Optimal Group Size in Joint Liability Contracts

We develop a model of repeated microcredit lending to study how group size affects optimal group-lending contracts with joint liability. In the setting being studied, a benevolent lender provides microcredit to a group of borrowers to invest in projects. The outcome of each risky project is not observable by the lender; therefore, if some of the borrowers default on their loan repayments, the lender cannot identify strategic default. The group will be entitled to a subsequent loan if total loan obligation is met. We characterize the optimal contract and determine the optimal size of the borrowers’ group endogenously. We find that although joint liability contracts are feasible under a smaller set of parameter values than individual liability contracts, joint liability has positive effects on the borrowers’ repayment amount and welfare. Our analysis also suggests that group size should increase with project risk. Furthermore, we analyze the effects of partial joint liability, less severe punishment, and project correlation on the feasibility and characteristics of joint liability contracts. Our results show that, first, although partial joint liability has a negative effect on the borrowers’ repayment amount and welfare, it can increase the loan ceiling of joint liability when collusion is not as likely, or when borrowers have high discount factors. Second, less severe punishment does not affect the borrowers’ repayment amount or welfare, but decreases the loan ceiling of joint liability. However, these negative effects created by partial joint liability and less severe punishment on the borrowers’ repayment amount, borrowers’ welfare, and loan ceiling can be offset by forming larger groups. Third, we also found that project correlation allows a higher loan ceiling in larger groups.