Credit Risk without Commitment

We study economies with credit risk in which, each period, borrowers cannot commit to borrow from only one lender. We extend the analysis in Bizer and DeMarzo (1992) by allowing for multiple borrowing periods. In particular, we remove the exclusive-borrowing- contract assumption from a quantitative model of household bankruptcy a la Chatterjee et al. (2007). We compare equilibrium allocations with and without commitment to exclusive contracts. In contrast with Bizer and DeMarzo (1992), we find that borrowing levels are much lower without commitment. Imposing commitment increases the average debt-to-income ratio in the simulations from 9% to 16%. This is the case because (i) the cost of defaulting is lower without commitment and (ii) only without commitment, an increase in current borrowing levels deteriorates future borrowing opportunities. These effects are not relevant in Bizer and DeMarzo’s (1992) model with a unique borrowing period. In contrast with the standard household bankruptcy model and consistently with the data, the model without commitment features (i) borrowing opportunities that resemble credit lines, (ii) borrowing opportunities that depend on the borrowing history (credit score), (iii) credit rationing, and (iv) a higher dispersion of interest rates across households. Introducing an interest rate limit to deal with the non-exclusivity problem produces ex-ante welfare gains equivalent to a permanent increase in consumption of 0.7%.