Debt Contracts with Short-Term Commitment

This paper analyzes the role of short-term commitment by the lender in a dynamic relationship where the borrower cannot be legally forced to make repayments. I show that short-term commitment can decrease social welfare compared to both the full and no-commitment cases considered by most of the literature. I show that the size of investment is positively related to the borrower's income. In addition, both underinvestment and overinvestment can occur in equilibrium. I also introduce the borrower's outside option and do comparative statics with respect to it. I show that the social welfare is non-monotonic in the borrower's outside option. If the borrower's outside option is interpreted as a measure of competitiveness of the credit market, this implies that an increase in the strength of competition has an ambiguous effect on welfare. Furthermore, numerical results suggest that as the outside option of the borrower increases, the renegotiation-proof equilibria converge to the Markov equilibrium, where the agents' strategies depend only on the borrower's liquidity. That is, the welfare gain from using complicated history-dependent strategies instead of simple Markov strategies is small when the borrower's outside option is high.