UA 323

Development Economics

Problem Set 4

Due: April 24th

•  Remember to include your name (and the names of any collaborators) on your independently written-up solutions.

•  Submit your solutions in the format outlined in the submission guide uploaded as part of this problem set. Please note that if you do not comply with the formatting requirements , you might lose points.

•  Before answering each questions, indicate clearly which question you are answering by including the question number (e.g.

3.1, 3.2, etc)

•  Show your work. Include brief and precise explanations of intuition and derivations as appropriate.

•  You should submit both your answers and your code. You have two options: (1) Submit two separate files: one file with your answers (pdf) and one file with your code (. R file); (2) Submit a knitted document (. Rmd knitted to PDF or HTML), where both your code and answers are visible. Option (2) is the safest and rules out any issues with your code not running when grading your problem set.

This problem set if based on the paper “Credit Access, Selection, and Incentives in a Market for Asses-Collateralized Loans: Evidence from Kenya” by William Jack, Michael Kremer, Joost De Laat, and Tavneet Suri (2023). Read the paper and answer the following questions:

1.    What is the key question that the paper tries to answer? Not the practical thing they actually do, but the Big Picture question.

2.    Why is the answer to this question important for understanding how to improve credit  access  in developing countries? Make sure you discuss the trade-off between credit take-up and repayment rates.

3.    Consider the following model of investment choice. Suppose that an individual can choose between a set of possible investments. Each investment is denoted by its probability of success p. Investment p yields a return of R(p) with probability p, and 0 with probability (1-p). Denote the expected return by E(p). Additionally, there are returns from scale to the investments that depend on how much capital k is invested. So, if an individual invests k in project p, the expected returns are F(k)E(p).

3.1 What is the expected return from investment p if the individual invests k units of capital in it?

Assume that the expected return is increasing and concave: E,(p)>0 and E,,(p)<0. Suppose the investor has wealth w. If she wants to invest k, she must borrow k-w. The lender is offering interest rate r. If the borrower  doesn’t  repay,  the  lender  takes  her  deposit w.  The  borrower  chooses  investment p to maximize:

3.2  Take the first order condition, namely take the derivative of this expression with respect to p and set it equal to zero.

3.3  Does the optimal investment p increase or decrease as the interest rate r increases?

3.4  Does the optimal investment p increase or decrease as the deposit w increases?

3.5  What is the intuition for your answers to questions 3.3 and 3.4? Hint: think about the moral hazard problem in credit markets.

4.     Now consider a different model. Suppose that p is a fixed characteristic of an investor: some investors are high success (i.e. they have high p), while other are low success. The lender does not observe the p of different individuals and offers the same credit product to everyone, at interest rate r. Investors can decide whether to take up the loan or not. Assume that, if they don’t take up the loan, their payoff is equal to w (i.e. they keep their wealth). If they take up the loan, their payoff is p[F(k)p - r(k - w)] + (1 - p)0.

4.1 Investors take up the loan when the payoff from taking up the loan is greater than the payoff from not taking up the loan. Write this condition in math terms and solve the inequality in terms of p.

4.2  Does the success rate of individuals who take  up loans p increase or decrease as the interest rate r increases?

4.3  Does the success rate of individuals who take  up loans p increase or decrease as the deposit w increases? Assume that 1/p>r.

4.4  What is the intuition for your answers to questions 4.3 and 4.4? Hint: think about the adverse selection problem in credit markets.

5.     Now, refer to the paper by Jack and co-authors. Explain what strategy the paper uses to detect whether the lack of deposit or guarantors increases moral hazard.

6.     Explain what strategy the paper uses to detect whether the lack of deposit or guarantors increases adverse selection.

7.    On Brightspace, you can find a dataset called KenyaLoans.csv with the data used for the analysis in Jack et al. (2023). The excel file “KenyaLoans Labels contains a description of the variables. In this question, we look at take-up rates.

7.1 Only keep individuals that took part in the Phase 1 of the intervention. Produce a bar graph that shows average loan take-up rates for each of the treatment groups. It should look like the graph  below  (notice that the  numbers  in  my graph  are  incorrect).  Make  sure you  include everyone who was assigned to the treatment, and not just the individuals who took up the loan.

7.2 Does allowing borrowers to use the water pump as collateral increase the take-up rate of the loans? Carefully justify your answer.

7.3 Would you expect higher loans take-up rate under individual or joint liability? Why?

7.4 Does the paper find a difference in loans take-up rate under individual vs. joint liability? Carefully justify your answer.

8.     Now, we look at treatment effects on the probability of default rates and late payments.

8.1 Create a table that shows average default rates and average probability of late payments for each of the treatment groups. For defaults, you will have to create a new variable equal to zero if the debt was fully repaid and equal to one otherwise. Make sure you drop individuals who did not take up the loan. The table  should  look like the one below (notice that the numbers in my table are incorrect).

8.2 Do the numbers in the table you produced for point 8.1 suggest that reducing the deposit requirements or not asking for a guarantor generates moral hazard? Carefully justify your answer.

8.3 Do the numbers in the table you produced for point 8.1 suggest that reducing the deposit requirements or not asking for a guarantor generates adverse selection? Carefully justify your answer.