Schooling Investment and Development

Transcription

1 Schooling Investment and Development Role of Schooling in Development Process, Child Labor and Gender bias Models of schooling and child labor (Human Capital Investment Approach) Reasons for low schooling investment and outcomes in developing countries Policy implications

2 Schooling and Development Education is an important objective of development, as reflected in Amartya Sens capability approach, and in the core values of economic development. It is an important component of growth and development input in the aggregate production function (e.g. Augmented Solow Model, Endogenous Growth Model ). Determines the capacity of societies to develop and absorb new technologies. Important determinant of earnings of individuals.

3 Schooling and Externalities Spill-overs and Externalities: Schooling of one worker may improve productivity of other workers (complementarity in skills), increase dissemination and development of new ideas. Greater education may improve the returns to investments in health. For example, public health programs need knowledge learned in school. Basic hygiene and sanitation may be taught in school. Education needed in training of health personnel These suggest that the social return from schooling may be higher than the private return.

4 Figure 1: Literacy Rates Across Regions

5 Figure 2: Expected Years of Schooling Across Regions Mean Year of Expected Year of Schooling (2010) Schooling (2010)

6 Figure 3: Gender Bias in Schooling

7 Figure 4: Child Labor

8 Figure 5: Returns From Schooling

9 Basic Human Capital Model Two-period model Two-period lived risk-averse individual. There is a financial market and the individual can borrow or save at the gross rate of interest R. Individual invest in its human capital at the price, P, per-unit of human capital input. In the first-period, an individual chooses amount of human capital input, s, and savings, k. Human capital input in the first period increases earnings/human capital in the second period. The human capital function is given by φh(s; A) with h s () > 0 and h ss () < 0, where φ is wage per-unit human capital and A is vector of factors such as ability of individual, quality of schooling.

10 Optimization Problem The individual s problem is subject to max U(c 1) + βu(c 2 ) c 1,c 2,s,k c 1 + Ps + k = y 1 & (1) c 2 = φh(s) + Rk + y 2 (2) where y 1 and y 2 are endowment incomes in period 1 and 2 respectively and 0 < β < 1 is the discount factor. Throughout for notational simplicity, I will suppress A from the human capital function.

11 Optimal Choices The first order conditions are: s : PU c (c 1 ) = βu c (c 2 )φh s (s) & (3) Combining (3) and (4), we have k : U c (c 1 ) = βru c (c 2 ). (4) U c (c 2 )[φh s (s) PR] = 0. (5)

12 Optimal Choice (5) implies that the optimal s is given by φh s (s) = PR. (6) An individual will equate the marginal return from human capital investment to the rate of interest. This also characterizes efficient level of human capital investment.

13 Implications Human capital investment is independent of income levels. Lower is the interest rate, higher will be the human capital investment. Lower is the human capital input cost, higher will be the human capital investment. Higher is wages, φ, higher will be the human capital investment.

14 Borrowing Constraint and Human Capital Investment In the previous model, we have assumed that an individual can freely save or borrow in the financial market. Now suppose that credit-market is imperfect and an individual cannot borrow i.e. k 0. Let us consider the case where the individual would like to borrow, but it cannot borrow. How does it affect human capital investment? In this case, k = 0 & U c (c 1 ) > βru c (c 2 ). (7) Then using (3) and (7), it is straightforward to show that Implications: φh s (s) > PR. (8) Human capital investment is lower compared to the previous case i.e. borrowing-constrained individual will have lower human capital investment. Human capital investment will depend on endowment incomes. In particular, ds dy 1 > 0.

15 Parental Schooling Investment Two-period model A family consists of a parent and a child. Parent is altruistic and cares about the utility of child. Parent has endowment income of y 1 and y 2 in period 1 and 2 respectively. In the first-period, the parent chooses amount of its saving, k, and human capital input for its child, s. In the second period, the parent chooses amount of bequest, b, for its child. Rest of the model remains as before.

16 Parental Optimization Problem The parental problem is to subject to max U(c p c p 1,cp 2,s,k,b 1 ) + βu(cp 2 ) + δβu(c)] c p 1 + Ps + k = y 1 (9) c p 2 = Rs + y 2 b & (10) c = φh(s) + b (11) where δ (0, 1) is the degree of parental altruism and c is consumption of child in the second period. One can allow for consumption by child in the first-period without affecting any of the results.

17 Optimal Choices The first order conditions are: s : PU c (c p 1 ) = βδu c(c)φh s (s); (12) b : U c (c p 2 ) = δu c(c) & (13) k : U c (c p 1 ) = βru c(c p 2 ). (14)

18 Optimal Human Capital Investment Combining (12)-(14), we have U c (c p 2 )[φh s(s) PR] = 0. (15) which implies that the optimal s will be given by φh s (s) = PR. (16) Parent will equate the marginal return from human capital investment to the rate of interest as before. Implications of the model remain as before. In particular, human capital investment is independent of parental income levels.

19 Borrowing Constraint Now suppose that credit-market is imperfect and parent would like to borrow but cannot borrow (i.e. k 0). How does it affect parental choice of human capital investment? In this case, k = 0 & U c (c p 1 ) > βru c(c p 2 ). (17) Then using (12), (13) and (14), one can show that φh s (s) > PR. (18) Parental investment will be lower and higher is the first-period income of parent higher will be the human capital investment.

20 Bequest Constraint Now suppose that there is no imperfection in the credit-market. However, parent instead of leaving bequest to child would like to transfer income from its child (b < 0). But suppose that it cannot do so (i.e. b 0). How does it affect parental choice of human capital investment? In this case, b = 0 & U c (c p 2 ) > δu c(c) & (19) Then using (12), (14) and (19), one can show that φh s (s) > PR. (20) Parental investment will be lower and higher is the first-period income of parent higher will be the human capital investment. This implies that if the future income of parent and its altruism is relatively low parent will under-invest in the human capital of child (potential role for old-age pension).

21 Human Capital Investment and Child Labor We modify the previous model as follows. Suppose that child has one unit of time in the first period which can be used for schooling, s, and child labor, l. The earnings of child in the second period depends on time-spent schooling, s = 1 l. The utility function of parents is given by W p = U(c p 1 ) + 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. c p 1 + Ps + k = y 1 + wl; (22) c p 2 + b = y 2 + Rk & (23) c = b + φh(s). (24)

22 Optimization Since s = 1 l, (24) can be written as c p 1 + (P + W )s + k = y 1. (25) Child labor increases the cost of schooling. The parental optimization problem is subject to (23)-(25) max c p 1,cp 2,s,b,k U(c p 1 ) + βu(cp 2 ) + βδu(c)

23 First Order Conditions s : (P + W )U c (c p 1 ) = βδφu c(c)h s (s) (26) b : U c (c p 2 ) = δu c(c) & (27) k : U c (c p 1 ) = βru c(c p 2 ). (28)

24 Optimal Choices Using (26)-(28) one can easily show that the optimal human capital investment is given by φh s (s) = (P + W )R. (29) Since s = 1 l, (29) will also give us the optimal amount of child labor. Two immediate implications are: (1) possibility of child labor reduces human capital investment; (ii) higher is the wage of child labor, lower will be the human capital investment. If either parent is borrowing constrained or bequest constrained, then human capital investment will be lower and child labor will be higher. In addition, first period endowment income of parent will have a positive effect on human capital investment and a negative effect on child labor.

25 Gender Bias in Human Capital Investment and Child Labor (Kumar 2013) Kumar (2013) extends the previous model by allowing parents to have tow children, one male (m) and one female (f ) to analyze two types of gender biases: (1) Son-Preference: Parents favor sons over daughters. (2) Earnings Function Bias: Women discriminated in the labor market.

26 Importance of Son Preference Son preference is wide-spread in many regions of the world, particularly in Asia and Middle-East (Williamson 1976, Boserup 1980, Behrman 1988). - Large literature on its effects on: fertility and sex-ratio ( Ben-Porath and Welch 1976, Bloom and Grenier 1983, Leung 1991, Clark 2000) and excess mortality 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).

27 Importance of Earnings Function Bias The earning function bias towards male is widely prevalent in both developing and developed countries (e.g. Oaxaca 1973, Neumark 1988, Meng 1998, Blau and Kahn 2000, Weichselbaumer and Winter-Ebmer R. 2005, Ahmed and Maitra 2010). Such bias can arise from price or wage effects or differences in the technology of human capital investment.

28 Gender Differentials in Child Labor 1. Higher incidence and intensity of child labor (including domestic 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 much higher compared to boys (64.8 percent) (Edmonds and Pavcnik 2005). 3. Girls are more likely to work long hours than boys percent of girl worked 20 hours or more per week, while the corresponding percentage for boys was 19.4 percent (Edmonds and Pavcnik 2005).

29 Kumar (2013) Model 1. Integrates two strands of theoretical literature: models of gender bias (Ben-Porath and Welch 1976, Bloom and Grenier 1983, Leung 1991, Behrman, Pollak, and Taubman, 1982, 1986) and models of child labor (Baland and Robinson 2000, Horowitz and Wang 2004) 2. Analyzes the effects of two types of gender bias: son preference and earnings differential on the gender differentials in child labor, schooling and efficiency.

30 Main Results: Gender Differentials in Child Labor and Schooling Proposition 1: In the unconstrained equilibrium case, (i) The time spent in schooling for both male and female children are at efficient level regardless of the form of gender bias. (ii) Pure Son-Preference: The time spent in schooling for both male and female children is equal, s m = s f. But male children have lower child labor levels, l m < l f. (iii) Pure Earnings Function Bias Towards Male: Male children have a higher level of time spent in schooling, s m > s f, and have a lower child labor level, l m < l f.

31 Constrained Equilibrium Proposition 2: The time spent in schooling is inefficiently low for the child whose bequest constraint is binding, b i = 0 for i = m or f. Proposition 3: The time spent in schooling is inefficiently low for both types of children when the borrowing constraint is binding, k = 0.

32 Risks and Human Capital Investment Basic Question: What is the effect of labor market risks on an individual s choice of human capital investment? Let us go back to our basic model and modify one of the assumptions as follows: Suppose that there is uncertainty about future wages. In particular, φ is a random variable with mean φ and variance, σ 2 φ. Now an individual has to choose human capital input, s, under uncertainty.

33 Optimization Problem The risk-averse individual s problem is subject to max U(c 1) + βeu(c 2 ) c 1,c 2,s,k c 1 + Ps + k = y 1 & (30) c 2 = φh(s) + Rs + y 2 (31) where y 1 and y 2 are endowment incomes in period 1 and 2 respectively. β is the discount factor and E is the expectation operator.

34 Optimal Choices The first order conditions are: s : PU c (c 1 ) = βeu c (c 2 )φh s (s) & (32) Combining (32) and (33), we have k : U c (c 1 ) = βreu c (c 2 ). (33) EU c (c 2 )[φh s (s) PR] = 0. (34)

35 Certainty Case Suppose that there is no uncertainty and φ = φ. Then (34) implies that the optimal s will be given by φh s (s) = PR. (35) An individual will equate the marginal return from human capital investment to the rate of interest.

36 Risky Human Capital Investment Variance-Covariance Decomposition: Suppose that X andy are two random variables. Then E(XY ) = E(X)E(Y ) + COV (X, Y ). (36) Now using (36), (34) can be written as EU c (c 2 )[φh s (s) PR] = [φh s (s) PR]EU c (c 2 ) + Cov(U c (c 2 ), φh s (s)) = 0. (37) Now we have [φh s (s) PR]EU c (c 2 ) = Cov(U c (c 2 ), φh s (s)). (38) Since, individual is risk-averse Cov will be negative and φh s (s) > PR. (39) The human capital investment will be lower than the certainty case.

37 Schooling Investment: Empirics Our previous theoretical models identified number of factors which affect schooling investment and outcomes: (1) Parental or Family Income, Attitude, Background and Involvement (2) Credit Market (3) Cost of Schooling (4) Labor Market Returns and its Riskiness, Possibility of Child Labor (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 schooling investment and outcomes: attendance, grade-completed, amount of money spent, amount of time-spent, learning?