MSU Development Field Exam May 9, 2008

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1 MSU Development Field Exam May 9, Mother's and Children's Human Capital A household chooses its consumption (c) and human capital of the child (h c ). Assume that there is only one child in each household. Assume that child human capital is produced using maternal time, child time, and maret goods. A mother's home productivity and labor maret productivity are increasing in her human capital at different rates. Therefore, the human capital production function of a child is defined by: h c = h( eh ( hm ) tm, tc, xc ) where t m is maternal home time, t c is child school time, e h ( ) denotes efficiency units of maternal labor in home production, x c is maret purchased inputs to human capital production, h c is child human capital, h m is maternal human capital. Efficiency units of maternal labor in the labor maret are denoted by e m ( ). Mother s wage rate in the labor maret is w m. The child s wage rate in the maret is w c. The household other income is y. The time endowment to each person (mother and child) is T. The price for other consumption is p c and the price for maret inputs to human capital production is p x. (a) Write down the Lagrangian. Identify endogenous variables and exogenous variables. [Note: you may use p tm and p tc as notional prices of maternal time and child time.] (b) Derive the effect of an increase in maternal human capital (h m ) on child human capital (h c ). (c) (d) Assume the income effects are negligible. Find necessary conditions on e h ( ) and e m ( ) for your answer to (b) to be signable. During the Green Revolution in India, there was a substantial increase in women s schooling even in the absence of returns to women s schooling in the labor maret. Interpret this phenomenon based on your answer to (c). Is there any other interpretation that you can suggest?. Returns to Schooling/Birthweight A. Returns to Schooling Between 1973 and 1978, the Indonesian government engaged in one of the largest school construction on record. We would lie to evaluate the effects of the primary school construction on children s educational attainment and earnings. Two factors affect the intensity of the construction program: children s region of birth and their year of birth. The government was targeting low enrollment regions. Therefore, there is substantial variation in program intensity across districts. Further, children who were born in 196 or earlier are 1 or older in 1974, and cannot benefit from the program. Children who were born in 1967 are 7 in Therefore, children born after 1967 can fully benefit from the program. Children attend primary school until age 1. Table A presents means of children s education by cohort and level of program cells. The educational attainment was measured as of There are three age groups: Young (aged to 6 in 1974), Old (aged 1 to 17 in 1974), and Very Old (aged 8 to 4 in 1974). There are two different regions: High (regions with high level of program) and Low (regions with low level of program). 1

2 (a) (b) How would you measure the effect of the program? What are the assumptions for your suggested measure to be an appropriate one? How would you test the assumptions using the information in Table A? Are the assumptions satisfied? According to the suggested measure, was the program effective in increasing educational attainments of the affected children? Grouping the regions into two groups and cohorts into three groups would throw away a lot of information. There are 80 districts in Indonesia, and we now how many schools in each district were built. Also, we have 3 different age groups. Exploiting all the variations, we can run the following regression: y S ij ij 3 = l= 3 = l= ( Pjd il ) γ 1l + c1 + α1 j + β1 + ε ij ( Pjd il ) γ l + c + α j + β + ε ij (1) () where S is the education of an individual i born in district j, in year, y is the logarithm of the j 1995 wage of an individual i, born in district j, in year, is a dummy that indicates whether individual i is age l in 1974, Pj is the number of schools in district j, α 1 j and α j are district of birth fixed effects, β1 and β are cohort of birth fixed effects. What is γ 1l? For what values of l should we see a positiveγ 1l? Under which assumptions do we expect that γ l will tracγ 1l? d il ij (c) Consider the following equation which characterizes the causal effect of education on wages: y ij = d + α + β + S b + η (3) j ij ij where α j and β denote district-of-birth and cohort-of-birth fixed effects, respectively. Assuming that we now all the parameter estimates in (1) and (), can you calculate b? How many different ways do you have in calculating b? (d) What is the main concern in estimating equation (3)? How would you solve this problem? What are the assumptions to be met for your method to produce an unbiased b? B. Returns to Birthweight Consider the following two equations for identical twin births. Equation (4) is the birthweight production function and equation (5) defines the reducedform linear relation between an adult twin s log wage and his or her intrauterine nutrient intae: B = C + C + B (4) j j o ln W α + μ + υ (5) j = 1 ( C j + C ) + α Bo + Z α 3 j

3 Where BBj is the birghweight for twin j in twin pair (household), C j is deviation in nutrient intae for twin j from average nutrient intae of pair, C is nutrient intae common to both twins in pair, o B is common generic endowment to the pair, Z is a vector of exogenous family and community characteristics determining postbirth human capital investment in the twins, μ is the common earnings endowments of the twins, and υ j is a random, twin-specific error. Neither the nutrient inputs nor the endowments are observed. By assumption, C and BBo are correlated and C j is independent of C and o B. (a) The simple difference regression in terms of the observable birth outcome is defined by: ln α + Δυ (6) Δ W j = 1ΔB j j What is the ey identifying assumption in this regression? Suppose that you instead run a cross-sectional regression of the log wage on birthweight for non-identical individuals. Under which assumption both regressions will generate the same results? (b) In Returns to Birthweight, Behrman and Rosenzweig (004) found that birthweight has no significant effect on the adult wage using a cross-sectional regression, whereas the twin difference regression suggests a significant positive effect. Assuming that both the birthweight and earnings endowments positively contribute to earnings ( α, μ >0), what does the result imply regarding the relationship between endowments and nutrient intae (cov(c, B o ), cov (C, μ ) ) and birthweight endowment and earnings endowment (cov(b o, μ ) )? Table A. Means of Education by Cohort and Level of Program Cells Notes: Standard errors are in parenthesis. 3

4 3. Describe the empirical strategy in one of the following three papers: Dean Karlan, Jonathan Zinman. Observing Unobservables: Identifying Information Asymmetries with a Consumer Credit Field Experiment. Woring paper, July 007. Patric Barron, Benjamin Olen. The Simple Economics of Extortion: Evidence from Trucing in Aceh. BREAD Woring Paper 151, May 007. Rafael Di Tella, Ernesto Schargrodsy. The Role of Wages and Auditing during a Cracdown on Corruption in the City of Buenos Aires. Journal of Law and Economics, April 003. Specifically, a) what theory or theories are the authors trying to test, b) what data do they use, and c) what are the details of their identification strategy how do they attempt to avoid potential endogeneity problems and/or omitted variable bias? Finally, d) what results do they show? 4-5. Solve two of the following four analytical questions (i-iv). i. Consider the Maniw,Romer,Weil 199 model. The production function is Y t = Aγ t K t α H t θ N t 1-α-θ, or in per-worer terms, y t = Aγ t t α h t θ, where γ 1 is the (gross) growth rate of technology. The worforce grows at (net) rate n>0: N t = (1+n) t N 0. Capital depreciates at rate δ. The two types of capital/worer evolve according to: Δ t = sy t (n+δ) t, and Δh t = qy t (n+δ)h t, where s and q are the (constant) rates of investment in physical and human capital, respectively. a. Let γ=1. Derive the long-run (i.e. steady-state) capital/worer ratios. Derive the long-run level of income per worer in the economy. Write all answers in terms of s, q, A, n, and δ. b. Let γ>1. What are the growth rates of y t, c t (=C t /N t ), t, and h t on a balanced growth path? How do they depend on the policy parameters of the model, s, q, A, and n? For parts c.-f., discard the assumption of fixed investment rates, s and q. Assume instead the representative household maximizes CRRA utility: U(c t ) = c t 1-σ /(1-σ), σ>0. The household s budget constraint in per-worer terms is: c t + (1+n) t+1 + (1+n)h t+1 y t + (1-δ) t + (1-δ)h t. c. Write down two Euler equations, one for physical capital and one for human capital. If both types of capital are invested in, what must their ratio be? d. On a balanced growth path, what are the growth rates of c t, y t, t, and h t? Let γ=1 for parts e.-f. e. Derive the long-run (i.e. steady-state) capital/worer ratios. Derive the long-run level of income per worer in the economy. How do β, n, and δ affect long-run income? f. Give the endogenous expressions produced by this model for s and q. In other words, in the long-run, what fraction of income is invested in physical capital? Human capital? How do they depend on n, δ, α, θ, and β? Interpret these relationships, including any conflicts with the comparative static answers of part e. 4

5 ii. Consider the following variant of the model from Karlan,Zinman 007 (KZ07). Agents differ by ris-type, p, which is drawn from [p l,p h ], where 0<p l <p h <1. An agent of type p has a project that gives output of either Y(p) (success) or 0 (failure). The probability of success as a function of ris-type p and effort e, π(p,e), is a separable function: π(p,e) = p e 1/, where e [0,1]. Assume that p Y(p) Y, so that expected output is π(p,e)y(p) = e 1/ Y. Cost of effort (non-monetary) is κ e; assume κ = Y /. Agents are ris-neutral and maximize expected income net of effort cost. Besides the effort cost, there is no other opportunity cost of labor. a. Find the first-best effort level, i.e. the effort chosen by an entrepreneur using his own funds. Find the associated first-best payoff (gross of the opportunity cost of capital). How do these quantities depend on ris-type, p? b. Assume instead that the entrepreneur borrows the funds (in a static context, i.e. a one-shot transaction) and owes gross interest rate r when he succeeds and 0 otherwise. What effort level does he exert, and how does it compare to the first-best? How does effort vary with r? How does effort vary with ris-type, p? Give an interpretation for each of these comparative static results. c. Derive the borrower s probability of success π(p,e) as a function of ris-type p, incorporating the borrower s optimal effort choice. Can the probability of success be a decreasing function of ris-type p over [p l,p h ]; what condition must r satisfy for this to be the case? Explain intuitively how it can be possible for the probability of success π(p,e) to decrease as the inherent probability of success, p, rises. d. For a given gross interest rate r, which types of borrowers are excluded (assuming some are), high-p or low-p? Justify your answer explicitly. e. Now, assume there is a repeated relationship between entrepreneur and lender, and that the borrower places a value of B on this relationship. Assume, as do KZ07, that B>r and that the lender ends the relationship (i.e. the borrower forfeits B) whenever the borrower defaults. Thus, the payoff to borrowing is the same as in part b., except an additional payoff B is enjoyed if and only if the project is successful. For a given gross interest rate r, which types of borrowers are excluded (assuming some are), high-p or low-p? Justify your answer explicitly. [Hint: mae sure to remember that e [0,1], i.e. effort is capped at 1.] iii. Consider the occupational choice framewor of Banerjee/Newman (1993, BN93). However, mae the following modifications. There are three technologies. Subsistence requires 1 unit of labor and 0 units of capital and produces an output of u with certainty. Self-employment requires 1 unit of labor and 1 unit of capital and produces net (of the opportunity cost of capital, not of labor costs) output h, m, and l with probabilities π h >0, π m >0, and π l >0, respectively; h>m>l, and assume π h h+π m m+π l l = m, i.e. m is the mean return. Entrepreneurship requires n+1 units of labor (the entrepreneur s plus n 1 worers ) and h>1 units of capital. It produces net (of the opportunity cost of capital, not 5

6 of labor costs) output H and L with probabilities π L >0 and π H >0, respectively; H>L. Let M= π H H+π L L be the mean return. Expected net (of all costs save the individual s labor) payoffs are thus u in subsistence; v in wage labor (where v is the equilibrium wage); m in self-employment; and (M n v) in entrepreneurship, since n worers must be paid v. Define s M/(n+1) and assume that u<m<s. Imagine there is no credit maret, so all investment must be self-financed. Letting G( ) be the wealth distribution, let p L be the size of the lower class, G(1); p M be the size of the middle class, G(h) G(1); and p U be the size of the upper class, 1 G(h). a. Analyze labor supply and labor demand. Give the three possible equilibrium wages and the conditions (on p L, p M, and p U ; ignore nife-edge cases) under which each obtains. Show on a graph of the unit simplex (as in BN93 Figure 3a) the three wage regions. For parts b.-d., assume that the offspring of lower-class subsisters remain in the lower class. Assume that when the wage is at its lowest level, the offspring of wage earners remain lower class; when the wage is at its intermediate level, the offspring of wage earners become middle class; and when the wage is at its highest level, the offspring of wage earners become upper class. Assume that the offspring of the self-employed become lower class if the return is l, middle class if the return is m, and upper class if the return is h. Finally, assume that successful upper class entrepreneurs (return = H) remain in the upper class regardless of the wage; and unsuccessful upper class entrepreneurs (return = L) remain upper class if the wage is at its lowest level, become middle class if the wage is at its intermediate level, and become lower class if the wage is at its highest level. For parts b.-d., continue to ignore nife-edge cases. b. Assuming 1/n < π h /π l, analyze the evolution of the economy as it depends on initial conditions. Specifically, characterize as sharply as possible (via the simplex diagram; explicit formulas not necessary) the long-run outcome of every possible initial combination of (p L, p M, p U ). Give an example where an economy that starts worse off than another in the sense of higher p L, lower p M, and the same p U ends up with strictly higher GDP. c. Assuming π h /π l < π L /n, analyze the evolution of the economy as it depends on initial conditions. Specifically, characterize as sharply as possible (via the simplex diagram; explicit formulas not necessary) the long-run outcome of every possible initial combination of (p L, p M, p U ). Does an example as in part b. exist in this case? If so, give one; if not, justify your answer. d. Can micro-credit (specifically, an intervention that raises p M, lowers p L, and does not change p U ) bring an economy to development, defined as wages being at their highest level? 6

7 iv. Consider the model of Khalil,Lawarree,Yun (007). There the principal s problem is to minimize the cost of providing incentives for the agent to exert effort. If the agent exerts effort, output is high with probability π and low with probability (1 π); if he does not, output is low with certainty. The principal has access to a supervisor that observes the true effort level with probability p and nothing ( ) with probability (1 p). Letting w denote the agent s wage and s the supervisor s wage, the problem is: w h min π w + (1 )[ p( w + 1 s1) + (1 h π, w1, w, w0, s1, s, s0 p)( w + s )] subject to all choice variables (wages to supervisor and agent) being non-negative and π U ( w h ) + (1 π ) pu ( w1 ) + (1 π )(1 p) U ( w ) ϕ pu ( w0 ) + (1 p) U ( w ) (IC a ) Additional constraints may be imposed to eliminate some or all corruption, defined as the supervisor misreporting the signal he observes. a. Modify one aspect of the model: information is soft for both the coalition and the supervisor. That is, the supervisor can report anything he wants regardless of the truth. Show the incentive constraints for the supervisor and the coalition that will guarantee no corruption (i.e. misreporting and/or bribery). b. Derive the least-cost contract that eliminates corruption. Show that it is equivalent to ignoring the supervisor. c. Return to the basic model but consider a different modification: information is hard for both the coalition and the supervisor. Show the incentive constraints for the supervisor and the coalition that will guarantee no corruption (i.e. misreporting and/or bribery). d. Derive the least-cost contract that eliminates corruption. Show that it is equivalent to the contract with a non-corruptible supervisor (and thus cannot be improved upon). 7