Lecture 1Schooling Investment and Development

I Role of Schooling in Development Process, Child Laborand Gender bias

I Models of schooling and child labor (Human CapitalInvestment Approach)

I Reasons for low schooling investment and outcomes indeveloping countries

I Policy implications

Schooling and Development

I Education is an important objective of development, asreflected in Amartya Sens capability approach, and in thecore values of economic development.

I It is an important component of growth and development -input in the aggregate production function (e.g. AugmentedSolow Model, Endogenous Growth Model ).

I Determines the capacity of societies to develop and absorbnew technologies.

I Important determinant of earnings of individuals.

Schooling and Externalities

I Spill-overs and Externalities: Schooling of one worker mayimprove productivity of other workers (complementarity inskills), increase dissemination and development of newideas.

I Greater education may improve the returns to investmentsin health. For example, public health programs needknowledge learned in school. Basic hygiene and sanitationmay be taught in school. Education needed in training ofhealth personnel

These suggest that the social return from schooling may behigher than the private return.

Figure 1: Literacy Rates Across Regions

Figure 2: Expected Years of Schooling AcrossRegions

Mean Year of Expected Year of

Schooling (2010) Schooling (2010)

Figure 3: Gender Bias in Schooling

Figure 4: Child Labor

Figure 5: Returns From Schooling

Basic Human Capital Model

I Two-period modelI Two-period lived risk-averse individual.I There is a financial market and the individual can borrow or

save at the gross rate of interest R.I Individual invest in its human capital at the price, P,

per-unit of human capital input.I In the first-period, an individual chooses amount of human

capital input, s, and savings, k .I Human capital input in the first period increases

earnings/human capital in the second period. The humancapital function is given by φh(s;A) with hs() > 0 andhss() < 0, where φ is wage per-unit human capital and A isvector of factors such as ability of individual, quality ofschooling.

Optimization Problem

The individual’s problem is

maxc1,c2,s,k

U(c1) + βU(c2)

subject to

c1 + Ps + k = y1 & (1)

c2 = φh(s) + Rk + y2 (2)

where y1 and y2 are endowment incomes in period 1 and 2respectively and 0 < β < 1 is the discount factor. Throughoutfor notational simplicity, I will suppress A from the humancapital function.

Optimal Choices

The first order conditions are:

s : PUc(c1) = βUc(c2)φhs(s) & (3)

k : Uc(c1) = βRUc(c2). (4)

Combining (3) and (4), we have

Uc(c2)[φhs(s)− PR] = 0. (5)

Optimal Choice

(5) implies that the optimal s is given by

φhs(s) = PR. (6)

An individual will equate the marginal return from human capitalinvestment to the rate of interest. This also characterizesefficient level of human capital investment.

Implications

I Human capital investment is independent of income levels.

I Lower is the interest rate, higher will be the human capitalinvestment.

I Lower is the human capital input cost, higher will be thehuman capital investment.

I Higher is wages, φ, higher will be the human capitalinvestment.

Borrowing Constraint and Human Capital InvestmentIn the previous model, we have assumed that an individual canfreely save or borrow in the financial market. Now suppose thatcredit-market is imperfect and an individual cannot borrow i.e.k ≥ 0. Let us consider the case where the individual would liketo borrow, but it cannot borrow. How does it affect humancapital investment? In this case,

k = 0 & Uc(c1) > βRUc(c2). (7)

Then using (3) and (7), it is straightforward to show that

φhs(s) > PR. (8)

Implications:I Human capital investment is lower compared to the

previous case i.e. borrowing-constrained individual willhave lower human capital investment.

I Human capital investment will depend on endowmentincomes. In particular, ds

dy1> 0.

Parental Schooling Investment

I Two-period modelI A family consists of a parent and a child.I Parent is altruistic and cares about the utility of child.I Parent has endowment income of y1 and y2 in period 1 and

2 respectively.I In the first-period, the parent chooses amount of its saving,

k , and human capital input for its child, s.I In the second period, the parent chooses amount of

bequest, b, for its child.

Rest of the model remains as before.

Parental Optimization Problem

The parental problem is to

maxcp

1 ,cp2 ,s,k ,b

U(cp1 ) + βU(cp

2 ) + δβU(c)]

subject to

cp1 + Ps + k = y1 (9)

cp2 = Rk + y2 − b & (10)

c = φh(s) + b (11)

where δ ∈ (0,1) is the degree of parental altruism and c isconsumption of child in the second period. One can allow forconsumption by child in the first-period without affecting any ofthe results.

Optimal Choices

The first order conditions are:

s : PUc(cp1 ) = βδUc(c)φhs(s); (12)

b : Uc(cp2 ) = δUc(c) & (13)

k : Uc(cp1 ) = βRUc(c

p2 ). (14)

Optimal Human Capital Investment

Combining (12)-(14), we have

Uc(cp2 )[φhs(s)− PR] = 0. (15)

which implies that the optimal s will be given by

φhs(s) = PR. (16)

Parent will equate the marginal return from human capitalinvestment to the rate of interest as before. Implications of themodel remain as before. In particular, human capital investmentis independent of parental income levels.

Borrowing Constraint

Now suppose that credit-market is imperfect and parent wouldlike to borrow but cannot borrow (i.e. k ≥ 0). How does it affectparental choice of human capital investment? In this case,

k = 0 & Uc(cp1 ) > βRUc(c

p2 ). (17)

Then using (12), (13) and (14), one can show that

φhs(s) > PR. (18)

Parental investment will be lower and higher is the first-periodincome of parent higher will be the human capital investment.

Bequest Constraint

Now suppose that there is no imperfection in the credit-market.However, parent instead of leaving bequest to child would liketo transfer income from its child (b < 0). But suppose that itcannot do so (i.e. b ≥ 0). How does it affect parental choice ofhuman capital investment? In this case,

b = 0 & Uc(cp2 ) > δUc(c) & (19)

Then using (12), (14) and (19), one can show that

φhs(s) > PR. (20)

Parental investment will be lower and higher is the first-periodincome of parent higher will be the human capital investment.This implies that if the future income of parent and its altruismis relatively low parent will under-invest in the human capital ofchild (potential role for old-age pension).

Human Capital Investment and Child LaborWe modify the previous model as follows. Suppose that childhas one unit of time in the first period which can be used forschooling, s, and child labor, l . The earnings of child in thesecond period depends on time-spent schooling, s = 1− l . Theutility function of parents is given by

W p = U(cp1 ) + βU(cp

2 ) + βδU(c). (21)

Rest of the model remains as before.

The Budget Constraints

Let W be wage per unit of child labor.

cp1 + Ps + k = y1 + wl ; (22)

cp2 + b = y2 + Rk & (23)

c = b + φh(s). (24)

Optimization

Since s = 1− l , (24) can be written as

cp1 + (P + W )s + k = y1. (25)

Child labor increases the cost of schooling.The parental optimization problem is

maxcp

1 ,cp2 ,s,b,k

U(cp1 ) + βU(cp

2 ) + βδU(c)

subject to (23)-(25)

First Order Conditions

s : (P + W )Uc(cp1 ) = βδφUc(c)hs(s) (26)

b : Uc(cp2 ) = δUc(c) & (27)

k : Uc(cp1 ) = βRUc(c

p2 ). (28)

Optimal Choices

Using (26)-(28) one can easily show that the optimal humancapital investment is given by

φhs(s) = (P + W )R. (29)

Since s = 1− l , (29) will also give us the optimal amount ofchild labor. Two immediate implications are: (1) possibility ofchild labor reduces human capital investment; (ii) higher is thewage of child labor, lower will be the human capital investment.

If either parent is borrowing constrained or bequestconstrained, then human capital investment will be lower andchild labor will be higher. In addition, first period endowmentincome of parent will have a positive effect on human capitalinvestment and a negative effect on child labor.

Risks and Human Capital Investment

Basic Question: What is the effect of labor market risks on anindividual’s choice of human capital investment?

Let us go back to our basic model and modify one of theassumptions as follows:

Suppose that there is uncertainty about future wages. Inparticular, φ is a random variable with mean φ and variance, σ2

φ.Now an individual has to choose human capital input, s, underuncertainty.

Optimization Problem

The risk-averse individual’s problem is

maxc1,c2,s,k

U(c1) + βEU(c2)

subject to

c1 + Ps + k = y1 & (30)

c2 = φh(s) + Rs + y2 (31)

where y1 and y2 are endowment incomes in period 1 and 2respectively. β is the discount factor and E is the expectationoperator.

Optimal Choices

The first order conditions are:

s : PUc(c1) = βEUc(c2)φhs(s) & (32)

k : Uc(c1) = βREUc(c2). (33)

Combining (32) and (33), we have

EUc(c2)[φhs(s)− PR] = 0. (34)

Certainty Case

Suppose that there is no uncertainty and φ = φ. Then (34)implies that the optimal s will be given by

φhs(s) = PR. (35)

An individual will equate the marginal return from human capitalinvestment to the (gross) rate of interest as before.

Risky Human Capital Investment

Variance-Covariance Decomposition: Suppose that X andYare two random variables. Then

E(XY ) = E(X )E(Y ) + COV (X ,Y ). (36)

Now using (36), (34) can be written as

EUc(c2)[φhs(s)− PR] =

[φhs(s)− PR]EUc(c2) + Cov(Uc(c2), φhs(s)) = 0 (37)

Risky Human Capital Investment

Then (37) implies that

[φhs(s)− PR]EUc(c2) = −Cov(Uc(c2), φhs(s)). (38)

Since, individual is risk-averse Cov will be negative and

φhs(s) > PR. (39)

The human capital investment will be lower than the certaintycase.

Intuition: As the human capital becomes risky, individualsreadjust their portfolio towards safer asset k .

Gender Bias in Human Capital Investment and ChildLabor

Reference: Kumar, Alok (2013), “Preference Based Vrs MarketBased Discrimination: Implications for Gender Differentials inChild Labor and Schooling”, Journal of DevelopmentEconomics, 105, 64-68.

Kumar (2013) extends the human capital/child labor model byallowing parents to have two children, one male (m) and onefemale (f ) to analyze two types of gender biases:

(1) Son-Preference: Parents favor sons over daughters.

(2) Earnings Function Bias: Women discriminated in the labormarket.

Importance of Son Preference

– Son preference is wide-spread in many regions of the world,particularly in Asia and Middle-East (Williamson 1976, Boserup1980, Behrman 1988).

- Large literature on its effects on:

– fertility and sex-ratio ( Ben-Porath and Welch 1976, Bloomand Grenier 1983, Leung 1991, Clark 2000) and excessmortality among female infants (Das Gupta 1987, Sen 1990)

– differential access to health (Chen et. al. 1982, Pande, R.2003), nutrition (Sen and Sengupta 1983, Behrman 1988,Hazarika 2000)

– education (Behrman, Pollak, and Taubman, 1982, 1986).

Importance of Earnings Function Bias

– The earning function bias towards male is widely prevalent inboth developing and developed countries (e.g. Oaxaca 1973,Neumark 1988, Meng 1998, Blau and Kahn 2000,Weichselbaumer and Winter-Ebmer R. 2005, Ahmed andMaitra 2010).

– Such bias can arise from price or wage effects or differencesin the technology of human capital investment.

Gender Differentials in Child Labor

1. Higher incidence and intensity of child labor (includingdomestic work) for female children than male children(Edmonds and Pavcnik 2005, Edmonds 2007, Allais 2009).

2. The incidence of child labor for girls (72.1 percent) is muchhigher compared to boys (64.8 percent) (Edmonds andPavcnik 2005).

3. Girls are more likely to work long hours than boys. 22.1percent of girl worked 20 hours or more per week, whilethe corresponding percentage for boys was 19.4 percent(Edmonds and Pavcnik 2005).

Basic Features of the Model

I Unitary households consisting of parents and two children— one male (m) and one female (f )

I Altruistic parents

I While parents care about both children, they may put moreweight on the utility of their male children (son preference)

I Children incur disutility from both working and schooling

Basic Features of the Model (Continued)

The utility function of parents is given by

W p = U(cp1 ) + U(cp

2 ) + δmW m + δf W f (40)

with δm ≥ δf .Utility functions of children are given by

W m = U(cm) + V (1− lm − sm) & (41)

W f = U(cf ) + V (1− l f − sf ). (42)

The Budget Constraints

Normalize the rate of return on savings and wages perefficiency unit of labor to one.

cp1 + k = y1 + lm + l f ; (43)

cp2 + bm + bf = y2 + k ; (44)

cm = bm + hm(sm); (45)

cf = bf + hf (sf ). (46)

Optimization Problem

The parental optimization problem is

maxcp

1 ,cp2 ,l

m,l f ,sm,sf ,bm,bf ,k

2∑t=1

U(cpt ) +

∑i=m,f

δi [U(c i) + V (1− l i − si)]

subject to (43)-(46)

First Order Conditions

l i : Uc(cp1 ) = −δ

iVl(1− l i − si), for i = m, f ; (47)

si : Uc(c i)his(s

i) = −Vs(1− l i − si), for i = m, f ; (48)

bi : Uc(cp2 ) = δiUc(c i), for i = m, f ; (49)

k : Uc(cp1 ) = Uc(c

p2 ). (50)

Main Results

First-Order conditions imply that

δmVl(1− lm − sm) = δf Vl(1− l f − sf ). (51)

Proposition 1: Son-Preference (δm > δf ) leads to malechildren having a higher amount of leisure than female childrenand

lm + sm < l f + sf . (52)

In the absence of son-preference (δm = δf ), both male andfemale children have the same amount of leisure andlm + sm = l f + sf .

Main Results: Two Cases

1. Son-preference case: δm > δf & hm(sm) ≡ hf (sf ) (noearnings differentials)

2. Earnings function bias towards male Case: δm = δf &For any sm = sf , hm(sm) > hf (sf ) and hm

s (sm) > hfs(sf ).

The time spent in schooling is characterized by

hms (sm) = hf

s(sf ) = 1.

Implications

1. In the case of son-preference, the time spent in schoolingfor both male and female children is equal, but malechildren have lower child labor levels.

2. In the case of earnings function bias towards male, malechildren receive more schooling and work less.

Schooling Investment: Empirics

Our previous theoretical models identified number of factorswhich affect schooling investment and outcomes:(1) Parental or Family Income, Attitude, Background andInvolvement(2) Credit Market(3) Cost of Schooling(4) Labor Market Returns and its Riskiness, Possibility of ChildLabor(5) Availability and Quality of Schooling(6) Social Norms and Discrimination(7) Ability and Motivation of Child

Other important issue is how do we measure schoolinginvestment and outcomes: attendance, grade-completed,amount of money spent, amount of time-spent, learning?