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Investment in Childrens Human Capital:Implications of PROGRESA

Yoonyoung Cho

November 2004

University of Wisconsin, Madison

Abstract: This paper investigates the effects of an educational subsidy program in Mexico,

PROGRESA, on investment in childrens human capital. I develop a dynamic behavioral model

to pursue three objectives. First, I quantify the effect of the subsidy on schooling and human

capital accumulation. Second, I investigate how the effects vary by household and individual

characteristics. Third, I draw policy implications using the model and empirical estimates

from it. My model shows that when parents use childrens earnings as a general source of

household income, either under a borrowing constraint or impure altruism, parents under-invest

in childrens education. An educational subsidy program such as PROGRESA can mitigate

this inefficiency and increase educational attainment. The model suggests that the positive

effects of the subsidy are greater for children from larger families and for older female children.

These model predictions are confirmed in the empirical estimates. Moreover, I use the model

and underlying parameters to conduct policy experiments and find that an educational subsidy

program that applies differential subsidy rates by ability and family size can be more effective

in reallocating resources to encourage human capital accumulation.

JEL Classification: J24, I21, H52.

Keywords: Human capital accumulation, schooling, subsidy.

This paper owes an enormous debt of gratitude to John Karl Scholz and Ananth Seshadri for constant support

and encouragement. Robert Haveman and Barbara Wolfe made valuable comments. I would like to thank all

seminar participants at the University of Wisconsin, Northern Illinois University and the University of Buffalo.Department of Economics, 1180 Observatory Dr., Madison, WI 53706, email:[email protected]

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I. Introduction

Increasing formal education is considered by many to be a way to reduce child labor, alleviate

poverty, and, in the long run, contribute to the growth of the whole economy. For these reasons,

education has received a great deal of attention. Despite this attention, however, individual

households may not be able to invest enough in childrens human capital. Especially in de-

veloping countries, child labor and poverty is considered to be a main deterrent of education.

Consequently, policy makers in these countries have implemented interventions to encourage

human capital accumulation.

The educational subsidy program PROGRESA1 in Mexico has been recognized as a policy

that successfully encourages school attendance among low income households children in the

countrys rural areas. Much research has been devoted to evaluating the effects of the program

on numerous aspects of household behaviors, including schooling decisions. These studies show

there is a significant increase in schooling due to the program.

For example, Schultz (2000, 2001) finds that there is a significant effect of PROGRESA on

increasing school enrollment. The analysis is based on a comparison of households before and

after program participation and the localities where the program does and does not take effect.

Although this difference-in-difference analysis clearly shows the effects, it is limited in that it

does not provide the answer to how effective the program is, nor can the estimates be usefuldirectly to explain what would happen when the policy is changed.

To investigate PROGRESAs effectiveness, I address the more fundamental questions of what

determines childrens schooling in the household, what are the factors that induce the govern-

ments intervention into the educational decision, and how can a subsidy program improve them?

In an attempt to answer these questions, I develop a dynamic model in which childrens human

capital accumulation is determined from the parents perspectives.

The human capital production and the optimal decision process follows Ben-Porath (1967),

which endogenizes the schooling decision considering the human capital production function.

Moreover, I incorporate parents as a decision maker so as to capture the households effect on

the decision of childrens human capital. In my model, parents are assumed to be altruistic

in the sense that they care about childrens income, which consists of childrens earnings and

parents transfers to children. As a result, the final stock of human capital affects the decision

makers utility. Capital market imperfection and a subsidy program are added to characterize

poor households and the policy environment in rural areas of Mexico.

1A Spanish acronym for Programa Nacional de Educacion, Salud y Alimentacion, which means national pro-

gram for education, health and nutrition.

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Human Capital and Schooling 2

Parents determine a childs time investment in human capital accumulation until the child be-

comes independent and leaves its natal household. A childs time is allocated between humancapital accumulation and earnings-generating activity. Since childrens labor earnings are con-

tributed to the households budget, parental investment in a childs human capital depends on

how productive the child is, how much the parents rely on the childs earnings, and how al-

truistic the parents are towards the child. A childs productivity depends on his or her ability.

The extent to which parents rely on the childs earnings depends on the flexibility of the capital

market and parents lifetime income flow.

By the time the child is independent and no longer pools its earnings into the parents budget,

the human capital that the child has accumulated will determine his or her lifetime earnings.

Since parents are altruistic and care about the childs income, parents will make a cash transfer

to the child if they can and if it is needed. Thus, in every period, when determining a childs

time allocation, parents mainly consider two factors about the childs human capital: one is the

amount of labor earnings that the child contributes to the household budget, and the other is

the parents altruism, which considers the childs future earnings.

My model considers factors that generate under-investment in human capital compared to the

social optimum. One of these are capital market imperfections that restrict parents from borrow-

ing against their future income. For this reason, parents put more value on current consumption,

and thereby use childrens earnings, which reduces investment in their childrens human capital.Another source is the fact that parents are making schooling decisions on behalf of their children.

Since parents are not able to extract a grown childs earnings, they do not fully consider the

lifetime earnings of the child. In addition, impure altruism reduces the extent to which parents

care about childrens future income.

There are several previous analyses that examine PROGRESA. Among them, Attanasio, Meghir

and Santiago (2001) and Todd and Wolpin (2003) endogenize the schooling decision and analyze

the subsidy effects of PROGRESA on schooling.

In Attanasio, Meghir and Santiago (2001), the decision maker chooses schooling so as to maxi-

mize the childs lifetime earnings, which are assumed to be a quadratic function of the years of

schooling of an individual. Since the decision maker is already assumed to be maximizing life-

time earnings, the model does not provide any reason why the government intervenes to change

the outcome of the decision. However, schooling level of governments intervention and analysis

is mainly primary or secondary school, where parents are more likely to make decisions on their

behalf. If parents educational investment decisions differs from maximizing each childs lifetime

earnings, estimates of the schooling decisions that ignore the contradictions discussed here will

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be biased. As mentioned above, in my model, parents are likely to under-invest in childrens

human capital.

In another study, Todd and Wolpin (2003) addresses parents decisions concerning fertility and

childrens schooling. They model parents utility as a function of diverse arguments including

childrens activities of either working, schooling, or staying home. The parameters of each

argument, which reflect parents preferences for it, are allowed to vary with childrens gender

and age according to the household characteristics. Grown children are assumed to have no

interaction with parents in the sense that they do not pool their income into household budget

and parents utility does not include any characteristics of their grown children. Therefore,

the positive incentive for parents to invest in childrens human capital here is solely dependent

on parents preference for schooling. However, Todd and Wolpins model is not explicit in the

reasons why parents might derive different utility from the schooling of children with different

characteristics, even after controlling for the differences in labor earnings.

My model takes a different approach by specifying human capital accumulation. Households face

borrowing constraints and the more these constraints bind, or the less altruistic the parents are,

the lower the parents investment in childrens human capital. When the subsidy is introduced, it

mitigates parents under-investment by increasing childrens time investment in human capital.

The effects of subsidy are expected to vary by household and individual characteristics, and

so does the educational decision. Specifically, I focus on the educational decision and subsidyeffects on children from different sizes of families and of different genders.

My model and its empirical test finds that larger households are more borrowing constrained and

therefore produce less education for their children. Subsidies, however, have greater effects on

households with more children than for households with fewer children. I also test and reject the

hypothesis that the gender difference in education might be due to parents unequal altruism.

The effects of the subsidy are the same across genders for primary school education, and are

greater for female than male children for secondary school.

The paper is organized as follows. In the next section, I describe the data used, including the

details of the program design and some descriptive statistics. Section 3 presents a dynamic

model through which parents decide educational investments in children. Section 4 calibrates

the model, presents the outcomes and discusses policy implications. Section 5 empirically tests

the validity of the model by analyzing the effects of PROGRESA on schooling. In section 6,

based on the model, I conduct policy experiments to examine ways that policy goals can be

more effectively achieved. Section 7 concludes.

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II. Data and Descriptive Analysis

IIa. Program Design and Data

PROGRESA began in 1998. It targets poor households in rural areas and provides subsidies

for selected households conditional on childrens school attendance and regular visits to a health

care clinic. The purpose of the program is to create incentives for poor households to invest in

the human capital of their children.

For this purpose, PROGRESA includes two components: a health and nutritional program and

an educational subsidy program. The health and nutritional component of the program provides

mothers and infants with regular health care, and conditional on the observance of the required

health check-ups, it also provides nutritional supplements. The educational component of the

program includes subsidies for parents who send their children to school.

A recent appraisal of PROGRESA shows that the program is growing. By the year 2000,

almost 40% of all rural families are covered by this program, which amounts to 20% of the

federal budget allotted to social programs and to 0.2% of the GDP. The Mexican government is

currently considering extending the program to urban areas.2

There are two notable aspects of PROGRESAs design. One is that the subsidies are contingenton school attendance. The other is the social-experimental aspect of random assignment that

determines which localities will take part in the program. PROGRESA is introduced sequentially

to program localities first and to others later. The selection of program localities and eligible

households, and the corresponding data collection process is as follows.

Localities, where a high proportion of households are living in extreme poverty in seven Mexican

states, are selected. According to the sequential expansion of the program, among the chosen

6,396 localities, 4,546 of them are covered by the first phase of the program and the other 1,850

localities are covered by the later phases. Based on a households economic situation, poor

households are designated to be eligible for this program.3

2The Mexican government changed the name of PROGRESA to Oportunidades but retained the programs

main elements.3The beneficiary households are selected by the following three steps. First, the poverty condition comparing

the families monthly income per capita and the cost of a basic food basket is estimated. In addition to the

approximate poverty condition, the classification is conducted according to the households characteristics, which

classifies the households either in extreme poverty or not in extreme poverty. Finally, taking account of regional

differences and incorporating the poverty conditions, the eligible households are selected. For detailed process

about defining poverty and selecting eligible households, see Skoufias, Davis and Behrman (1999).

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According to the structure of the program, corresponding samples are randomly selected from

each locality. These consist of 320 treatment localities, which represent the program localitieswhere the program is introduced in the first phase, and 186 control localities, which serve as a

control group in which the program is not introduced during the period of this analysis. Each

survey covers both eligible and non-eligible households.

The data I use include the 1997 census, the March 1998 baseline survey before the program

onset, and three evaluation surveys conducted in November 1998, June 1999, and November

1999, after the program was introduced. Each data set contains individual information such

as demographic characteristics and school attendance, household information including family

composition and income, and locality information, such as the presence of schools.

These data sets, tracking the same households and individuals in eligible and non-eligible house-

holds in both the treatment and the control localities, form a short period panel and serve as a

main data for analysis. Since there is attrition in the data,4 only those individuals covered by

at least two data sets are used for the analysis.

IIb. Descriptive Analysis

PROGRESA

Once the household in the program locality is designated an eligible household,

5

they can par-ticipate in the health and nutritional and/or the educational component according to the ages

of the children. The health and nutritional component usually provides health service to women

and infants, while the educational component subsidizes households with children aged from

eight to sixteen. For the purpose of this analysis, however, only the educational component of

the program is considered.

The conditional subsidy for schooling provides an exogenous shift of the costs of education,

where subsidy rates differ across the gender and the ages of children. Table 1 summarizes the

amount of scholarship that the participating households receive.6 At the ages of six or seven,

children usually enter primary school. To provide a greater incentive to the parents of older

and female children, the amount of subsidy increases with age and is slightly higher for female

children. The subsidy amount for secondary school is much higher, in order to encourage more

children to progress from primary to secondary school.

4In particular, the second baseline survey only covers children ages six through sixteen in the schooling segment

of the data, and the number of observations is far less than the other data sets. The other data sets usually have

information about all members in the household.5About 78 percent of the sample is identified as eligible for PROGRESA.6The subsidy varies by grade, but is not contingent on age.

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Table 1: Payments in Pesos per Month for School Attendance under PROGRESA.

Educational Level Corresponding Age Male Child Female Child

Primary

3rd grade 8-9 71 71

4th grade 9-10 81 81

5th grade 10-11 107 107

6th grade 11-12 138 138

Secondary

1st grade 12-13 204 214

2nd grade 13-14 214 240

3rd grade 15-16 230 260

Source: Schultz (2000, Table 1) All values in 1998 pesos.

Child Labor

The opportunity cost of sending children to school is the foregone labor earnings from work. 7

Table 2 shows the average earnings of children in the labor market by gender and age. Although

not a great number of children under fourteen work and the earnings data is noisy, earnings

from child labor are not trivial, considering that the average monthly earnings of working adults

over 17 years old are approximately 800 pesos.

Child labor, despite its illegality, is the main reason why children do not attend school.8 Children

aged from thirteen to sixteen, who are usually enrolled in secondary school, show a higher

tendency to participate in the labor market and have substantial earnings that increase steadily

with age.

Due to the increasing opportunity cost, the school enrollment rate for children decreases quickly

as children age. Table 3 shows the school enrollment rates for each age and gender in the 1997

census, before PROGRESA began. Since a number of children drop out of school to work in

the labor market or to participate in home production, the enrollment rate for older children isvery low.

7The Federal Labor Law in Mexico establishes age fourteen as the basic minimum age for work. Those children

under age eighteen are required to have permission from a legal guardian or parent in order to work. In addition

to that, primary and secondary education in Mexico is mandatory. However, government enforcement is far from

strict and is only applied in the formal sector, while a great number of children are working for a family business

or in the informal sector.8The earnings in this table are only the observed ones of those who work in the labor market and reported to

the survey. If working in the informal and non-paid market, or participating in home production are counted, the

opportunity cost of schooling would be larger.

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Table 2: Child Labor and Average Monthly Earnings of Working Children.

Male Female

AgeN of

Observations

N of

Working

Monthly

Earnings

N of

Observations

N of

Working

Monthly

Earnings

8

9

10

11

12

13

14

15

16

1,478

1,720

1,933

1,760

1,723

1,754

1,760

1,745

1,601

23

24

25

44

93

167

283

585

643

460

358

517

359

528

516

596

675

707

1,762

1,700

1,813

1,798

1,727

1,697

1,626

1,623

1,442

5

9

13

16

35

58

82

193

201

195

269

210

479

405

477

535

619

651

Source: PROGRESA, 1997 Census data. Earnings are in 1998 pesos.

The reduction in enrollment rate for older female children is even greater than it is for older

male children. Consequently the average years of schooling of adults between age seventeen

and forty in the data are 5.1 and 4.6 years for men and women, respectively. If adults older

than forty are included, the average years of schooling of men and women are 3.8 and 3.2 years

respectively. The average years of schooling increases and the gap between men and women

decreases in younger generations.

Table 3: School Enrollment Rates (%).

Age 6 7 8 9 10 11 12 13 14 15 16

Male 88.2 92.2 94.3 94.5 93.3 92.5 84.9 75.1 60.1 43.5 33.5

(3.2) (2.6) (2.3) (2.2) (2.4) (2.6) (3.5) (4.3) (4.8) (4.7) (4.7)

Female 87.2 92.2 94.1 94.9 93.6 91.7 78.0 65.3 50.0 35.3 24.7

(3.3) (2.6) (2.3) (2.0) (2.4) (2.7) (4.0) (4.7) (5.0) (4.3) (4.3)Source: PROGRESA, 1997 Census. The standard deviations are in parentheses. Number of observations: male=19,778 and female=18,835.

Returns to Schooling

The main incentive for parents to invest in childrens education is that childrens earnings in-

crease.9 Therefore, parents have an incentive to invest in childrens human capital as long as

9Many papers are devoted to estimate the increase in earnings due to the increase in education, as returns to

schooling: e.g. Mincer (1974), Wills (1986), and Card (1999).

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childrens earnings augment households budget. In addition, if the parents are forward looking

and altruistic, in the sense that they care about their childrens income in the future, they willalso invest in childrens schooling.

Consider Table 4 which summarizes the distribution of educational attainment and the mean age,

labor force participation and monthly earnings for each educational level by gender. Educational

attainment is categorized as no education, less than primary, less than secondary, secondary, ter-

tiary, and post tertiary education.10 As suggested in the table, education is positively correlated

with earnings.

Nevertheless, the majority of people living in rural areas of Mexico have less than primary

education. Although younger generations seem to obtain morer education, their educationalattainment is still low, and only about ten percent go beyond the secondary level.

Table 4: Age, Labor Force Participation (LFP) and Earnings by Educational Attainment.

Men Women

Last Grade Achieved % Age LFP Earnings % Age LFP Earnings

No Education 23.5 52 76.9 650 33.9 51 11.8 502

Less than Primary 40.4 42 86.2 772 34.9 39 13.2 620

Less than Secondary 24.0 28 84.3 881 21.8 26 18.0 803

Secondary 9.9 24 76.2 970 7.8 23 21.9 895Tertiary 1.7 27 69.4 1,398 1.3 25 35.0 1,725

Post Tertiary 0.6 33 81.6 2,319 0.4 30 54.5 2,170

Total 100.0 39 82.2 808 100.0 39 13.9 661

Source: PROGRESA, 1997 Census. Number of observations: men=33,198 and women=33,279

Other Factors

There are number of other factors that might affect parents decisions on childrens education.

For example, old age support may be a reason that parents invest more in sons than daughters,10Primary education, which corresponds to the Primaria in Mexico, is equivalent to elementary school in the

U.S. Children often attend Preescolar (Preschool) or Kinder (Kindergarten) b efore going to Primaria. Thus, Less

than Primary Education includes those who have attended Preschool, Kindergarten, or elementary school and fail

to finish elementary school. Secondary education, corresponding to Secundaria in Mexico, is a three year course

similar to junior high school. Less than Secondary includes secondary school dropouts, and Secondary includes

those who graduated from secondary school. There are two different kinds of tertiary institutes. Normal Basica

is a job-preparation technical institute, while Preparatoria is equivalent to U.S. high school education. Tertiary

includes those who graduated from either one of these institutes. The post tertiary education includes those who

finish Profesional which is college level, and Posgrado which is equivalent to a masters degree and above.

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or the first born child than the others. However, the remittances patterns that grown children

provide for their parents are not available from the PROGRESA data set.

To get some idea of this pattern, I examine an auxiliary data set, the Mexican Health and Aging

Study (MHAS).11 According to these data, in less urban areas of Mexico, the proportion of

grown children making reverse transfers to their aged parents is around 5 .1% overall, when the

households of children are poor. Although the definition of poor households in the data set is

not rigorously defined and rather depends on parents subjective perceptions, financial support

from children does not seem to be of great importance.

Some studies use parental preferences to explain the educational outcomes of each child and

the differences of these outcomes across children. Todd and Wolpin (2003), for example, findsthat parents derive different utility across children even when the children engage in the same

activity. Behrman, Pollak, and Taubman (1986) finds that parents have equal concern for sons

and daughters, or when returns to education in the marriage market are incorporated slightly

prefer daughters.

However, in this analysis, I focus on human capital as a main channel that affects parents

decisions rather than considering differential parental preferences towards each child.

III. Analytical Framework

I develop a dynamic model to investigate how parents invest in childrens education. In this

section, the description of the basic model, its solution and implications follow.

IIIa. Model

Suppose the life of the economic agent consists of three phases: childhood, young adulthood,

and old age. The decision process of each phase is summarized as follows.

Childhood: No direct decision is made by the agent. During this period children are under

the parents control, depend on their parents for their schooling decisions, and pool theirincome to augment the household budget.

Young Adulthood (young parent): From period t = 0 to period t = T 1 the economic

agent makes decisions about consumption (savings) and their childrens human capital

accumulation. The households budget is the sum of the parents and childrens income,

if the children work.11The MHAS is conducted by the National Institute for Statistics, Geography and Information Technology, in

alliance with universities in the U.S., including the University of Pennsylvania. They survey individuals over age

55 and focus mainly on their health.

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Old Age (old parent): From period t = T, when the child now becomes young adult himself

or herself, to periodt

=D

, the end of an agents life, the agent decides on its optimalconsumption path given accumulated assets from previous periods. During this period,

the independent childrens decision does not affect parents budgets nor utility. Altruistic

old parents, however, derive positive utility from their childrens general wellbeing, which

will depend on childrens income level determined from the previous periods.

Formally, an economic agents decision problem throughout life is maximizing the sum of the

present stream of discounted utility of each period, from young adulthood to old age. Let

B(AT, HT, F) be the value obtained from time T onwards, which depends on accumulated

assets AT, childrens human capital HT by the time t = T, and the amount of transfer fromparents to children F.12 Note that the agent begins young adulthood, with his or her human

capital and initial assets already decided by his or her parents.

The lifetime decision problem that the parents face through young adulthood to their old age,

defined as W(E+ A0) is,

W(E+ A0) = maxT1t=0

tu(Ct) + TB(AT, HT, F) (1)

s.t. Ct +Nk=1

Ckt + At+1 Et +Nk=1

Ekt + (1 + r)At, t = 0,...,T 2,

Ct +Nk=1

Ckt +Nk=1

Fk + At+1 Et +Nk=1

Ekt + (1 + r)At, t = T 1

where W(E+ A0) is some function of parents wealth, a sum of earnings (E) and initial assets

(A0), is a discount rate, N is the number of children, and r is risk-free interest rate. The

utility function has the usual properties including u() > 0 and u() < 0. Parents earnings are

determined by their human capital which are already determined from the previous generation:

Et is exogenous. The budget constraint shows that current parents consumption plus childrens

consumption, Ct +Nk=1

Ckt, and savings for the next period, At+1, cannot exceed the sum of

parents income, Et, aggregate childrens income,Nk=1

Ekt, and savings from the previous period,

(1 + r)At. At t = T 1, parents also make decisions about how much transfer they will make

to each child (Fk).

12Ht and F denote the aggregate human capital stock and transfer of each child at time t so that Ht =

{H1t,...,HNt}, and F = {F1,...,FN} , where N is the total number of children in this household.

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Each childs earnings consists of potential labor market earnings and subsidies for education

provided by the government. The childs labor earnings depend on the stock of human capitalaccumulated thus far and the market time of labor, while the government provides subsidies for

non-market time used for education to compensate for the loss of labor earnings due to human

capital accumulation. Subsidies are set at some proportion of potential wage earnings. Thus

the childs earnings which are composed of potential wage earnings and governments subsidies

are specified as

Ekt = (1 Ikt)RtHkt + IktRtHkt

where Ikt is the proportion of time spent accumulating human capital, Rt is the rental rate for

human capital, Hkt is the current stock of human capital and (0, 1) is a subsidy rate.

A child is costly but not as costly as an adult, so childrens consumption is scaled so thatNk=1

Ckt = (N)Ct where (N) is an equivalence scale depending on the number of children in

the household.13

Then the problem is to make the optimal decision for consumption paths (Ct), the proportion

of time spent accumulating human capital for each child (Ikt) and transfers to each child (Fk),

considering future utility. Formally, equation (1) is specified as

W(E+ A0) = maxCt,{Ikt},Fk

T1t=0

tu(Ct) + TB(AT, HT, F) (1

)

s.t. Ct (1 + (N)) + At+1 Et +Nk=1

{(1 Ikt)RtHkt + IktRtHkt} + (1 + r)At

(at t = 0,...,T 2)

Ct (1 + (N)) +Nk=1

Fk + At+1 Et +Nk=1

{(1 Ikt)RtHkt + IktRtHkt} + (1 + r)At

(at t = T 1).

In terms of the process of human capital accumulation, I adopt a standard production function

following Ben-Porath (1967) such that

Ht+1 = (1 )Ht + 0(ItHt)1 , (2)

where ItHt is effective time for human capital production, 0 > 0 is an ability parameter, 1 < 1

reflects returns to scale and is the depreciation rate of human capital. The initial human

13Deaton and Muellbauer (1986) introduce the concept of equivalence scale. The equivalence scale satisfies the

following properties:

(N) > 0 and

(N) < 0.

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capital level H0 > 0 is assumed to be exogenously given from parents educational attainment

determined by the previous generation.

Looking into the human capital production function and the budget constraint, there is a trade

off between current labor earnings and accumulating more human capital. So the parents deci-

sion is to determine when they should utilize childrens accumulated human capital. Additional

accumulation of human capital of a child provides parents not only with more labor earnings

when the child works, but also with positive utility for the parents old age.

Next, the the economic agent in old age (from t = T,...,D) is described as follows. The problem

faced in old age at time t = T is to find optimal consumption paths for the remainder of life. The

total utility in this period includes the utility derived from the childs human capital. However,parents are assumed to have impure altruism which means they care less about the child than

themselves: the utility derived from a childs income is discounted by .14 The sum of discounted

utility from t = T onwards is

B(AT, HT, F) = maxCt

Dt=T

tTu(Ct) + Nk=1

W(RTHkT + Fk) (3)

= b(AT) + Nk=1

W(RTHkT + Fk)

s.t. Ct + At+1 Et + (1 + r)At, t = T,...,D 1,

CD = ED + (1 + r)AD, t = D,

where (0, 1) is an altruism factor and W(RTHkT + Fk) is the utility that parents derivefrom the childs wealth. The continuation value from an optimal consumption decision for the

rest of life in old age can be specified as b(AT), a function of asset level at time t = T. (See

Appendix A for a derivation.)

IIIb. Model Solution

To solve the dynamic problem described above, I rewrite the problem in recursive form using

the Bellman equations and solve it using backward induction. Note that the parents start an

old phase of lives and child starts his or her own adulthood at time t = T. Given the value of T

onwards, I solve the problem from the last period of parents decision at t = T1. At t = T1,

parents decide the level of consumption, the fraction of time investment spent accumulating

human capital and transfer to each child.

14Aiyagari et al. (2002) also investigates the implication of impure altruism in terms of the effect on investment

in childrens human capital and bequests.

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Solutions at t=T-1

The problem that the young parent faces at time T 1 is

vT1(AT1, HT1, F) = maxAT,{HkT},{Fk}

u(CT1) + {b(AT) + Nk=1

W(RTHkT + Fk)}

s.t. CT1 (1 + (N))+Nk=1

Fk+AT ET1+Nk=1

{(1IkT1)RT1HkT1+IkT1RT1HkT1}+(1+r)AT1.

Since determining current time investment in human capital production is equivalent to deter-

mining the next periods stock of human capital from the human capital production function, I

solve the problem with respect to HkT instead of IkT1. Then the choice variables are HkT, Fkand AT, and the first order necessary conditions with respect to each of them are

HkT :u(CT1)

1 + (N)RT1HkT1(1 )

IkT1

HkT= RTW1(RTHkT + Fk) (4)

Fk :u(CT1)

1 + (N)= W1(RTHkT + Fk) (5)

AT :u(CT1)

1 + (N)= b1(AT). (6)

Rearrange equation (4), replacingIkT1HkT

from the production function of human capital.

HkT :u(CT1)

1 + (N)

RT1(1 )

01(

HkT (1 )HkT10

)111 = RTW1(RTHkT + Fk). (4)

These equations present the simple rule of equating the marginal cost and benefit in determining

each choice variable. The left hand side of equation (4) is the marginal cost of human capital

accumulation, which is the utility loss from losing current earnings. The right hand side of it is

the marginal benefit, which is the utility gain from the additional income of each child.

The marginal cost of accumulating assets and making transfers to children are utility loss from

giving up consumption. The marginal benefits of each are discounted utility from increased old

age consumption and increased childrens income.

Solutions at t=T-2,...,0

The dynamic problem that the young adults face during t = 0,...,T 2, is

vt(At, Ht, F) = max{Hkt+1},At+1

u(Ct) + vt+1(At+1, Ht+1, F) (7)

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s.t. Ct (1 + (N)) + At+1 Et +Nk=1

{(1 Ikt)RtHkt + IktRtHkt} + (1 + r)At, t = 0,...,T 2.

The first order necessary conditions for each variable Ht+1 and At+1 are15

Hkt+1 :u(Ct)

1 + (N)

(1 )Rt01

(Hkt+1 (1 )Hkt

0)

111 = vHk,t+1(At+1, Ht+1, F) (8)

At+1 :u(Ct)

1 + (N)= vA,t+1(At+1, Ht+1, F). (9)

The Envelope conditions are

vHk,t(At, Ht, F) =u(Ct)Rt1 + (N)

{1 +(1 )(1 )

01(

Hkt+1 (1 )Hkt0

)111 } (10)

vA,t(At, Ht, F) =u(Ct)(1 + r)

1 + (N). (11)

Combining equations (8) and (10) determines the solution for human capital, which is

u(Ct)

1 + (N)

(1 )Rt0

1

(Hkt+1 (1 )Hkt

0

)111

=u(Ct+1)Rt+1

1 + (N){1 +

(1 )(1 )

01(

Hkt+2 (1 )Hkt+10

)111 }. (12)

Similarly, combining equations (9) and (11) yields the familiar Euler equation,

u(Ct) = (1 + r)u(Ct+1) (13)

which simplifies equation (12) to16

(1 + r)(1 )

01 (

Hkt+1 (1 )Hkt

0 )

111

= 1+

(1 )(1 )

01 (

Hkt+2 (1 )Hkt+1

0 )

111

. (14)

Equations (12) and (14) show that the marginal cost (benefit) of human capital accumulation

is the loss (gain) of labor earnings that depends on educational attainment, and it should

be expressed in terms of utility loss (gain) as in equation (12). With perfect capital markets,

however, where the discounted marginal utility of consumption over time is constant, the decision

is equivalent to equating the monetary marginal cost and benefit as in equation (14).

15Let vHk,t(At,Ht, F) denote the partial derivative of value function vt(At,Ht, F) at t, with respect to Hkt.16Assume that Rt = R for all t.

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IIIc. Model Implication and Comparative Statics

There are two ways in which the educational decision described in the model may be considered

as under-investment, which the government aims to improve with subsidies. First, parents

investment in childrens human capital is less than the investment that the children would have

made for themselves. Second, the borrowing constraint reduces the investment in human capital.

Parents vs. Childrens Decision

My model suggests that schooling decisions made by parents on behalf of children may not

be optimal because the decisions are different from what would have been made by children

themselves. The discrepancy between parents and childrens own decisions are larger when

parents altruism is impure.

Clearly, parents consider b(AT) + W(RTHkT + Fk) at time t = T 1 as a future value.Parents concern for childrens income is currently reflected only in W(RTHkT+ Fk). However,if children become the decision maker and their lifetime utility for the remainder of life are

considered instead, then the educational attainment would be larger.17

Thus, in the environment where parents use childrens earnings as a general source of income,

parents decision on behalf of children for their human capital results in less education because

parents do not fully consider childrens lifetime utility.

Borrowing Constraints

A borrowing constraint is another source of under-investment in childrens human capital. With-

out borrowing constraints, the economic decision maker smoothes the consumption according

to the Euler equation (13). However, if borrowing is constrained, the Euler equation holds only

when At+1 > 0. Otherwise, u(Ct) > (1 + r)u

(Ct+1), which implies the decision maker values

current consumption more than discounted future consumption. Thus, the borrowing constraint

increases current consumption and reduces future consumption by reducing educational invest-

ment in children.17Specifically, the future value at t = T1 is kb(AT) +W(RTHkT, Fk), where k is the childs altruism toward

parents. The lifetime utility for the remaining life for the child is W(RTHkT, Fk) = maxCt

Dt=T

tTu(Ct) with the

budget constraint thatDt=T

Ct(1+(Nk))

(1+r)tT=

Qt=T

RTHT(1+r)tT

+Fk, where Nk, D, and Q denote the number of children,

end of life, and retirement of the child, respectively. If the childs altruism toward parents is negligible, and the

curvatures ofW andW are same, the marginal utility of accumulating additional human capital is much greaterin the childs decision than in parents.

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Hkt+1Hkt+1H

kt+1

RHS

LHS

Figure 1: Determination of Human Capital Stock

the effect of a borrowing constraint

Figure 1 illustrates the human capital accumulation with and without borrowing constraint.

The two curves present the monetary marginal cost of human capital accumulation (LHS: lefthand side) and marginal benefit (RHS: right hand side) in equation (14).18 Without borrowing

constraint, equating monetary cost and benefit determines optimal human capital at Hkt+1.

However, when borrowing constraint is imposed and u(Ct) > (1 + r)u(Ct+1), satisfying equa-

tion (12) requires greater monetary benefit in the next period to compensate for the lower utility

of consumption. Thus the optimal level is reduced to Hkt+1.

As suggested above, parents investment in childrens human capital falls short of the optimal

level and the under-investment is worsened due to the credit constraints. I will examine the

18When 1 > 0.5, it is shown thatLHSHkt+1

> 0 and 2LHS

H2

kt+1

< 0, and RHSHkt+1< 0 and

2RHSH2

kt+1

< 0 by the

following equations:

LHS

Hkt+1=

(1 + r)(1 )(1 1)

(01)2(Hkt+1 (1 )Hkt

0)1/12

2LHS

H2kt+1=

(1 + r)(1 )(1 1)(1 21)

(01)3(Hkt+1 (1 )Hkt

0)1/13

RHS

Hkt+1=(1 )2(1 1)(1 )

(01)2(Hkt+2 (1 )Hkt+1

0)1/12

2RHS

H2kt+1=

(1 )(1 )3(1 1)(1 21)

(01)3(Hkt+2 (1 )Hkt+1

0)1/13

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comparative statics of key variables how the credit constraints affect the households decision

according to these key variables. First, I consider family size because family size reflects theextent to which a household is borrowing constrained. Second, I visit the familiar question of

gender gap in education and investigates what my model implies about it. Third, I investigate

the effects of constraints according to the ability of a child.

Family Size: Number of Children (N)

Equation (14) indicates that the decision on human capital is not affected by the consumption

level or the number of children in the household when there is no borrowing constraint. The size

of household only matters when there is a borrowing constraint. Increasing the number of chil-

dren is costly in households consumption and makes the household more borrowing constrained,

although children may contribute earnings to the household as they get older.

My model suggests that children from larger families have lower educational attainment because

these households are more borrowing constrained and the opportunity cost of accumulating

human capital for these households is greater. This implication will be empirically tested and

discussed.

Gender: Rental Rate for Human Capital (Rt) and Altruism Factor ()

As shown in Table 3, there is a slight difference in the school enrollment rate across gender.

Encouraging female childrens schooling by providing a slightly higher subsidy is to remedy this

lower investment in female children. In the model, there are two sources that can induce different

allocations between genders: the rental rate for human capital and the different altruism factor

toward each child.

The rental rate for human capital Rt is the price of it. Although human capital and the rental

rate are not observable, the wages must reflect the total price for the stock of human capital paid

in the labor market. It is easy to think that the higher rental rate for human capital might induce

more human capital accumulation. However, since the higher rental rate for human capital also

means the higher opportunity cost of human capital accumulation, whether the higher rentalrate results in greater investment in human capital is not obvious.

Meanwhile, the greater altruism factor in this model seems to imply greater transfer from

parents to the child and greater investment in human capital of the child. Combining equation

(5) and (6) clearly shows that greater altruism factor implies greater transfer to the child. The

effect of altruism factor on human capital accumulation, however, is not so straightforward.

Equations (4) and (5) show that the different altruism factor does not make a difference in

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human capital accumulation as long as parents make a transfer to the child.19 When excluding

the case that parents receive a reverse transfer from children, then the altruism factor makes adifference, with smaller altruism resulting in lower investment in human capital.

The price for human capital is the shadow price of education. Although it is not obvious whose

rental rate for human capital is valued higher, the difference in rental rate for human capital

between gender can induce different educational investment. In addition, difference in parents

altruism toward each gender of children would make difference. In particular, attention has been

paid to whether the difference in educational outcome by gender is due to difference in parents

altruism.(e.g. Behrman et al. (1986)) In the empirical test, I will revisit this issue.

Ability: The Ability Factor (0)

In the model, one of the most important factors that affect the parents decision about human

capital is the ability of a child. The childs ability determines the productivity of accumulating

human capital. A higher-ability child is able to accumulate human capital faster with the same

time input than a lower-ability one. Then, combined with the larger stock of human capital

accumulated, the higher-ability child can accelerate human capital accumulation.

The greater the childs ability, the higher the accumulated human capital and the steeper the

human capital accumulation. Then the household with a higher-ability child receives more

earnings from the child as the child gets older compared to the household with lower-abilitychild. This means that the consumption smoothing requires more resources for households with

higher-ability child than the other counterpart. Therefore, when the households income is low

and there is a borrowing constraint, the households with higher-ability would be disadvantaged

further by the credit constraint and poverty.20

Without a borrowing constraint, it is obvious from the equation (14) that the time investment in

human capital accumulation is monotonic to the ability of a child: a higher-ability child spends

more time accumulating human capital. However, with a borrowing constraint, this relationship

is no longer apparent. Since a higher-ability child has a higher opportunity cost of accumulating

human capital, the higher-ability child may leave quicker for labor market. Thus, whether time

investment is monotonic to the childs ability over his or her entire childhood is not obvious.

19Equations (5) and (6) gives W1(RTHkT + Fk)=b1(AT), and equations (4) and (5) gives(1)01

(HkT(1)HkT1

0)111 = 1. These equations hold only when the amount of transfer from parents to

the child is positive.20Numerically, the ratio of marginal utility of current and future consumption for households with a higher-

ability and a low-ability child shows the inequality as [ u(Ct)

u(Ct+1)]H > [

u(Ct)u(Ct+1)

]L. Then the reduction in human

capital accumulation is greater for a higher-ability child as shown in the Figure 1.

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In this section, I have presented the model and the solution for it, which determines households

educational investment in children. The model implies that parents educational decision forchildren is not optimal. The extent to which the sources of parents under-investment reduces

education varies with the family size, gender, and ability of the child. Throughout next sections

of calibration and estimation, these implications will be examined, and the differential subsidy

effects according to these key variables will be investigated.

IV. Calibration

Having considered some implications of the factors that affect childrens education, I calibrate

the model to further investigate the effects of each factor, its magnitude and the effects of the

subsidy. Thus, in this section, I parameterize the model, assume specific functional forms, and

present the findings from the model.

IVa. Subsidy Effects

Assume utility is CRRA: i.e., u(Ct) =C1t1 and

W(RTHkT + Fk) = (RTHkT+Fk)11 . The modelis calibrated using the following parameter values summarized in Table 5.

Table 5: Benchmark Parameter Values.

Preferences

-Discount Factor, = 0.96

-CRRA: Consumption, = 2.0

-CRRA: Childs Income, = 2.0

-Altruism Factor, = 0.3

Production Function

-Ability, 0 log N(, 2)

= 0.1, = 0.3

0 = 0.52, 0.70, 0.95, 1.28, 1.73, 2.34

-Return to Scale, 1 = 0.73

-Initial Human Capital, H0 = 100

-Depreciation Rate, = 0.0

Period of Analysis

-Beginning of Old Age at T, T = 43

-Retirement at Q, Q = 65

-Death at D, D = 75

Educational Subsidy-Subsidy Rate, = 0.20

-Subsidized Ages of a Child, Age 16

Other Parameters-Gross Interest Rate, r = 1.06

-Equivalence Scale, = 1.05

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Preferences: The time period of the model is a year and the time discount rate is set at 0.96.

For the CRRA utility functions, let the coefficient of relative risk aversion of consumption,,

assume a standard value of 2.0 and the coefficient for human capital stock, , start with 2.0.21

Since there is no theoretical or empirical grounds for the altruism factor, which measures how

much parents care about a childs wealth relative to their own utility, let be set to 0.3.22

Human Capital Production: Assume that 0, which is the parameter of ability, is distributed

as log normal; i.e., log 0 N(, 2). Setting = 0.1 and = 0.3, I calibrate the model

at 6 different levels of ability ranging from 0.52 to 2.34.23 The estimate for the depreciation

rate and returns to scale parameter varies. For example, Heckman (1976) found the estimate

of the Ben-Porath model and his own model gives 0.81 and 0.52 for 1, and 0.09 and 0.04 for

depreciation rate , respectively. I will begin with 1 = 0.73 and = 0.0. For the benchmark

case, the initial human capital is homogenous for everyone.

Period of Analysis: I assume that the agent is a young parent between the ages of 23 and

43. During this period, between the childs ages of 6 and 22, parents make decisions on time

investment in accumulating human capital for children as well their own consumption and asset

accumulation. At the parents age of 43, when the child turns into young adult and leaves the

natal household, the parents enter the phase of old age. In this phase, they have a positive

earnings stream until they retire at age 65.

Educational Subsidy: The PROGRESA subsidy is provided to children who enroll in school

when they are between the third year of primary school to the third year of secondary school.

Therefore, in this simulation, I assume the subsidy is provided for children younger than 16,

which is the corresponding age for PROGRESA. The subsidy rate is fixed at 20% for all ages.

Other Parameters: The real interest rate is set at 6%.24 The equivalence scale is set as a

concave function of the number of children in the household. Thus, for a three child household,

the = 1.05.25

21There are few literature that estimated the coefficient of relative risk aversion (the reciprocal of the intertem-

poral elasticity of substitution) using Mexican data. According to the summary in Reinhart and Talvi (1998), the

intertemporal elasticity of substitution in Latin American countries including Mexico range from 0.43 to 0.56.22Since there is no standard number for altruism factor, 0.3 is used for illustrative purpose. The effect of impure

altruism of parents on a childs human capital accumulation by changing altruism factor will be discussed.23This covers 2.5 standard deviations from the mean.24According to the report by the Ministry of Finance and Public Credit of Mexico, the real interest rate in 1997

was about 6%.25If the consumption is same for all three children, that = 1.05 implies that a child consumes 35% of parents

consumption. Considering that parents are two adults, the consumption of one child in three children household

is equivalent to 70% of an adults consumption.

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Table 6: Years of Schooling by Age: Data and Simulation Comparison

Years of Schooling Age 7 8 9 10 11 12 13 14 15 16

Without Data 1.12 1.75 2.55 3.32 4.10 4.81 5.41 5.95 6.05 6.10

PROGRESA Simulation 0.95 1.78 2.52 3.21 3.86 4.47 5.06 5.63 6.16 6.45

With Data 1.35 1.92 2.64 3.37 4.25 5.03 5.84 6.42 6.80 7.12

PROGRESA Simulation 0.89 1.81 2.74 3.58 4.37 5.12 5.83 6.53 7.11 7.49

Table 6 shows the average years of schooling for each age for the PROGRESA data and simula-

tion, comparing data for children without and with the subsidy program. The subsidy increases

the average years of schooling in each age. The increase appears to be especially greater for the

older children between the ages of fourteen and sixteen. The results from the simulation show a

model prediction of years of schooling with and without the PROGRESA subsidy, and predicts

the similar effect of the subsidy on years of schooling as observed in the data.

6 8 10 12 14 16 18 20 220

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Childs Age

Time

Time Investment in Human Capital Accumulation

Without Subsidy

With Subsidy

6 8 10 12 14 16 18 20 220

200

400

600

800

1000

1200

Human Capital Accumulation

Childs Age

HumanC

apital

With Subsidy

WIthout Subsidy

Figure 2. The Effects of Subsidy:

Time Investment and Human Capital Accumulation

Figure 2 presents the outcomes of time investment and human capital accumulation paths of

the ages of children, and compares these outcomes with and without the subsidy.26 As shown in

the figure, the increase in time investment is significant while the subsidy is provided until the

26For the comparison of these outcomes in the case without credit constraint and with parents pure altruism,

see Appendix B. It discusses the source of inefficiency that results in under-investment and thus provides the

rationale for governmental intervention. Moreover, the paths of assets and human capital accumulation, and time

investment in human capital production are presented.

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age of 16, after which the reduction in time investment is steep. The overall increase in human

capital due to the subsidy and thus the increase in labor earnings is around 19%.

The introduction of subsidy increases schooling and human capital accumulation. In terms of

evaluating what the increase in human capital implies and whether the subsidy rate is optimal,

I will consider two ways to quantify the effects. The first is in terms of the cost and benefits of

the subsidy program and the other is by the comparison to the human capital achieved in an

ideal economy without either borrowing constraints or without impure altruism.

IVb. Benefits and Costs of the Subsidy Program

Based on the simulations, I calculate the benefits and costs of PROGRESA. The benefits of

increasing human capital accumulation as a result of subsidy are from two sources. One is the

present discounted value of the increase in earnings contributed to the household due to the

introduction of the subsidy. The second is the present discounted value of the increase in the

lifetime earnings of the child.27 The costs of the subsidy is simply the present discounted value

of the subsidy amounts provided to households.28

The simulations show that with a subsidy rate of 20%, the benefits of the program exceeds the

cost by 60%.29 The benefit-cost ratio is higher for children from larger families, implying that

the subsidy is more effective for those children.

IVc. Comparison to a No Credit Constraint and Pure Altruism Case

In addition, I examine whether PROGRESA can raise human capital to the level that could

have been obtained in an economy without credit constraint and with pure altruism.30

On average, the subsidy increases human capital accumulation, although the extent to which

the level of human capital becomes closer to the outcome of the no constraint case varies by

the ability and family size of the child. The lower-ability children and children from smaller

families achieve even greater human capital by the introduction of the subsidy than what they

27

There can be indirect b enefits of subsidizing and increasing education. For example, Barnett (1992) calculatebenefits of early education using five types of benefits including the value of child care and reduction in the costs

of crime. However, I consider main benefits of education which increases household income and lifetime earnings.28There must b e administrative costs related to implementing this program. However, for this calculation,

subsidies provided to households are only included to the costs of the program.29The lifetime earnings are calculated assuming that the individuals make the same level of labor earnings from

the age of 23 onwards until they retire at age 65, with the real interest rate fixed at 6%.30Note that this idealistic environment with no credit constraint and pure altruism does not mean that there

is no under-investment at all. Parents are still making decision on behalf of children without full consideration

of childrens lifetime utility. Although parents utility from altruistic motive captures parents concern about

childrens lifetime utility, it is not necessarily same with childrens own lifetime utility.

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could have achieved without constraint, while the human capital accumulation of higher-ability

children and children from larger families fall short. The overall level of human capital is shortof the no constraint level by 8%.

The effect of subsidy is different across households and individuals. The effect would be greatest

for those households which are borrowing constrained without any subsidy and become not

constrained with subsidy, since the negative effect of borrowing constraint on education is huge.31

Considering this, the effects on marginal households would be greater and the subsidy has a

greater impact on children from larger family on average, since the larger families are more

likely to be on the margin than the smaller families.

In summary, through this calibration, my model replicates the observed schooling decisions andthe effects of the program. The results show that the subsidy increases overall years of schooling

and, thus, human capital accumulation. The benefit of the subsidy, by increasing education,

exceeds the cost of the subsidy when the lifetime effect of increase in earnings are taken into

account. The magnitudes of the effects are not uniform: the magnitude depends on various

factors including to what extent households are credit constrained. The model implies that the

effect of subsidy is greater for children from larger families.

V. An Empirical Test

In this section, I test whether the effect of PROGRESA is greater for larger families. In addition,

I examine gender differences in schooling. First, I test whether the gender difference in educa-

tional attainment is due to parental preferences. Second, I investigate the effects of subsidy on

both genders.

Va. Family Size and Subsidy Effects

If the credit markets were perfect, the educational attainment of children would be the same

across households regardless of family size. However, with borrowing constraints, children in

larger families are not able to attend school for as long a period of time as children in smallerfamilies. Increasing the number of children in the household is costly, which implies that bor-

rowing constraints are more severe in these families. Thus educational attainment is lower for

children from larger families, other things equal.

However, when the subsidies are introduced, their effects are expected to be greater for larger

families. In other words, for a child in a smaller family who would have attended school regard-

less of the subsidy program, since those households are not greatly borrowing constrained, the

31Recall the effect of borrowing constraint on time investment and human capital accumulation from Appendix

B.

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subsidy does not greatly affect the schooling decision. However, a child in larger family may

now be able to attend school due to the introduction of the subsidy, otherwise the child wouldnot have been able to attend school. In that sense, the effects of subsidy are expected to be

greater for children from larger families. From the simulation, it is also shown that the effect of

the subsidy is greater for these children.

To test this hypothesis, the following equation of school attendance is specified and estimated

with the experimental data. Let sit indicate school attendance at time t for individual i. The

event of attending school (st = 1), is determined by a latent variable st , which can be explained

by individual, family, and locality characteristics. In other words,

sit = xit + i + it (15)

sit = {1 if sit > 0

0 if sit 0, i = 1,...,N, t = 1,...,T

where xit denotes the characteristics of individual i, at time t, it is unobservable individual

heterogeneity and it is white noise. Since this individual heterogeneity (i) is unobservable,

it is considered as a individual random variable. Thus, the random effects logit regression is

estimated.32 Because the data set is a panel, following the same individuals over time, I estimate

the equation controlling for the unobservable characteristics (i).

The individual characteristics include age, gender and the indicator of the eldest child of each

gender. Family characteristics include a measurement of parents education level and the age

of the youngest child. As a variable showing the family size, the number of adults and dummy

variables for the number of children are included. The characteristics of the locality include the

presence of a primary school and a secondary school within the locality, and the local wage rate

for child labor at each age.

To capture the effects of the program, I include the indicator of program locality, eligible house-

holds, and the indicator of the time when the program began. Finally, the differential effects

of the program on households with different numbers of children are reflected in the variable of

the interaction between indicators of program locality, eligible households and after the programonset.

The summary statistics of the variables which are used in this analysis and the results from the

random effects logistic regression are presented in Tables C1 through C3 in the Appendix. The

32The conditional distribution of this variable conditioning on other observable variables are assumed to

follow normal distribution: G(i|xit) N(0, 2). Then the conditional probability of schooling specified as

Pr(sit = 1|xit, i) = F(

xit + i) where F satisfies F(w) =ew

1+ew. Then the log likelihood function is

log L =Ni=1

log Tt=1

F(

xit + i)sit{1 F(

xit + i)}1sitdG(|x). According to Heckmans the Monte Carlo

experiments, the fixed effect estimate for the parameters is not consistent when T is finite. (Heckman(1981))

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Table 7: Random Effects Logit Regression-Family Size.

(1) (2)

Variables Coefficient S.E. Variables Coefficient S.E.

N=1 (dropped) Poor*N=1 -1.056 (0.217)

N=2 0.243 (0.127) Poor*N=2 -0.785 (0.186)

N=3 -0.029 (0.129) Poor*N=3 -0.903 (0.184)

N=4 0.071 (0.133) Poor*N=4 -0.757 (0.173)

N=5 0.005 (0.137) Poor*N=5 -0.761 (0.176)

N6 -0.312 (0.138) Poor*N6 -0.984 (0.184)

Treat*After 0.024 (0.070) Treat*After*Poor 0.574 (0.150)

Treat*After*N=1 -0.141 (0.166) Treat*After*Poor*N=2 0.091 (0.197)

Treat*After*N=3 0.482 (0.124) Treat*After*Poor*N=3 0.408 (0.188)



Treat*After*N6 0.547 (0.114) Treat*After*Poor*N6 0.451 (0.178)

*, **, *** significant at 10%, 5% and 1% confidence levels.

results are consistent with intuition: School attendance decreases with the age of a child. The

higher the household heads education, the more likely the child is to attend school; The eldest

and female child is disadvantaged in schooling; The more adults in the household, the less school

attendance for the child; The locality characteristics also have a great effect on schooling. The

localities where there are primary and secondary schools and localities with lower local wage

rates for child labor, have higher school enrollment.

The effects of the subsidy on families of different sizes are presented in Table 7. The first

specification analyzes the effect of PROGRESA on the localities of the program after it starts.

The results show that the child from families with six children or more has significantly lower

school enrollment compared to the child from one child family. The effects of subsidy program

on the school enrollment of children in program localities, presented in the bottom panel of thetable, are significantly greater for children from larger families.

Since only eligible (poor) households receive cash transfers from the PROGRESA program, even

though the entire program locality benefits from indirect supports of the program, the second

specification captures the programs effect only on eligible (poor) households. Compared to

non-poor households with each number of children, poor households show significantly lower

school attendance of children.

The bottom panel shows the effects of subsidy on the school enrollment of children in eligible

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(poor) households in program localities after the program starts. There is an overall significant

increase in school enrollment for these children. The effects are shown to be larger for childrenfrom 3 child families and 6 or more child families, compared to children from one child families.

The results from both specifications consistently show that the effects vary with the size of the

family. Although the school attendance of children from larger families is significantly lower than

that of smaller families, the effects of subsidies are greater for families with a larger number of

children. This suggests that the PROGRESA subsidy mitigates the negative effect of the number

of children in the household and thus the credit constraints.

Vb. Gender and Subsidy Effects

In this section, I examine whether parents have unequal concern by gender, and whether this

causes different educational outcomes between the genders. According to my model, differences

in educational attainment of children between genders can be due to two factors: rental rate for

human capital and parents altruism factor. The fact that men and women with the same level

of education make different labor earnings (Recall Table 4.) suggests that there is difference in

the rental rate of human capital by gender.

However, there is little evidence that parents have unequal concern for children of different

gender. The expenditure on clothes and shoes of female and male children, which is often

used as measure that reflects parents altruism toward the children of each gender, shows thatthe households spend about the same proportion of the entire expenditure for children of each

gender; 24.8% for male children and 23.9% for female children on average.33 Therefore, whether

parents altruism differs towards children of each gender is not obvious.

The hypothesis to be tested is that the school enrollment of female children from households with

only female children should be different from that of households with male and female children,

if what makes a difference in school attendance of children across gender is parents preference.

I again estimate random effects logistic regression for school enrollment of female children.

The empirical specification is similar to equation (15). The indicator of female-children-only

households interacted with poverty status is included to reflect differences that might be due to

the parents altruism. The following table shows the results from the equation.34

The results show that there is no significant differences in school enrollment of female children

in households with only female children compared to children in households with female and

33Data source: PROGRESA 1998 household survey34See Table C4 in the Appendix for the complete results.

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Table 8: Random Effects Logit Regression-Gender (1).

Variables Coefficient S.E.

Female Only 0.003 (0.183)

Female Only*Poor -0.264 (0.203)

Treat*After*Poor 0.953 (0179)

Treat*After*Poor*Female Only -0.020 (0.107)


male children.35 The outcome of female children in poor households with only female children

is not different from that of female children in poor households with female and male children.

In terms of the subsidy effect, there is no significantly different effect on female children in both

types of households.

In addition, the effects of the subsidy on children of each gender is investigated. Since the

subsidy rate for older female children is higher, while the rate is the same for both genders of

younger children, the effects of subsidy on school attendance of older female children should be

larger than the effects for older male children, while the effects on younger children are expected

not to differ by gender.36

Table 9: Random Effects Logit Regression-Gender (2).

Variables Coefficient S.E.

Female -0.020 (0.817)

Older Female -0.405 (0.198)

Treat*After*Poor 1.696 (0.159)

Treat*After*Poor*Female -0.186 (0.131)

Treat*After*Poor*Older*Female 0.601 (0.184)


As presented in Table 9, the school enrollment is much lower for older female children.37 The

effects of the subsidy program is consistently found to be positive and significant. The effect

of the subsidy on school enrollment of female children is not significantly different from that of

35Note that this regression estimates only female childrens school enrollment. The number of observations

used for this regression is 50,368 which is about half of the total observation in data. The proportion of female

children in households with only female children is 38%, and the other 62% of female children are in households

with female and male chilren.36Older children refer to those who are over 12 years old and corresponds to the secondary school level.37See Table C5 in the Appendix for the complete results.

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male children. However, the subsidy significantly increases the school attendance of older female

children.

VI. Policy Experiments

Having investigated the households investment in childrens human capital and the effect of

the educational subsidy program using PROGRESA, policy implications are now considered.

Specifically, simulations with alternative subsidy schedules are examined to consider alternative

policies that might be more effective.

Va. Subsidy Varying by Ability

In the previous calibration of the benchmark model, the subsidy rate is fixed at 20% for all

children. The reason why the policy makers should implement a higher subsidy rate for higher-

ability children is that higher-ability children are more disadvantaged by credit constraints.38

In this exercise, for the lower-half of children by ability distribution is subsidized at the rate

of 15% and the other half is subsidized at the rate of 25%. The cost and benefits of this new

subsidy schedule is compared to the benchmark case. A higher subsidy rate for higher-ability

children increases cost of subsidy by 70%, while the benefit of the subsidy increases by 87%.

Thus, the ratio of benefit to cost of this subsidy slightly increases, meaning that ability-basedscholarship is more effective in terms of benefit and cost aspect.

Since the government is not able to observe individual childs ability, the merit-based subsidy

such as larger scholarship for children with better test scores might be implementable.39

Vb. Subsidy Varying by Family Size

A higher subsidy rate for larger families is more effective than a flat subsidy rules, because the

effects of subsidies are greater for children in larger families. Considering that children from

larger families are more disadvantaged by borrowing constraint, the greater subsidy for them

seems justifiable.

Although I find that the subsidy rate varying by family size is more effective, it may not be

practically implementable. It is currently assumed that the family size is exogenous. However,

38The reduction in education due to a borrowing constraint is greater for higher-ability children and children

from larger families. In that sense, they are more disadvantaged by credit constraint. See Appendix B again for

the effect of borrowing constraints.39The data of childrens school performance such as test scores are not available at the period of analysis.

Examining the effects of the PROGRESA subsidy on school performance across children with different test scores

can be a subject for further research.

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considering that a family size and fertility are also decisions that the household makes, greater

subsidies for larger families might cause people to have additional children which would resultin more credit constraint.40

VII. Conclusion

In this study, I quantitatively assess the effect of PROGRESA on the education of the children.

I develop a dynamic model of household behavior to determine how parents determine childrens

schooling. My model shows that parents who rely on childrens earnings for household consump-

tion, and either face the credit constraints or have impure altruism toward children, under-invest

in childrens human capital. The educational subsidy contingent on school attendance reduces

the problem of under-investment.

The educational subsidy program aims to achieve the goal of increasing human capital accumu-

lation in an effective and efficient way. I evaluate the program in two ways. First, I analyze the

benefits and costs of the subsidy. Second, I investigate the increase in human capital induced by

a subsidy, and whether this increase is large enough to achieve human capital that could have

been achieved without credit constraints and with purely altruistic preferences.

I find that PROGRESA increases average years of schooling by one year and human capitalaccumulation by 19%. Higher-ability children and children from larger families are disadvantaged

and obtain less human capital than compared to an economy without borrowing constraints and

with pure altruism. Although the subsidy increases the human capital, it falls short of the

unconstrained level. And this shortage is even greater for higher-ability children and children

from larger families. From a benefit-cost perspective, the benefit of PROGRESA exceeds the

cost at the current subsidy rate.

The model implies that the subsidy has greater a effect on children from larger families. I test

whether the PROGRESA data are consistent with this implication of my model. I find the effect

of subsidy on school enrollment is greater for the children from larger families. The model also

suggests that parents impure altruism reduces childrens schooling when a borrowing constraint

exists. I reject the hypothesis that the difference in schooling of children by gender is due to

the difference in parental altruism toward them. The effects of the subsidy are not significantly

different by gender when the children is in primary school. Due to the higher subsidy rate for

older female children, the effect is greater for older female than older male children.

40For this reason, PROGRESA impose maximum amount of subsidy to the households, which does not exceeds

three times of the per child amount of subsidy

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My model shows that parents decision on schooling on behalf of their children is not optimal

because it is different from what children would have make if they made on their own. Theborrowing constraint and impure altruism reduces education even further. The government,

therefore, has incentive to intervene to remedy the under-investment. I examine policy exper-

iments that provide varying subsidy rates according to ability and family size. I find that a

larger subsidy for higher-ability children and children from larger families are more effective in

both increasing human capital.

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Appendix

A. Solution for Old Age

For old age, the following assumptions are made: 1) parents have no bequest motive nor are

they able to leave their offspring a debt. 2) There is no uncertainty about their retirement, Q,

and death, D. By imposing these assumptions, the borrowing constraint is no longer binding as

long as the asset at t = T is positive. Then the continuation value of parents b(AT) is equivalent

to

b(AT) = maxCt

Dt=T

tTu(Ct)

s.t.

Dt=T

Ct

(1 + r)tT=

Qt=T

Et

(1 + r)tT+ (1 + r)AT. (A1)

By the Euler equation, u(Ct ) = (1 + r)u(Ct+1), and u

(Ct) = Ct , the following equation

holds for k = 0,...,D T

CT+k = {(1 + r)}k/CT.

Using this equation which holds for optimal consumption, CT is derived as a function of AT

from the budget constraint (equation (A1)), so that

CT

DTk=0

{(1 + r)}k/

(1 + r)k=

Qt=T

Et

(1 + r)tT+ (1 + r)AT

equivalently,

CT =

Qt=T

Et(1+r)tT

+ (1 + r)AT

DTk=0

{(1+r)}k/

(1+r)k

. (A2)

Meanwhile, the Bellman equation for the old age problem is written as

b(AT) = maxCT

u(CT) + b(AT+1)

s.t.

Dt=T

Ct

(1 + r)tT=

Qt=T

Et

(1 + r)tT+ (1 + r)AT. (A3)

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The Envelope condition gives a following equation.

b1(AT) = (1 + r)u(CT).

Then, by replacing CT with equation (A2), the first derivative of the value function of old age

with respect to asset level, b1(AT), is found.

B. Outcomes under a Perfect Capital Market and with Pure Altruism

This section presents the outcome of household assets and childrens human capital accumula-

tion, and time investment paths assuming a perfect capital market and parents pure altruism.

By projecting the outco

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