Expectation Traps, Intergenerational Redistribution and Child Labor

Patrick M. Emerson Department of Economics

University of Colorado at Denver Denver, CO 80217

pemerson@carbon.cudenver.edu

Shawn D. Knabb Department of Economics

University of Colorado at Denver Denver, CO 80217

sknabb@carbon.cudenver.edu

September 2004

Abstract

This paper develops a dynamic model with overlapping generations and child labor, where there are two possible equilibria. There is a ‘good’ equilibrium with a high level of education and no child labor, and a ‘bad’ equilibrium with a low level of education and positive child labor. It is first shown that a government program of intergenerational transfers, such as social security, can eliminate the low schooling-child labor equilibrium by replicating a missing intergenerational contracts market. This government intervention is Pareto improving in a deterministic setting. The model then introduces uncertainty to the dynamic system, where it is shown that if society does not believe that the government will implement the transfer program, then in fact it won’t, thus fulfilling society’s expectations. This is true even if the government would have implemented the Pareto improving transfer program in the absence of uncertainty. This result implies that governments may be powerless to prevent the low education-child labor equilibrium if the government lacks credibility, thus leaving the country in an expectations trap. (JEL classification numbers: D91, E60, J20, O20) (Keywords: Expectation Traps; Uncertainty; Intergenerational Transfers; Child Labor) Acknowledgements: For valuable comments and insight we would like to thank Kaushik Basu, Henning Bohn, David Stifel, seminar participants at Cornell University and two anonymous referees of this journal. This paper has also benefited from presentations at the 2003 Latin American and Caribbean Economics Association Conference and the 2003 Western Economic Association International Conference.

1

Expectation Traps, Intergenerational Redistribution and Child Labor

I. Introduction

Child labor is widespread in the contemporary world. In fact, the International

Labor Organization estimates that 246 million of the world’s children aged 5 to 17, or 16

percent, are child laborers, most living in developing countries.1 Recently there has been

renewed interest in this topic among economists, which has led to a series of theoretical

studies with the aim of better understanding the causes and consequences of child labor in

order to help guide appropriate policy responses (see Gootaert and Kanbur (1995), Basu

(1999), and Basu and Tzannatos (2003) for useful literature surveys).

Typically, theoretical models designed to address the important policy issues

surrounding child labor posit that a family’s decision to send a child to the labor market is

taken only as a last resort in order to escape the dire consequences of poverty (e.g. Basu

and Van, 1998). Baland and Robinson (2000) show that this response on the part of the

family may be stronger in a dynamic setting because contracts between children and

adults are not self-enforcing, and capital markets are incomplete.2 In this case, an adult

decision maker may not only send their children to work to escape poverty in the present,

but do so to escape poverty in the future as well. This decision will hinder a child’s

ability to accumulate human capital and can lead to persistent cycles of poverty and child

labor across generations.3

1 ILO (2002). Child labor was also common in developed countries until fairly recently, see, e.g., Kruse and Mahony (2000). 2Other dynamic models studying child labor are Emerson and Souza (2003); Bell and Gersbach (2001); Lopez-Calva and Myiamoto (2004); Ranjan (2001); Hazan and Burdugo (2002); Jafarey and Lahiri (2002). 3 See Emerson and Souza (2003) and Wahba (2002) for the empirical support of child labor persistence.

2

This paper begins by showing that a benevolent government can address the

incidence of child labor that results from the non-enforceability of intergenerational

contracts and incomplete capital markets through the appropriate use of fiscal policy, and

that this policy is Pareto improving in a deterministic environment. It is then shown that

once uncertainty is introduced to the economy, this same fiscal policy may be rendered

ineffective. In other words, if households don’t believe that the government will follow

through on their policy promise, then in fact, it is quite possible that the government will

not be able to follow through on their promise as a result of these beliefs.4 This self-

fulfilling nature of fiscal policy in the presence of uncertainty can leave a country in an

expectations trap with a low level of human capital and child labor.5

To formally demonstrate this argument, we employ a three period overlapping

generations model in which child labor exists. This stylized setup will keep the dynamics

manageable and allow us to highlight the effects of uncertainty. Also, within this

framework we introduce a missing intergenerational contracts market, in conjunction

with a temporary increasing return to scale human capital production function, which

gives rise to two locally stable steady states. There is a ‘bad’ equilibrium where there is a

relatively low level of parental human capital, which results in a low level of income and

positive child labor (a poverty trap), and there is a ‘good’ equilibrium where there is a

4Rodrik (1989) uses a similar line of reasoning to demonstrate that expectations can affect the optimal design of trade policy reforms. As in the current paper, he interprets uncertainty in the context of an informational asymmetry between households and the government. In another related paper, Rodrik (1991) demonstrates that uncertainty can also affect (international) capital flows using a partial equilibrium model of investment in a developing country context. 5 It is important to distinguish the arguments made in this paper form those made in the time-consistency literature established by Kydland and Prescott (1977), Calvo (1978), and Fischer (1980). We argue that it is the perception of uncertainty by households that potentially renders a Pareto improving policy ineffective in a time-consistent framework. In other words, the government’s optimal decision rule is independent of time in our current setup but now depends on the households’ perception of the government’s willingness or ability to implement the program.

3

relatively high level of parental human capital, which results in a high level of income

and no child labor.

It is then shown that a benevolent government can replicate the missing

intergenerational contracts market with a pay-as-you-go social security program, thereby

eliminating this component of child labor in a deterministic environment. In addition, it

is also shown that this policy is Pareto improving in the sense that all generations are

strictly better off under this policy, except the initial old who are no worse off. The

reason why this policy is Pareto improving is because future generations benefit from a

human capital externality that is self-sustaining, as long as the human capital benefits are

greater than the implicit cost of maintaining the pay-as-you-go social security program.

The dynamics of this social security program are intuitive: if child labor is one

possible mechanism adults can use to redistribute resources from their children, then the

government can reduce this incentive by announcing a social security program that will

begin during the current adults’ old age (an institutional intergenerational contract). This

policy results in an increase in lifetime wealth for the initial generation because they

receive the social security transfer during their old age, but do not pay into the system

during their current working years. Thus, the adults of this initial generation will no

longer need to use their children’s labor to supplement current consumption and savings

for future consumption because of this increase in lifetime wealth. The subsequent

reduction in child labor that results from this increase in lifetime wealth increases the

child’s education, which in turn increases the child’s human capital, potentially setting

off a chain of events that allows the household and/or country to escape from poverty.

4

Therefore, the government can eliminate the ‘bad’ equilibrium, or poverty trap, through

the appropriate use of fiscal policy.6

The success of this intergenerational redistribution program, however, rests

critically on its ability to change people’s behavior in anticipation of this policy. In

developing countries, where there may be a high degree of uncertainty surrounding the

stability and intentions of the government, the deterministic results above may not carry

over to a more realistic setting that takes this type of uncertainty into account.7 To

formally demonstrate this possibility we add a specific form of uncertainty to the model

that is the result of asymmetric information between the households and the government,

which is similar to the approach taken by Engel and Kletzer (1991), and Rodrik (1991,

1989). Consider the following motivational scenario. The public believes there are two

possible government types. The first type is a benevolent government with a Rawlsian

social welfare function that assigns an equal weight to each generation. By assumption,

this government is in power, or is the ‘true’ government type. This government type will

implement the program or policy as long as it does not reduce the welfare of any

generation, that is, the policy is Pareto improving. The second type is a ‘false’

government that is not in power. The public believes that this government type will keep

the tax revenue for itself. Therefore, households do not expect to receive the social

security transfer during their retirement in this counterfactual case. Based on these

6 The idea that an intergenerational transfer program, along with the regulation of the child labor market (mandatory schooling or the banning of child labor), may be Pareto improving is informally discussed in Becker and Murphy (1988) and formalized in Hazan and Berdugo (2002). We show that the regulation requirement is unnecessary with an appropriately designed intergenerational transfer program in a deterministic environment. Bell and Gersbach (2001) also study redistribution policy, but in their case they examine an iterative series of within-generation transfers through time. 7 Even in more stable democratic countries uncertainty necessarily exists over long-term policies and programs due to the regularly changing leadership of the government. The United States and its Social Security program is a perfect example.

5

perceived government types households optimally choose current consumption, savings,

and child labor (human capital) based on the expected value of the social security transfer

from the government.

These subjective beliefs might arise because a new reformist government has

been installed but a portion of the population do not believe or trust that it is indeed

committed to reforms. Another possibility is that the uncertainty is purely extrinsic and

unrelated to the current fundamentals of the economy (see e.g. Azariadis, 1981; Cass and

Shell, 1983; and Farmer, 1999). Regardless of the interpretation, this paper demonstrates

that there exists a minimum level of confidence in government that is necessary for the

Pareto improving social security program to be successful. If the level of confidence is

below this minimum, then a benevolent government will not be able to implement the

Pareto improving policy, although it would have in a deterministic environment or if

households had more confidence in their government. It is in this sense that the model

generates an endogenous expectations trap that is inherently self-fulfilling in nature.8 In

other words, the households’ subjective beliefs, in addition to the initial level of parental

human capital, serve as the equilibrium selection mechanism.

The rest of the paper is as follows: Section II presents the benchmark model of

child labor. Section III demonstrates that a pay-as-you-go social security program can

eliminate the ‘bad’ equilibrium with child labor under certain conditions. Section IV

adds uncertainty to the model and demonstrates the existence of a minimum level of

confidence in government, which is sufficient to render the government’s transfer

program ineffective fulfilling the households’ pessimistic expectations. Section V

8Typically, expectation traps are discussed in the context of monetary economies. For monetary applications see Albanesi, et al. (2003), Chari, et al. (1998), and Weil (1987). Also see Cole and Kehoe (2000) for an application to sovereign debt.

6

describes our interpretation of uncertainty in greater detail and places our modeling

strategy in the existing literature. This section also discusses possible extensions to the

paper. Finally section VI concludes with a summary.

II. The Basic Model

The model consists of an infinite sequence of identical overlapping generations

living for three periods, where a household is defined as one child and one working age

adult. The last period of life is spent outside the household, thus the working age adults

have no filial responsibility to their elders.9 The population is constant and each

generation is normalized to unity. These simplifying demographic assumptions allow us

to concentrate on the key issue of the paper: the dynamic interaction between education,

child labor, government policy, and government credibility. Also imperfect capital

markets make it impossible for the adult to borrow against their child’s future earnings

and any future redistribution from the government.

In the first period of life the child receives an education and may work in the labor

market. If the child participates in the labor market he or she earns an adult equivalent

[ ]1,0∈a for physical labor only. Thus, a child is endowed with no human capital. The

decision to educate the child, [ ]1,0∈e , or have the child participate in the labor market,

( )e−1 , is made by the child’s parent. In the second period of life, the adult supplies

human capital h and one unit of physical labor to the labor market, has one child, and

9 This problem may be overcome if there exists a sufficient degree of reverse altruism or some sort of social norm of filial obligation on the part of the children, see, e.g., Lopez-Calva and Myiamoto (2004), although allowing some reverse altruism would not change our main results.

7

saves for retirement. Finally in the last period of life the adult consumes his or her

savings plus interest, where the gross return is 1>R .10

The representative adult of generation 1−t maximizes household utility,

(1) ( ) 1312111 lnlnln,, ++++ ++= tRt

Wtt

Rt

Wt hcchccU ααα ,

subject to the following constraints:

(2) ( ) ( )tttWt eahsc −++=+ 11

(3) tRt Rsc =+1

(4) ( ) ttt ehHh =+1 .

The parameters ( ) 3,2,1,1,0 =∈ iiα assign different weights to consumption utility

during the working years, Wtc , consumption utility during old age, R

tc 1+ , and the utility the

parent derives from the child’s human capital, 1+th . This form of paternalistic altruism

implies that the parent cares about the child’s potential for success.11,12 We also impose

the restriction 1321 =++ ααα on the preference parameters. The last constraint facing

the household is the education technology. 13

The solution provides us with the following optimal linear expenditure system:

(5) [ ]ahc tWt ++= 11α

10 Savings in our model does not necessarily include (or exclude) financial assets in the form of stocks and bonds. In developing countries with weak, or possibly absent financial markets, savings will more than likely take on different forms. As an example, a father maintains his family land holdings by investing his and his child’s time, and then promises to bequeath this land to his son in exchange for income during retirement. 11 The paternalistic form altruism appears to have more empirical support than the non-paternalistic form, see Altonji, et al. (1997, 1992). This is the same form of altruism implicitly employed in Baland and Robinson (2000) since they restrict their analysis to a single generation. 12 This paternalistic specification of the utility function is similar to that of Galor and Zeira (1993), but instead of measuring parental utility as a function of bequests we measure parental utility as a function of the child’s human capital. Galor and Weil (1996) and Glomm (1997) employ similar modeling strstegies. 13 These constraints are consistent with either a linear technology (Hansson and Stuart, 1989; Baland and Robinson, 2000) or a small open economy framework.

8

(6) [ ]ahRc tRt ++=+ 121 α

(7) [ ]aha

e tt ++= 13α.

A household allocates a proportional amount of total potential income, aht ++1 , to

consumption in both periods of life, and the child’s education. In particular, equation (7)

demonstrates that there is a positive relationship between the child’s time spent receiving

an education and parental human capital. This implies that children in poorer households

will spend more time in the labor market.

The child’s time spent receiving an education, described in equation (7), and the

education technology, described in equation (4), combine to determine the dynamic

behavior of human capital across generations:

(8) ( ) ( )

aahhH

h ttt

++=+

131

α.

For analytical purposes, we assume ( )thH takes the form of a threshold step-function:

(9) ( )⎪⎩

⎪⎨⎧

≥

<=

η

η

t

tt hiffA

hiffhH

1

This non-linearity captures any potential differences in the education technology for

various levels of parental human capital, see Azariadis and Drazen (1990), and is

responsible for the existence of a Pareto improving policy, which we discuss shortly.

This exact specification is not necessary – any human capital function that generates an s-

shaped curve (i.e. that intersects the 45 degree line twice) will produce the same

relationship. In fact, simple convexity could also generate multiple equilibra since we

9

have a defined upper bound.14 In any case, the non-linearity in the return to education

appears to be empirically well founded (see, e.g., Hungerford and Salon, 1987; Moretti,

2004).

Combining the threshold function (9) and the dynamic human capital

accumulation function (8) results in the following first order difference equation on

opposite sides of the threshold η :

(10)

( )

( )⎪⎪⎩

⎪⎪⎨

⎧

≥++

<++

=+

tanyforhiffha

Aa

aA

tallforhiffhaa

a

h

tt

tt

t

ηαα

ηαα

33

33

1 1

1

.

The steady states for these equilibrium paths are:

(11)

( )

⎪⎩

⎪⎨

⎧

≥=

<−+

==

tanyforhiffAh

tallforhiffa

ah

h

tH

tT

η

ηα

α

3

3 1

.

To impose stability on the low equilibrium and generate positive child labor ( )1,0∈Te we

assume ( ) 33 1 αα −<+ aa , which also implies that a<3α . To ensure that child labor is

zero in the high-income equilibrium, 1=He via equation (4), we assume aA >3α .

These dynamics properties are shown in Figure 1. For the case where initial parental

human capital is below the threshold value, η<0h , the economy converges to the low

human capital equilibrium Th since 13 <aα . For the case where initial human capital is

above or equal to the threshold value, η≥0h , the economy converges to the high human

capital equilibrium AhH = . This follows from the assumption 13 >aAα , which implies

divergence, and the fact that human capital is bounded from above at 1>A . An economy

14 We thank Kaushik Basu for pointing out this alternative interpretation.

10

that follows this human capital trajectory will reach the upper bound in finite time and

remain there in perpetuity. The (dark) horizontal line in figure 1 at the value A represents

the continual mapping back to this upper bound once it is reached.

Based on these dynamics, along with the following assumption pertaining to the

location of the threshold,

Assumption 2.1: The threshold value lies in the interval [ ]HT hh ,∈η ,

we have two important propositions in our stylized economy without government.

Proposition 2.1: A country with an initial level of parental human capital below the

threshold value η monotonically converges to the low human capital equilibrium Th . A

country with an initial level of human capital above or equal to the threshold value η

monotonically converges to the high human capital equilibrium Hh .15

This proposition demonstrates that an initially poor country will remain poor and an

initially wealthy country will remain wealthy in our stylized economy.

Proposition 2.2: A country with an initial level of parental human capital below the

threshold value monotonically converges to the positive child labor equilibrium. A

country with an initial level of human capital above or equal to the threshold value η

monotonically converges to the no child labor equilibrium.

15 The formal proofs for all the propositions in the paper are in the appendix.

11

This proposition demonstrates that child labor will persist if parental human capital is too

low and will disappear over time if parental human capital is sufficiently high. Also note

that these dynamics do not depend on the standard under-investment in education

argument or coordination failure that typically relies on increasing social returns alone.

Poor households may fully internalize the human capital externality, but the missing

capital market and poverty causes them to optimally choose a lower level of education for

their children with positive child labor.

III. The Model with Government Intergenerational Transfers

Given that there are two possible steady states and dynamic paths an economy can

follow, the question then becomes: what, if anything, can the government do to move a

country trapped in poverty, with child labor, out of this trap? This section demonstrates

that a government can announce a social security program that will begin transferring

resources from next period’s working generation to next period’s retirees (or old), the

current workers.16 This announcement reduces the current working generation’s need to

save for retirement (e.g. Feldstein, 1974) by replicating the missing intergenerational

contracts market, thus freeing up lifetime resources for current consumption and the

child’s education. If this increase in lifetime wealth is large enough, the social security

program can generate a critical mass of human capital that allows the economy to escape

from the poverty trap.

16 There are many other policy mechanisms that could accomplish this same redistribution across generations, such as issuing vouchers (pieces of paper) to the current working generation redeemable next period, or announcing the future issuance of debt to redistribute resources next period. We focus on social security for expositional reasons and because it replicates any other lump-sum intergenerational transfer scheme in our current deterministic environment.

12

3.1. Escaping the Poverty Trap

The only role for government in our stylized economy is to introduce and manage

the social security program using lump-sum transfers and taxes to operate the system.

Thus, we abstract from government purchases and operation costs. We also assume that

at time 0=T the benevolent government announces a plan to start the pay-as-you-go

social security program next period and that the country of interest starts in the low

income-child labor steady state of Th . The representative household maximizes the same

utility function (1) subject to the following modified household budget constraints, which

include working period taxes tT along with social security transfers 1+tTR :

(2’) ( ) ( ) ttttWt Teahsc −−++=+ 11

(3’) 11 ++ += ttRt TRRsc

This results in an optimal linear expenditure system that includes intergenerational

redistribution:

(5’) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+++= +

tt

tWt T

RTR

ahc 11 1α

(6’) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+++= +

+ tt

tRt T

RTR

ahRc 121 1α

(7’) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+++= +

tt

tt TR

TRah

ae 13 1

α.

The only difference between this system of equations, and the system of equations

without the government, is that the household now allocates any net resources (or net

losses) the program generates toward consumption and the child’s education.

The human capital dynamics are also similar, with the following modifications.

13

(10’)

⎪⎪⎩

⎪⎪⎨

⎧

≥+⎥⎦⎤

⎢⎣⎡ −+

<+⎥⎦⎤

⎢⎣⎡ −+

=+

tanyforhiffha

ATR

Rra

aA

tallforhiffha

TRRra

ah

tt

tt

t

ηαα

ηαα

33

33

1

1

1.

The steady states for these equilibrium paths are:

(11’) ⎪⎩

⎪⎨

⎧

≥=

<⎥⎦⎤

⎢⎣⎡ −+

−=

=

tanyforhiffAh

tallforhiffTRRra

ah

h

tH

tT

η

ηα

α1

3

3

.

Equations (10’) and (11’) assume the tax and transfer program is constant across

generations, TTR = . We will justify this constant tax and transfer assumption shortly.

Also, the parameter 1−= Rr defines the net return on savings.

Before determining the size of the transfer necessary to move the economy out

poverty and to achieve the critical mass of human capital ( ) η=TRh1 , we must first

formally define the threshold value.

Assumption 3.1: Let the threshold value equal a weighted average of the two steady

states, ( ) HT hh θθη −+= 1 , where [ ]1,0∈θ .

Using this threshold value we have the following proposition.

Proposition 3.1: There exists an intergenerational transfer ∗TR sufficient to induce the

current working generation to invest enough resources in their child’s education to reach

the threshold value η using the pay-as-you-go social security program.

14

More formally, we can see this result by looking at the education choice made by

the initial generation benefiting from the government transfer program:

(12) ( ) ( )TR

Raaa

TRh

Th

3

3

31

1 αα

α+⎥

⎦

⎤⎢⎣

⎡−+

=43421

.

This equation shows that when 0=TR human capital is mapped directly back to the low

income-child labor equilibrium, and if 0>TR , this increases the child’s education and

human capital. If the promise of a social security transfer to the current working

generation is large enough to increase the child’s human capital, so that ( ) η=TRh1 , the

country can escape from poverty as shown in Figure 2.

To find the necessary size of the transfer we equate equation (12) with the

threshold defined in assumption 3.1, ( ) HT hh θθη −+= 1 , and solve for TR :

(13) ( )( )TH hhRaTR −−=∗ θα

13

.

The size of the necessary transfer is increasing in the productivity of the child, the less

weight a parent assigns to the child’s human capital, the closer the threshold value is to

the high income - no child labor steady state (the closer θ is to zero), and the interest

differential between private savings and the social security program (the return from

social security is zero because the population is constant).

3.2. Feasibility of the Social Security Program (Deterministic Case)

When can a government implement such a program? To answer this question we

consider the case where the government behaves benevolently towards its population and

uses the following policy or decision rule, which is consistent with a Rawlsian social

welfare function with an equal weight assigned to each generation.

15

The Government’s Policy Rule: (i) Choose the minimum intergenerational transfer

necessary to reach the threshold value η . (ii) Implement and maintain the

intergenerational transfer program only if no generation is made strictly worse off.

The first part of this policy rule supposes that the government chooses the

minimum intergenerational transfer necessary to reach the threshold value. This is

consistent with the benevolence assumption. A larger transfer would reduce lifetime

consumption for future generations, relative to what it could have been, because the net

return to savings 01 >−= Rr is greater than the net return from the social security

system under our constant population assumption. Also from equation (10’) and (11’) we

can see that anything smaller will eventually return the household to a lower level of

human capital and income in the poverty equilibrium due to the lower return on social

security. Thus, part (i) of the government’s policy rule determines a unique transfer ∗TR

defined in equation (13) and proposition 3.1. The second part of the policy rule (ii)

implies that the government will only implement the program if no generation is made

strictly worse off, consistent with our Rawlsian social welfare function assumption.

To determine the feasibility of a program under this policy rule we can look at

each generation sequentially. Obviously the initial generation is strictly better off since it

receives only transfers. The first generation to actually pay taxes, 1T , is next period’s

working generation. This generation also benefits from the program in two ways: First

they receive transfers during their retirement years offsetting some of the tax burden.

Second, they receive more education and a higher level of human capital, increasing their

16

earnings during their working years. The problem here is that this generation does not

benefit from the human capital externality. Finally, since all future generations benefit

from the human capital externality and face the same tax burden under the above policy

rule, the transfer program is feasible for all future generations if it is feasible for next

period’s working generation (formalized shortly). Thus, we can use next period’s

working generation as a benchmark to determine whether or not the program is feasible.

To determine whether the program’s benefits outweigh the costs for next period’s

working generation we look at the household’s savings decision,

(14) ( ) ( )( )( )

( )4434421

444 3444 21

TRgTRz

TRR

raTRhTRs ⎟

⎠⎞

⎜⎝⎛ +

−++= 2121

11

αα ,

where ( )TRh1 is defined in equation (12). The first part of this savings equation, ( )TRz ,

demonstrates that the transfer program increases human capital and the earnings capacity

for this generation (the benefit), and is shown in Figure 3. The second part of the savings

equation reduces savings because lifetime income falls by ( )TRRr , which is shown as

( )TRg in Figure 3. The trade-off between these two effects provides us with a sufficient

condition, which is observable by the government, and determines whether or not the

program is feasible.

Proposition 3.2: There exists a positive range of government transfers

[ ]max,0 TRTTR ∈= ∗∗ where the pay-as-you-go social security program is feasible under

the defined policy rule. This feasible range has a finite upper bound that equals

( )( ) 322

2max 1

1ααα

α−+

++=

raahRaTR T , which satisfies the sufficient condition 0)( max1 =TRs .

17

If maxTRTR >∗ the government does not implement the program. If maxTRTR ≤∗ then the

program is feasible and the government implements the program.

We now generalize this result and formally argue that if the policy is feasible for

next period’s working generation it is feasible for all future generations as well. This

implies that if maxTRTR ≤∗ the intergenerational transfer program can generate a Pareto

superior outcome in a deterministic environment.

Proposition 3.3: If the social security program is feasible, then the current working

generation and next period’s working generation are strictly better off under the pay-as-

you-go social security program. This implies that all future generations are strictly better

off as well. Thus, the social security program is Pareto superior to the no program

equilibrium and dynamics.

This result holds because human capital and earnings capacity are higher for all future

generations relative to next period’s working generation. Recall that future generations

also benefit directly from the externality in the education technology.

3.3. A Child’s Human Capital and Parental Savings: A Graphical Approach

Before turning to the issue of government credibility in an uncertain environment

we first translate our model into the following graphical representation. This approach

simplifies the analysis in the next section. The first order conditions from the household’s

optimization problem, with respect to savings ts and education te , are as follows:

18

(15) ( ) TRRsR

seahT +=

−−++ 0

2

00

1

11αα

(16) ( ) 0

3

00

1

11 eseaha

T

αα=

−−++.

Equation (15) equates the marginal utility loss from an increase in savings (decrease in

first period consumption) to the marginal utility gain from an increase in savings

(increase in consumption next period). Equation (15) also shows how an increase in

transfers reduces the marginal gain in utility from an additional unit of savings. This

reduces the household’s desire to save, freeing up resources for current consumption and

the child’s education. Equation (16) equates the marginal loss in utility from an increase

in the child’s education with the direct marginal benefit of more human capital.

After eliminating 0e from (15) using (16) we have:

(17) ( )

( ) ( )4342144 344 21

TRsfsg

T TRRsR

sah;

0

2

0

2

00

11

+=

−++− αα .

Figure 4 shows ( )0sg is an upward sloping function of the initial working generation’s

savings and ( )TRsf ;0 is a downward sloping function of the initial generation’s savings

for a given level of social security transfers. If 0=TR , the solution is identical to the no

government case where ( )ahs T ++= 120 α . Using equation (16), after solving for 0e as a

function of 0s , we can determine the level of human capital accumulation for next

period’s working generation following the announcement of the social security program.

If the government chooses an initial transfer of ∗TR savings will fall, as shown in

equation (17). This decrease in savings in response to ∗TR increases the human capital of

19

next period’s working generation so that ( ) η=∗TRh1 placing the economy in the high

income - no child labor equilibrium’s basin of attraction.

IV. Credibility and the Effectiveness of Government Policy

If this type of intergenerational redistribution program is feasible and can lead to a

Pareto superior outcome, then why don’t we observe its implementation around the world

in developing countries? One possible answer is that governments lack credibility. If

today’s working generation does not believe that the government will follow through on

this transfer program their response will be different than it would have been in a

deterministic environment. In other words, it is the perception of a dynamic policy that

alters an individual’s behavior not the policy itself. For our specific example, it is shown

that the mere perception of uncertainty, or lack of government credibility, can render the

Pareto improving government transfer program infeasible leaving the country in an

expectations trap that is self-fulfilling in nature.

4.1 Adding Uncertainty to the Stylized Economy

We assume the only generation uncertain about the implementation of the social

security program is the current working generation. If the government implements the

program, the policy continues forever under the government’s policy rule. If the program

is not feasible because of society’s shared expectations that the program is unlikely to be

implemented, then the government does not implement the program, thus, fulfilling the

households’ pessimistic expectations. In this case, the policy will never be implemented.

Society therefore learns whether or not the government will implement the program.

20

To demonstrate the potentially self-fulfilling nature of this transfer program, or

perhaps more appropriately the success of the program, we consider the following

modified problem that incorporates the household’s subjective beliefs. The household’s

objective function now takes the following form:

(1’) ( ) 1310201110 lnlnln,,~ hcEchccU RWRW ααα ++=

All of the parameters in the utility function are the same as in equation (1) except for the

addition of the expectations operator 0E . Households in the initial working generation

now form expectations over whether or not they believe the government will follow

through on their promise to implement the social security program. There are two

perceived possible states of nature. Households believe that the government will either

implement the program with probability q or will not implement the program with

probability q−1 . We summarize the households’ subjective probability distribution in

the following equation.

(18) ⎪⎩

⎪⎨⎧

=−

==

dimplementenotpolicyiifq

dimplementepolicyiifqi

1)(0π

We define the value [ ]1,0∈q as the level of confidence society has in its government. As

q gets smaller society has less faith in their government.

Since our model assumes that the government in power is benevolent and would

implement the Pareto improving social security program in a deterministic environment

we interpret uncertainty as follows. Households believe there are two possible

government types: The first type of government is the ‘true’ government, which is

currently in power, but households believe this government is power with probability q .

21

The second type of government is a ‘false’ government that will keep the tax revenue for

itself. Households believe this government type is in power with probability q−1 . It is

important to note that these are perceived probabilities not actual probabilities because

the benevolent government is already in power. Thus, implicit in the model’s

construction is an informational asymmetry between the government and the households.

Given that households believe there is a positive probability that the government

will not implement the program, the next step is to demonstrate that these beliefs can in

fact become self-fulfilling. To formally demonstrate this result we use the first order

conditions for savings and education, respectively, in the presence of uncertainty:

(19) ( )( )

0

2

0

2

00

1 111 s

qTRRsqR

seahT

−+

+=

−−++ααα

(20) ( ) 0

3

0

1

11 eseaha

T

αα=

−−++.

Note that equation (20) is identical to equation (16), and equation (19) is identical to

equation (15), if the household believes the government will implement the program with

certainty, 1=q . Also, when 0=q , equation (19) captures the deterministic case without

transfers. This demonstrates that when society does not believe their government at all,

the outcome is the same as having no policy at all. These two extreme cases nest all other

possible scenarios, where ( )1,0∈q .

We once again we represent this dynamic system graphically in Figure 5.

(21) ( )

( )

( )

( )444 3444 2144 344 21

qTRsfsg

T sq

TRRsqR

sah,,

0

2

0

2

0

2

010

11

1 −+

+=

−++− ααα

(22) ( )( ) ( ) 0

2

3

2

3001 11

1)( s

aaah

seh T

αα

αα

−−

−++

==

22

The left-hand side of equation (21) is identical to equation (17), where ( )0sg is an

upward sloping function of savings. The right-hand side nests the two cases discussed

above. First, when 0=q government policy is completely ineffective regardless of the

size of the social security transfer payment and we have ( )0,,01∗TRsf . Second, under

certainty when 1=q , the necessary transfer ∗TR is sufficient to reach the threshold value

η by assumption. This deterministic transfer scheme also pins down the savings ∗0s

necessary to achieve the critical mass of education and the child’s human capital via (22).

Graphically, this case is represented by ( )1,,01∗∗ TRsf .

From the lower figure in Figure 5 we see that for ( )0,,01∗TRsf the human capital

accumulation equation maps directly back to the low income - child labor steady state.

For the case when ( )1,,01∗∗ TRsf , the country crosses the threshold η and falls into the

high income - no child labor equilibrium’s basin of attraction and converges to Hh . In

Figure 5 we also show an intermediate case when the probability ( )1,0∈q . In this case,

the level of confidence society has in their government is not complete and shows how

the size of the transfer ∗> TRTR A must increase as q falls to reach the threshold. This

discussion yields the following proposition:

Proposition 4.1: There exists a minimum level of confidence in government minq where

the pay-as-you-go social security program is no longer feasible if minqq < .

23

We demonstrate this argument graphically in Figure 6. From equation (21) we know

that as the level of confidence in the government falls, the necessary size of the transfer

increases at an increasing rate, and approaches infinity as the level of confidence

approaches zero. From proposition 3.2 we know there exists a finite maximum transfer,

maxTR . This implies that there exists a minimum level of confidence, minq , at which

point the necessary size of the transfer is just feasible, or maxTRTR N = . Below minq the

policy is no longer feasible under the policy rule. We can also see this result implicitly in

Figure 5. As q gets smaller, ( )qTRsf ,,01∗∗ moves closer to ( )0,,01

∗TRsf , which implies

that transfers must increase by larger and larger amounts to reach the critical mass of

education that allows the child’s human capital to reach η .

Proposition 4.1 formally demonstrates the main point of the paper. If society’s

level of confidence in their government is so low that they do not believe that their

government will implement the social security program the benevolent government does

not implement the program. This is true even if the government could have, and would

have, implemented the program if q were greater than minq . In other words, even if the

social security program is feasible in a Pareto sense and the government policy could

eliminate the ‘bad’ equilibrium or poverty trap in the deterministic environment, it is no

longer feasible when minqq < . This formally defines what we refer to as an expectations

trap. The mere fact that households do not believe that their government will follow

through on the policy promise is sufficient to ensure that the government does not follow

through on the policy promise, thus fulfilling the households’ pessimistic expectations.

This suggests that the households’ subjective beliefs can also serve as an equilibrium

selection mechanism in the presence of uncertainty in a dynamic environment.

24

4.2 Empirical Evidence

The empirical evidence of the effectiveness of transfer programs in reducing child

labor and increasing schooling is still being received, but early studies suggest that these

programs are less effective at reducing child labor than they are at increasing schooling.

Unconditional cash transfer programs have been found to have relatively small marginal

effects on both child labor and school enrollment (e.g. Behrman and Knowles, 1999;

Nielsen, 1998). This could be the result of uncertainty surrounding future transfers. If the

adult of the household perceives this as a temporary transfer the permanent income

hypothesis comes into play. Ravallion and Wodon (2000) find that a food-for-education

program in Bangladesh did indeed increase schooling among the participants, but the

concomitant reduction in child labor was quite small. Bourguignon, et al. (2002), in their

study of the Bolsa Escola educational subsidy program in Brazil, find similar results.

Skoufias and Parker (2001), however, find that the conditional transfer program,

PROGRESA, in Mexico showed significant effects on both school enrollment and child

labor. In this case perhaps the transfer programs were perceived as permanent and the

household responded accordingly.

Although the policies above are not identical in practice, the general idea carries

through. Even if countries implement identical policies, these programs may succeed in

some countries and fail in others as a result of government credibility. For policy design

this implies that only after the transfer program is implemented in a particular country

will we be able to determine whether or not the program is successful. Ex-ante analysis

from past policy successes or failures in different countries may not be appropriate for

determining a policy’s effectiveness for a particular country of interest.

25

V. Interpreting Uncertainty and Extensions

The expectations trap argument demonstrates that policy design and analysis for a

deterministic environment may be misleading if government’s lack credibility. By

assuming households form expectations over the future of the government’s policies, we

have demonstrated that these expectations can actually cause a Pareto improving policy

to fail, even if the government intends to follow through on their promises. This implies

that uncertainty can remove Pareto improving polices from a benevolent government’s

choice set. If the government is not truly benevolent then this can only exacerbate the

problem.

The key to this argument is that if households have a shared expectation that the

government will not follow through on their policy promise, that is, the government lacks

credibility, then households undertake actions that render the policy infeasible. In other

words, the mere fact that households do not believe that the government will implement

the Pareto improving policy with certainty can eliminate this policy from the benevolent

government’s choice set, thus fulfilling the households’ pessimistic subjective beliefs.

This modeling strategy, where subjective beliefs and expectations can in fact be

self-fulfilling, has been employed in a vast and diverse literature (see, e.g., early papers

by Azariadis,1981; and Cass and Shell, 1983; and more recent papers by Weil, 1987; and

Cole and Kehoe, 2000). In development, this strategy has similarly been used by Engel

and Kletzer (1991) and Rodrik (1989, 1991). Although these development papers do not

address the existence of a self-fulfilling expectations trap and the elimination of Pareto

26

improving policies from a benevolent government’s choice set as a result of society’s

subjective beliefs, the basic modeling of perceived uncertainty is the same.

One question remains: can an objective probability distribution develop over the

government’s type? This is another possible interpretation not highlighted in the current

paper.17 Suppose there are two competing factions within an incoming government: a

benevolent government faction with a Rawlsian social welfare function and a selfish

government faction that plans to keep any tax revenue for itself. The ex-ante (and known)

probability distribution is such that the benevolent faction of the government takes

control of policy with probability q and the selfish faction of the government takes

control of policy with probability q−1 . Next, suppose that the benevolent government

takes control of policy design and that this result is unobservable to the households in the

private sector. As a result of this asymmetric information, the perception of uncertainty

remains (the government type is no longer random). Ex-post, households still perceive

that the benevolent government (the “true” government) is in power with probability q ,

and that the selfish government (the “false” government) is in power with probability

q−1 .18 Although we do not formally use a game theoretic setting, given the objective of

the paper, we can still think of “nature” as selecting the type of government from the

following ex-ante objective probability distribution { }qq −1, .

However uncertainty is motivated, it is natural to wonder whether the benevolent

government can signal its type. Given the heterogeneous nature of the problem

(overlapping generations), we can no longer simply assume that the social welfare

17 Here the appropriate ex-ante interpretation is risk rather than uncertainty (by definition uncertainty implies that the agent’s beliefs are subjective). 18 This modeling strategy dates back to Harsanyi (1967).

27

function coincides with a representative agent’s utility function since the agents in this

type of stylized economy are alive at different points in time. Therefore, as already

mentioned, we motivate the government’s optimal behavior with a Rawlsian social

welfare function where each generation receives an equal weight. This implies that costly

policy signals will not be implemented by the benevolent government. In other words, if

any generation is made worse off by a particular “policy signal” that can identify the true

government type, then this policy signal is not available to the government. Thus, the

only type of policy signal that the benevolent government could possibly send would

have to be Pareto improving itself. In addition, if this policy has a dynamic component,

not only does the policy signal have to be Pareto improving for all generations, but it

must be immediate in nature. Whether or not a policy signal of this type exists is an

important question, but beyond the scope of this paper and is left for future research.

VI. Conclusion

This paper develops a model of child labor in a dynamic, general equilibrium,

setting. It is shown that lack of access to capital markets gives rise to a Pareto inferior

outcome that is characterized by the presence of child labor and a low level of human

capital. When a pay-as-you-go social security program is introduced in a deterministic

environment, it is shown that this type of intergenerational transfer program can move the

economy out of this inferior equilibrium by allowing families to redirect household

income, they would otherwise have saved for old age or consumed in the current period,

towards the education of their children.

28

It is also shown that the effectiveness of the intergenerational transfer program

relies critically on its ability to change the behavior of households through their

expectations. If there is uncertainty surrounding the government’s intention to follow

through on the program, we demonstrate that households may not change their behavior

sufficiently to move the economy from the ‘bad’ equilibrium with child labor to the

Pareto superior or ‘good’ equilibrium with no child labor leaving the country in an

expectations trap. This demonstrates that confidence in, and the trust of the government

is potentially a key element in effective policy design.

29

Appendix: proofs

Proof of Proposition 2.1: Using the parameter restriction ( ) 33 1 αα −<+ aa , which implies a<3α , along with equation

(10) produces a monotone sequence { }∞=0iih converging to low equilibrium Th . Using the

parameter restriction aA >3α implies 13 >a

Aα. Combining this result along with equation

(10) produces a monotone sequence { }∞=0iih converging to AhH = and 1=He via equation (4), the upper bound. ■ Proof of Proposition 2.2:

The parameter restriction ( ) 33 1 αα −<+ aa implies a

a+

<23α . This last condition implies

that ( )

11

3

3 <−+

=α

αa

aeT and 01 >− Te , positive child labor, in the low human capital steady

state. The restriction aA >3α implies that 1=He given AhH = in the high human capital steady state. The dynamics follow directly from proposition 2.1. ■ Proof of Proposition 3.1: By (A3.1) and equation (12) the government chooses the unique transfer that satisfies

η=)(1 TRh . Existence follows directly from (12) given that η is a constant and greater than zero by assumption, and ( ) 01 >′ TRh with ( ) 001 >h . ■ Proof of Proposition 3.2: Next period’s working generation, the first generation to pay taxes, savings equation is

( ) ( )( ) TRR

raTRhTRs ⎟

⎠⎞

⎜⎝⎛ +

−++= 2121

11

αα . Feasibility under the government’s policy rule

states that savings must remain positive ( ) TRR

rTR

aahT ⎟

⎠⎞

⎜⎝⎛ +

≥+++ 2322

11

αααα and that

ra>3α . This implies that there exists a unique maximum ( )

( ) 01

1

322

2max >

−+++

=ααα

αra

ahRaTR T

given ( )r232 1 ααα +< . ■ Proof of Proposition 3.3: First we assume that [ ]max,0 TRTR ∈∗ . Trivially, the current working generation is strictly better

off because they receive only transfers. Given that ∗TR is feasible, Thhh => 01 , and using the

government’s budget constraint ∗∗ = TTR , next period’s working generation is strictly better off

under the assumption that ar>3α because ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+++= ∗TRR

arahc T

W 311 1

αα ,

30

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+++= ∗TRR

arahRc T

R 321 1

αα , and ( ) 01 ≥∗TRs . This implies all future generations

are also strictly better because the sequence of human capital satisfies the condition 011 hhhh tt >>>>+ L converging to the upper bound A . Also note, since the non-negativity

constraint is non-binding for 1h then it is non-binding for th when 1>t because ∗TR is constant. ■ Proof of Proposition 4.1: From equation (22) we have )( 001

∗∗ == sehη . Using this result, along with equation (21), we can pin down the necessary size of the transfer with uncertainty

( ) ( )∗∗∗

−+

+=

−++−

0

2

0

2

0

2 11

1s

qTRRsqR

sah NT

ααα for a given q . By the implicit function theorem,

after totally differentiating equation (21) with respect to NTR and q , we find

( )⎥⎦

⎤⎢⎣

⎡ +−=

∗

RqTRTRRs

dqdTR NNN

0 . In the limit as 0→q we have −∞→dq

dTR N

which implies

∞→NTR as 0→q given 0>∗TR when 1=q . From (P3.2) we know there exists a ∞<< max0 TR . This implies there must be some value minq satisfying

( ) ( )0

min2

max0

min2

0

2 11

1s

qTRsq

sahT

−+

+=

−++− ααα

with ( )1,0min ∈q . Below minq we have

maxTRTR N > , thus the policy is no longer feasible under the policy rule. ■

31

References Albanesi, Stefania, V.V. Chari, and Lawrence Christiano. (2003) “Expectation Traps and

Monetary Policy,” Review of Economic Studies, 70:4, pp. 715-741.

Altonji, Joseph G., Fumio Hayashi and Laurence J. Kotlikoff. (1997) “Parental Altruism

and Inter Vivos Transfers: Theory and Evidence,” Journal of Political Economy,

105:6, pp. 1121-66.

Altonji, Joseph G., Fumio Hayashi and Laurence J. Kotlikoff. (1992) “Is the Extended

Family Altruistically Linked? Direct Tests Using Micro Data,” American

Economic Review, 82:5, pp. 1177-98.

Azariadis, Costas. (1981) “Self-Fulfilling Prophecies,” Journal of Economic Theory, 25,

pp. 380-396.

Azariadis, Costas and Allan Drazen. (1990) “Threshold Externalities in Economic

Development,” Quarterly Journal of Economics, 105:2, pp. 501-526.

Baland, Jean-Marie, and James A. Robinson. (2000) “Is Child Labor Inefficient?”

Journal of Political Economy, 108:4, pp. 663-679.

Basu, Kaushik. (1999) “Child Labor: Cause, Consequence, and Cure,” Journal of

Economic Literature, 37:3, pp.1083-1119.

Basu, Kaushik, and Pham Hoang Van. (1998) “The Economics of Child Labor,”

American Economic Review, 88:3, pp. 412-427.

Basu, Kaushik, and Zafiris Tzannatos. (2003) “The Global Child Labor Problem: What

Do We Know and What Can We Do?” World Bank Economic Review, 17, pp.

147-173.

Becker, Gary and Kevin Murphy. (1988) “The Family and the State,” Journal of Law and

Economics, pp. 1-18.

Behrman, Jere, and John C. Knowles. (1999) “Household Income and Child

Schooling in Vietnam,” World Bank Economic Review 13:2, pp. 211–56.

Bell, Clive, and Hans Gersbach. (2001) “Child Labor and the Education of a Society.”

IZA Discussion Paper No 338.

Bourguignon, François, Francisco H. G. Ferreira, and Phillippe G. Leite. (2002) “Ex-

Ante Evaluation of Conditional Cash Transfer Programs: The Case of Bolsa

Escola,” mimeo, Pontifica Universidade Católica do Rio de Janeiro.

32

Calvo, Guillermo. (1978) “On the Time-Consistency of Optimal Policy in a Monetary

Economy,” Econometrica 46, pp. 1411-1428.

Cass, David and Karl Shell. (1983) “Do Sunspots Matter,” Journal of Political Economy,

91, pp. 193-227.

Chari, V.V., Lawrence Christiano, and Martin Eichenbaum. (1998) “Expectation Traps

and Discretion,” Journal of Economic Theory, 81:2, pp. 462-492.

Cole, Harold L., and Timothy J. Kehoe. (2000) “Self-Fulfilling Debt Crises,” Review of

Economic Studies, 67:1, pp. 91-116.

Emerson, Patrick M., and André Portela Souza. (2003) “Is there a Child Labor Trap?

Inter-Generational Persistence of Child Labor in Brazil,” Economic Development

and Cultural Change, 51:2, pp. 375 - 398.

Engel, Charles and Kenneth M. Kletzer (1991). “Trade Policy under Endogenous

Credibility,” Journal of Development Economics, 36, pp. 213-228.

Farmer, Roger. (1999) The Economics of Self-Fulfilling Prophecies, second edition. MIT

Press, Cambridge, MA.

Feldstein, Martin. (1974) “Social Security, Induced Retirement, and Aggregate Capital

Accumulation,” Journal of Political Economy, 82, pp. 905-926.

Fischer, Stanley. (1980) “Dynamic Inconsistency, Cooperation, and the Benevolent

Dissembling Government,” Journal of Economic Dynamics and Control, 2, pp.

93-107.

Galor, Oded, and David N. Weil. (1996) “The Gender Gap, Fertility and Growth,” The

American Economic Review, 86:3, pp. 374-387.

Galor, Oded , and Joseph Zeira. (1993) “Income Distribution and Macroeconomics,”

Review of Economic Studies, 60:1, pp. 35-52.

Glomm, Gerhard. (1997) “Parental Choice of Human Capital Investment,” Journal of

Development Economics, 53:1, pp. 99-114.

Grootaert, Christiaan, and Ravi Kanbur. (1995) “Child Labor: An Economic

Perspective,” International Labour Review, 134:2, pp. 187-203.

Hansson, Ingemar and Charles Stuart. (1989) “Social Security as Trade among Living

Generations,” American Economic Review, 79:5, pp. 1182-1195.

33

Harsanyi, John. (1967) “Games with Incomplete Information Played by Bayesian Players

Parts I, II, and III,” Management Science, 14, pp. 159-182, 320-334, 484-502.

Hazan, Moshe, and Binyamin Berdugo. (2002) “Child Labor, Fertility and Economic

Growth,” The Economic Journal, 112, pp. 810-828.

Hungerford, Thomas, and Gary Salon. (1987) “Sheepskin Effects in the Returns to

Education,” Review of Economics and Statistics, 69:1, pp. 175-177.

International Labour Organization. (2002) Every Child Counts: New Global Estimates on

Child Labour. (Geneva: International Labour Office).

Jafarey, Saqib, and Sajal Lahiri. (2002) “Will Trade Sanctions Reduce Child Labour?

The Role of Credit Markets,” Journal of Development Economics, 68:1, pp. 137-

156.

Kydland, Finn E., and Edward C. Prescott. (1977) “Rules Rather than Discretion: The

Inconsistency of Optimal Plans,” Journal of Political Economy, 85:3, pp. 437-

491.

Kruse, Douglas L., and Douglas Mahony. (2000) “Illegal Child Labor in the United

States: Prevalence and Characteristics,” Industrial and Labor Relations

Review, 54:1, pp. 17 - 40.

Lopez-Calva, Luis Felipe, and Koji Miyamoto. (2004) “Filial Obligations and Child

Labor,” Review of Development Economics, 8:3, pp. 489-504.

Moretti, Enrico. (2004) “Estimating the Social Return to Higher Education: Evidence

from Longitudinal and Repeated Cross-Sectional Data,” Journal of Econometrics,

121, pp. 175-212.

Nielsen, Helena Skyt. (1998) “Child Labor and School Attendance: Two Joint

Decisions.” Working Paper 98-15. Aarhus, Denmark: Center for Labor Market

and Social Research and the University of Aarhus School of Business.

Ranjan, Priya. (2001) “Credit Constraints and the Phenomenon of Child Labor,” Journal

of Development Economics, 64:1, pp. 81-102.

Ravallion, Martin, and Quentin Wodon. (2000) “Does Child Labour Displace Schooling?

Evidence on Behavioral Responses to an Enrollment Subsidy,” The Economic

Journal, 110:462, pp. C158 - C175.

34

Rodrik, Dani. (1991) “Policy Uncertainty and Private Investment in Developing

Countries,” Journal of Development Economics, 36, pp. 229-242.

Rodrik, Dani. (1989) “Promises, Promises: Credible Policy Reform via Signaling,” The

Economic Journal, 99:397, pp. 756-772.

Skoufias, Emmanuel, and Susan W. Parker. (2001) “Conditional Cash Transfers and

Their Impact on Child Work and Schooling: Evidence from the PROGRESA

Program in Mexico,” Economía, 2:1, pp. 45 – 96.

Weil, Philippe. (1987) “Confidence and the Real Value of Money in an Overlapping

Generations Economy,” Quarterly Journal of Economics, 102:1, pp. 1-22.

Wahba, Jackie. (2002) “The Influence of Market Wages and Parental History on Child

Labor and Schooling in Egypt,” mimeo: University of Southampton.

45o

A

ht

ht+1

tth

a

A

a

aAh

33

1

)1( ���

��

�

tth

aa

ah

33

1

)1( ���

��

�

Th

Figure 1: Human Capital Dynamics in a Deterministic Setting

�H

h

(upper bound)A

45o

h0

h1

Th

Figure 2: Minimal Effective Transfer

��)(1 TRh

*TR

A A

)(1 TRh��

TR

TR

h(TR)

TR*

TR*TR

max

TR*

TR*

)1(2 ahT

���

322

2

)1(

)1(

���

�

��

���

ra

ahRaT

Figure 3: Feasible and Infeasible Transfers

FeasibleNotFeasible

TRR

rTRg �

�

��

��

21)(

�

TRa

ahTRzT

32

2 )1()(

���

����0)(1 �TRs

0)(1 �TRs

s0

T s0

h1

Th

s *0

s0

h =1

ahT

��1

0

2

3

2

31

)1()1(

)1(s

aah

ah

T ��

�

�

��

�

�

����

�

ahT

��1

)1(

)1(

2

3

�

��

a

ahT

ahT

��

�

1

1 2

*

2

T R

R

)( 0sg

);( 0 T Rsf

)0;( 0 TRsf

*);( 0 TRsf

)( 0sg

Figure 4: The Effect of Transfers on Savings

�

s0

Ts

0

h1

Th

s *0

s0

h =1

ahT

��1

)( 0se

ahT

��1

)1(

)1(

2

3

��

���

a

ahT

ahT

��

�

1

1 2�

*

2

T R

R �

)( 0sg

);( 0 TRsf

)0*,;( 0 �qTRsf

)1*,;( 0 �qTRsf

)( 0sg

Figure 5: The Effect of Transfers on Savings with Uncertianty

s '0

h <1

TR >TR*A

TR >TR*A

))1,0(*,;( 0 �qTRsf

TR>TR*

�

�

TRN

q

TR =TR*N

qMIN 1

Figure 6: Feasibility and Infeasibility with Uncertainty

TR =TRNMAX

TR qN( )

NotFeasible Feasible