Competing for Customers: A Search Model of the Market for Unsecured Credit

This paper proposes a quantitative theory of unsecured borrowing via credit cards. We explicitly model key features of credit cards: (i) they are pre-approved lines of credit, (ii) they are long-lasting relationships with endogenous duration. We endogenize duration by modeling explicit frictions of soliciting and screening credit account customers. The calibrated model reproduces the main features of the unsecured credit market in the US: high indebtedness, high bankruptcy rate and high chargeoff rates. Moreover, compared to models based on the standard Eaton and Gersovitz (1981) competition structure, we show that the predictions of the model are improved in important dimensions. These differences are driven by an extra role of credit cards versus short-term loans: credit cards provide more insurance against risks in life due to their long-lasting nature and no repricing after bad shocks.