) 1 1. Hene we get the following proposition. Proposition 2. If bequests are at a orner, then h (1 l ) 1 1 and the laissez-faire level of hild labor, l, is ineffiiently high. The family annot be expeted to solve this soure of ineffiieny on its own. The reason is that hildren do not have any resoures from whih they an ompensate parents; they an promise to do so only when they are adults and are earning inome. But suh promises are 11 This is of ourse also the ondition under whih family inome is maximized.

8 670 journal of politial eonomy not redible. 12 Moreover, as long as soiety does not legally enfore ontrats signed by hildren, this problem annot be solved by apital markets. Under what irumstanes does this result apply? From the first-order onditions one an easily see that bequests are more likely to be at a orner the lower A and d are. Moreover, one an also infer from the first-order onditions that l / d! 0. This implies that as parents attah more weight to the utility of their hildren, they redue the amount of hild labor. On the other hand, it is also true that l / A! 0, so that a fall in parental endowment (i.e., inreased poverty) inreases hild labor. Therefore, the extent of hild labor and its ineffiieny an be interpreted as due to either poverty or lak of altruism. We now show that even if bequests are interior, hild labor is ineffiiently high if the nonnegativity onstraint on savings binds. This ours as apital markets are imperfet so that parents annot borrow. Intuitively, even though parents fully internalize the negative effets of hild labor on seond-period inome through their bequest, they value period 1 inome more highly. With imperfet apital markets they transfer inome into period 1 by making hildren work more than the soially effiient amount. 13 Proposition 3. If savings are at a orner, then the laissez-faire level of hild labor, l, is ineffiiently high. 2 To see this result, note that b 1 0 arises when U ( p) p dw ( ). The 1 first-order ondition for s p 0 then gives U ( p) 1 dw ( ), again implying that h (1 l ) 1 1. Proposition 2 also holds when bequests are also at a orner sine in that ase parents value their own onsumption in period 2 more than that of their hildren, and one an still derive the impliation that h (1 l ) 1 1. Even though we did not formally introdue a disount fator, it is lear that the ineffiieny pointed to in proposition 3 is more likely to arise as parents disount the future more heavily. III. Two-Sided Altruism We now show how the results of Setion II extend to the situation in whih hildren are simultaneously altruisti toward their parents. The 12 In a repeated or dynami game, families ould use intergenerational punishment strategies (e.g., of the type onsidered in Ehrlih and Lui [1991]) in order to sustain the redibility of ontrats. While this is ertainly a theoretial possibility, we doubt that it has muh explanatory power in poor ountries. For example, when mortality risk is high and life expetany short, agents disount the future heavily, and this makes it unlikely that the threat of future punishment an sustain the redibility of transfers. Moreover, suh punishments may well not be renegotiation proof. 13 Areas in whih redit shemes oriented toward the poor, suh as the Grameen Bank, have developed reently may provide an interesting empirial test of the impat of apital market imperfetions on hild labor.

9 hild labor 671 timing and endowments of all agents in the eonomy are idential to those defined in Setion II, as is the utility funtion of parents, whih 1 2 is the same funtion as (1), namely, Wp p U( p) U( p) dw. However, instead of hildren s utility funtion W being defined simply over their own onsumption in period 2, we now assume that hildren are also altruisti toward their parents so that W p V( ) lw p, where 1 1 l 1 0 measures the extent of filial altruism. In this ase, when these two onditions are solved simultaneously, parents maximize subjet to the new budget onstraints and 1 2 U( p) U( p) dv( ) Wp p (8) 1 dl 1 p p A l s (9) 2 p p A b s t, (10) where t 0 is a transfer from hild to parent. Children hoose t to maximize subjet to 1 2 V( ) l[u( p) U( p)] W p 1 dl p h(1 l ) b t. Family hoies are timed as follows. In the first period parents hoose hild labor and saving, and in the seond they hoose the level of bequests followed by the hoie of transfers by hildren. Thus the hoie of t is onditioned on all previous hoies by parents, and parents take into aount the way in whih transfers are affeted by their own hoies in maximizing (8). We an therefore solve for the equilibrium alloation of resoures by solving for the optimal hoie of t onditional on l, s, and b. This satisfies the first-order ondition V (h(1 l ) b t) p lu (A b s t). (11) In making their initial hoies, parents antiipate the effets on the transfer they get from their hild. Note that a positive transfer from hild to parent is like a negative bequest. Sine what is important is the net transfers between parent and hild, t is positive only when b p 0, and vie versa. When b is stritly positive, the two first-order onditions below redue to those of Setion II, and the results demonstrated there apply. We therefore restrit attention to the situation in whih b is at a 2 orner so that U ( ) 1 dv ( ). p

10 672 journal of politial eonomy The respetive first-order onditions for and s are and dt dt 1 2 U ( p) U ( p) p dv ( ) h (1 l ) (12) dl dl l [ ] dt dt U ( p) dv ( ) p U ( p) U ( p). (13) ds ds Note first that even if reverse altruism exists and even if bequests are at a orner, it may still be the ase that t p 0. This will be true if the following ondition is satisfied: V ([1 h(1 l )]) 1 lu (A s ). This ours, for example, when l is small. In this ase the result of the previous setion goes through unhanged, so that if bequests are at a orner then the laissez-faire level of hild labor, l, is ineffiiently high. More interestingly, we now show that the intuition that reverse altruism will solve the ommitment problem by relaxing the nonnegativity onstraint on bequests is true only when apital markets are perfet. Proposition 4. If apital markets are perfet and transfers are interior, then the laissez-faire level of hild labor, l, is effiient. The easiest way to prove the result is to note that the first-order onditions (12) and (13) hold at the Pareto-effiient level of hild labor, that is, when h (1 l ) p 1. Perfet apital markets imply that (13) 1 holds. We use this ondition to substitute U ( ) from (12), giving ( ) [ ] dt dt dt dt 2 U ( p) 1 p dv ( ) h (1 l ). (14) dl ds dl ds When the derivatives dt/dl and dt/ds from equation (11) are omputed, it is easy to show that dt dt p 1. dl ds As a result, the left-hand side of equation (14) is equal to zero. As dv ( ) 1 0, it follows that h (1 l ) must be equal to one. Even though bequests are at a orner, parents are hoosing the soially effiient level of hild labor. We now show that, with imperfet apital markets, when savings are at a orner, the equilibrium amount of hild labor is ineffiiently high despite the presene of reverse altruism. In this ase, equation (13) an be rewritten as dwp dt dt p U ( p) dv ( ) U ( p) U ( p)! 0, s p 0. (15) ds ds ds p

11 hild labor 673 We now have the following result. Proposition 5. When apital markets are imperfet, the laissez-faire level of hild labor, l, is ineffiiently high even if transfers are interior. To prove this result, note that, from equation (15), we an define a D 1 0 suh that dt dt U ( p) p D U ( p) U ( p) dv ( ). ds ds Now, following the proof of proposition 4, we find that, at the soially effiient point at whih h (1 l ) p 1, dw p/dl p D 1 0, so that parents hoose a level of hild labor that is ineffiiently high. 14 IV. Endogenous Fertility We now return to the model of Setion II to endogenize the hoie of family size by parents. 15 As is onventional, we shall assume that n is a ontinuous variable. We assume that it osts j 1 0 units of inome to have a hild. We fous on the ase in whih bequests are at a orner and apital markets are perfet. 16 In this ase the objetive funtion of the parents is U(A nj nl s) U(A nb s) dnw (h(1 l ) b). (16) Therefore, in addition to the three first-order onditions (5) (7), we have 1 U ( p)(l j) dw( ) p 0, (17) where l j! 0 if the hoie of fertility is to be interior. One an easily show that the impat of a redution in hild labor on fertility is in general ambiguous. To see why, first imagine a hypothetial situation in whih parental inome is unhanged when the amount of hild labor is redued (for instane, they get fully ompensated by the state). As the net marginal ost of a hild in period 1 is also unhanged by the transfer, the net effet of a redution in hild labor is to inrease 14 Interestingly, it is not generally true that the ultimate soure of ineffiieny in our model is the fat that parents, and not the hildren themselves, have the property rights over hild labor. Consider the ase in whih the effiient level of hild labor is positive. Then if l were hosen by the hildren, it would be effiient only when bequests are interior. Otherwise, hildren would hoose an ineffiiently low level of l. 15 A referee has pointed out to us the following interesting problem with the Beker model of altruism when fertility is endogenous: The optimal fertility deision is sensitive to positive monotone transformations of hildren s utility funtion. To avoid this problem, the results of the paper ould be derived using a different formulation of parental utility 1 2 suh as U( p, p, n, ) (with U34 1 0), where the utility funtion of hildren does not enter diretly into the utility funtion of parents. 16 The results in the ase in whih apital markets are imperfet follow losely those derived in this paper.

12 674 journal of politial eonomy the marginal value of a hild in the future (through the rise in W ), whih stimulates higher fertility. On the other hand, onsider now a situation in whih hild labor is redued by law, with no expliit ompensation to the parents (remember that, beause of the tehnology, wages remain onstant). A redution in hild labor now has three effets: a negative inome effet on the parents, an inrease in the urrentperiod net ost of a hild, and an inrease in the future value of the hild. Differentiating equation (17) and using the first-order onditions (6) and (7), one an show that dn n p, dl l j so that the net effet of a redution in hild labor is to redue fertility. This disussion was arried out assuming that the tehnology is linear so that wages are onstant. With more general prodution tehnologies, wages vary and an generate a positive inome effet on parents, reversing the sign of dn/dl. We onsider this issue in the next setion. V. General Equilibrium and Poliy Impliations So far we have argued that, under plausible assumptions about timing and apital markets, it is highly unlikely that families themselves will be able to solve the ineffiienies isolated in this paper. This suggests that there may be a welfare-enhaning role for government poliy. What form might this take? It might be thought that a simple ban on hild labor would not implement a Pareto improvement sine parents would be worse off if unompensated. Interestingly, this is not neessarily so. To investigate these issues, we now revert to the one-sided altruisti model of Setion II with n p 1. In order to use alulus tehniques, we analyze the ase of a marginal, rather than a omplete, fored redution in hild labor. In reality this would our if the government were to pass legislation to redue the hours hildren are allowed to work. For expositional simpliity, we arry out the disussion by fousing on the ase in whih bequests are at a orner whereas savings are interior. A similar disussion, yielding idential results, an be arried out with interior bequests and savings at a orner. We first show that, with a linear tehnology, a marginal ban on hild labor is Pareto improving. Suh a ban does not affet firm profits or any wages. Next, sine parents hoose l optimally, by the envelope theorem a small redution in the amount of hild labor has no first-order effet on parental welfare. Finally, when bequests are assumed to be at a orner, the effet on hild welfare is unambiguously positive sine dw /dl p W ( )h! 0. In other words, the effet on parental utility is

13 hild labor 675 seond-order and that on hild welfare is first-order. This gives the following result. Proposition 6. With a linear tehnology, a marginal ban on hild labor is a Pareto improvement when bequests or savings are at a orner. While proposition 6 is of interest, our view is that in reality the general equilibrium effets of a ban on hild labor are likely to be important. 17 A ban on hild labor redues the supply of hild labor while inreasing the supply of adult labor in the future. As a result, one would expet urrent wages, those of both adults and hildren, to rise and future wages to fall. Therefore, while we expet hildren s utility to rise in most ases, parental welfare will inrease only when the effet on urrent wages dominates. We now show that suh a situation an exist so that a small ban on hild labor an be Pareto improving. The firm maximizes the sum of profits, denoted p, over the two periods and is endowed with nonlinear tehnologies for onverting effiieny units of labor into output. For simpliity, we assume that output is separable in parental and hild labor, so that output in any one period is fp f, where f p(al p) is the output produed by parents in both periods and f (ll) p and f (Lph(1 l )) are the outputs produed by hildren in periods 1 and 2, respetively. We assume that the prodution funtion fi for i p p, is twie ontinuously differentiable, stritly inreasing, and onave so that the elastiity of the wage rate to the amount of labor demanded an be defined as wit Lit f i (7)L it eit p { for i p p,, t p 1, 2. L w f (7) it it i Let w it stand for the wage rate for agent i in period t. Firms hoose L it to maximize p p 2 i tp1 ipp, [f(l ) wl], it it it so that labor demand solves f i(l it) p w it. Let L it(w it) denote the optimal demand for labor funtion with derivative L it(w it)! 0. In period 1, parental labor supply (in effiieny units) is AL p and hild labor supply is Ll p. In period 2, parental labor supply is idential and adult labor supply is Lh(1 l ). Thus equilibrium wages w solve the p it 17 Historially, trade unions were influential in pressing for banning hild labor, one reason being that it was thought to depress wages. For example, Davin (1982, pp ) notes that organized workers attitudes to hild and juvenile labour were also oloured by the extent of its use to underut adults. The support of setions of the working lass for regulation of hild labour thus stemmed from the reognition that the regulation would at least partly redue ompetition on an over-stoked labour market. Zelizer (1994, p. 63) argues that in the United States opposition to hild labor partly developed beause by the turn of the entury the heap labor of hildren threatened to depress adult wages.

14 676 journal of politial eonomy market-learing onditions ALp p L p1(w p1), Ll p p L 1(w 1), ALp p L p2(w p2), and Lh(1 p l ) p L 2(w 2). We now investigate the effets of a small ban of hild labor on the welfare of all agents in the eonomy, taking into aount the general equilibrium effets. First note that, by the envelope theorem, the effet of suh a ban on profits is given by dp w1 w2 p L1 L 2. (18) dl l l Differentiating the market equilibrium onditions, we have and w1 Lp p! 0 l L (w ) 1 1 w 2 h Lp p 1 0. l L (w ) 2 2 Substituting these into (18), we find [ ] dp L1 hl2 p p dl L 1(w 1) L 2(w 2) p L p ( w e hw e )L, whih is negative if w1e1 hw2e 2. Consider the effet of the ban on parental welfare when bequests are at a orner. This is ( ) ( ) dwp w1 w 1 2 p U ( p) w1 l dw ( ) hw2 h. (19) dl l l We have used the envelope theorem to remove terms in savings. 18 From the first-order ondition on hild labor, this simplifies to dw p 1 dl p U ( )w (e e ), p whih is negative if the urrent hild wage rises faster than the future wage falls. The effet on hildren s utility is ( ) dw w 2 p W ( ) hw2 h p W ( )hw 2(1 e 2), dl l whih is negative if e 1. 2 This ondition implies that the elastiity 18 If savings are at a orner, we annot use the first-order ondition to simplify the expressions; nevertheless, the result holds a fortiori.

15 hild labor 677 is suh that the total wage bill aruing to adult hildren rises. We therefore have proved the following result. Proposition 7. A marginal ban on hild labor is a Pareto improvement when parental bequests or savings are at a orner if e 1 and 2 w w 1 2 e e h e. The onditions under whih the result holds are ompatible. In partiular, when e2 1 and the two demand elastiities are equal, the result holds if and only if hild labor is ineffiient, that is, if hw2 1 w 1. Proposition 7 has been derived under the assumption that the pro- dution funtions were separable in parental and hild labor inputs. In a more general setting, we an expet those inputs to be at least partial substitutes, so that parental wages inrease in the first period 19 but fall in the seond period. The net effet of these hanges on parental utility is omplex. Note, however, that when savings are at a orner, the marginal value of urrent onsumption is higher than that of future onsumption so that the positive effet on parental welfare of rising urrent wages is given a higher weight. The impat of some poliy interventions, other than a marginal government ban, an be dedued from the results above. For example, imagine that a firm within a ountry deides not to employ hild labor or that output is partially exported and that an external ountry bans the import of goods produed with hild labor. These interventions learly have effets similar to those of a marginal ban. 20 An alternative way to attain effiieny would be for the government to subsidize human apital reation (whih in essene it does through massive publi support for eduation or through more sophistiated shemes suh as a food for eduation program suh as developed in Bangladesh). Suh a poliy ould be Pareto improving if paid for by a tax on adult earnings. 21 The state an also tax hild labor. Thus in Europe, family allowanes (and tax rebates) are given on the expliit ondition that hildren are not wage earners and regularly attend shool. 19 This is the effet stressed by Basu and Van (1998) in reahing the onlusion that parents benefit from a ban on hild labor. 20 Simple bans or trade restritions an be ountereffetive if they foster illegal and hidden forms of hild labor (suh as prostitution). In this respet, poliies based on inentives, instead of prohibitions, may be muh more effetive. 21 Beker and Murphy (1988) onjetured that ompulsory eduation in onjuntion with a soial seurity system might be Pareto improving when parents underinvest in their hildren beause soial norms are not strong enough for hildren to ompensate parents in old age. When the phenomenon of hild labor is ombined with human apital aumulation, proposition 7 shows that the general equilibrium effets of ompulsory eduation may be suh as to make it Pareto improving without the need for a ompensation sheme suh as the one proposed by them.

16 678 journal of politial eonomy VI. Conlusion In this paper we have developed two new arguments about why hild labor exists in equilibrium despite the fat that it may be soially ineffiient. Child labor is ineffiient when it is used by parents as a substitute for negative bequests (to transfer inome from hildren to parents) or, beause of apital market imperfetions, as a substitute for borrowing (to transfer inome from the future to the present). The ineffiieny annot be solved through intrafamily ontrating sine suh ontrating would be either not self-enforing or illegal. We investigated the role that a (small) ban on hild labor may play. Our demonstration that hild labor may be Pareto ineffiient raises the issue as to why it appears to be so diffiult to abolish hild labor in reality. As the disussion of the last setion made lear, there are a number of poliies that are potentially Pareto improving. In order to think about this question, it is neessary to extend our model to introdue heterogeneity of both firms and families. In this ase, while, for example, banning hild labor an potentially improve welfare (at least if the onditions of proposition 7 are satisfied), it may have distributional impats that may not be offsettable given the feasible set of fisal instruments. For example, some firms may benefit from hild labor and have (or have adopted) tehnology in whih human apital is not highly valued, whereas other firms would benefit signifiantly from a more eduated workfore. For a ban to be Pareto improving and thus unanimously supported, the first set of firms would have to be ompensated by taxing the seond set. Equally interesting, and in line with the analysis of Weiner (1991) for India, imagine a situation in whih there is inequality between families. Rih families do not send their hildren to work, whereas poor families do (this is an impliation of our model). In this ase a ban on hild labor affets the distribution of inome in the eonomy sine if the hildren of poor people beome more eduated as adults, the wage of the already eduated adult workers may be depressed. This generates losers from the eradiation of hild labor whom it may not be possible to ompensate through feasible fisal mehanisms. Referenes Basu, Kaushik, and Van, Pham Hoang. The Eonomis of Child Labor. A.E.R. 88 (June 1998): Beker, Gary S. A Theory of Soial Interations. J.P.E. 82 (November/ Deember 1974): A Treatise on the Family. Cambridge, Mass.: Harvard Univ. Press, Beker, Gary S., and Murphy, Kevin M. The Family and the State. J. Law and Eon. 31 (April 1988): 1 18.

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