ECON 3650/5650 Problem Set 6 Spring 2023

Turn in via gradescope by 11:59pm on Wednesday, 4/19.

The demand for schooling

Use the two-period model of the schooling decision and your knowledge from this course to answer these questions.

1. Why does the ability to send migrants to urban areas increase the demand for schooling in rural areas?

2. One puzzle in many urban areas is that, despite cheap or free secondary schooling and high returns to secondary education, many teenagers choose to drop out.  Urban dropouts can earn a fairly high wage (compared to rural areas), but they are foregoing large future returns by doing so. Again, using the two- period model, what specific factor causes teenagers to forego large future returns in favor of immediate employment? Can you suggest a policy intervention aimed at teenagers that would address this specific factor directly, i.e. not just trying to overcome it with a conditional cash transfer?  Note:  in lecture, we mostly talked about parents being the decision-makers in schooling decisions. Here, I want you to think of teens as the decision-makers.

Educational policy in general equilibrium

We talked in detail about the Muralidharan and Sundararaman (2015) Indian voucher study. The purpose of the following questions is to think about what can be learned from impact evaluations and whether those findings might change when an intervention is scaled-up and long-lived.

3. What was the paper’s primary finding with respect to learning outcomes and cost-effectiveness?

4. This study took place over the course of four years.  This was long enough to see effects on students’ outcomes, but it wasn’t long enough of a time horizon for structural changes in the market for primary  education.  Furthermore, voucher quantities were limited (hence the use of a lottery). Suppose that the  voucher program were made a permanent law that guaranteed vouchers to all students who wanted one. The voucher would pay for a fixed amount of tuition (say, equal to the typical private school price in the  village prior to the policy, so that in the first year of the program a voucher would cover tuition at most schools). What do you expect will happen to the demand for private schooling when this policy is enacted? Explain.

5. We can’t say for sure, but given the change in demand induced by this program, what is a likely effect of the policy on the number of private schools and the average tuition level charged? Explain. It may help to make a supply and demand graph.

6. We saw in the paper that private school teachers were usually locals who were paid little compared to their public counterparts; this was part of the private schools’cost advantage. Suppose that village-level labor markets for private school teachers are competitive. What happens to the demand for private school teachers, and how does that change in demand affect their wages? In a competitive market, how will this affect the tuition charged by private schools? Explain.

7. This question doesn’t have a clear-cut answer, so points will be given for internally consistent/coherent responses even if I disagree. Give one reason that this proposed voucher law might increase private school quality in the long-run and explain. Then give one reason that this voucher law might decrease private school quality in the long-run and explain.

Evaluating impacts of agricultural technologies

Suppose that a yield-increasing fertilizer is sold in a village. Farmers choose whether to use (adopt) fertilizer or not. A farmer’s profit is only a function of the adoption decision (T = 0 if no adoption, T = 1 if adoption) and a fixed farmer-specific characteristic M. This farmer-specific characteristic takes one of two possible values: for half of the population M = 1, and for half of the population M = 2. The profit function is (T ; M) = 1 + T ∗ (M2 − 1.5). Farmers know the profit function and their own value of M. Each farmer freely chooses whether to adopt or not, according to what maximizes profits.

8. Which farmers adopt and which don’t? Explain.

9. What is the average return to adoption (the average additional profit from adoption compared to non- adoption) for the adopters? Show how you got this number.

10.  Researchers would like to know the returns to adoption for the adopters, like you just found. Since they can’t do an RCT determining who gets access to the fertilizer or not (it’s already freely sold in stores), they settle for a demand-side RCT. They create a list of farmers who did not adopt last year.  This lists everyone you said doesn’t adopt in question 8. Then, they randomize 1/2 of these non-adopting farmers to get discount vouchers (treatment) and the other 1/2 to get no voucher (control). The voucher reduces the price of fertilizer by 1, so that the new profit function faced by treated farmers is (T ; M)  = 1+T ∗(M2 −0.5). The profit function is unchanged for control farmers. Which farmers in the treatment group adopt? Which farmers in the control group adopt? Explain.

11. The impact evaluation compares mean profits between treatment and control groups, subtracting the value of the voucher from the recorded profits for any farmer who used one. This guarantees that differences in profits between groups aren’t coming from the value of the voucher. That is, profits are measured as for everyone instead of . Compute this difference in mean profits between treatment and control groups. Show how you arrived at this number.