Problem
Consider a bank extending similar loans to people in two identical villages, each of them inhabited by 100 households. All households in both villages are identical, and each loan is worth $100. With a $100 loan, a household can invest in a two-year project. Ex ante, the project succeeds with probability 0.75, in which case the household can get a gross return of $240. If the project fails, which occurs with probability 0.25, the household doesn't get anything. Assume that the cost of extending each individual loan is $20, and that the bank just wants to break even. Individuals are protected by limited liability.
a. What would be the gross interest rate upon signing the loan contract with a borrower?
b. Now suppose that during the course of the two year project, village 1 has been negatively affected by an unexpected aggregate shock that reduced the project's probability of success to 0.50. What will be the financial self-sufficiency ratio for the bank in this case?
c. Instead, suppose that in village 2, the weather conditions were abnormally better than expected, and that this increased the rate of success in this village to 0.85. What is the financial self-sufficiency ratio for the bank in this village? Can we conclude that the bank's program in village 2 is better than that in village 1? Explain your answer.
d. What would you propose in order to correctly estimate the treatment effect of microfinance in this case? Suppose you have data from an un-shocked third village that is identical to villages 1 and 2 but where there is no access to credit.