Exploiting Naivete about Self-Control in the Credit Market∗

We develop a model of the credit market where competitive lenders offer long-term contracts specifying a non-linear schedule of possible repayment schedules to borrowers who may differ both in their taste for immediate gratification (β) and their prior beliefs about that taste (β̂). The equilibrium contract to a borrower with given beliefs β̂ is discontinuous: it features an advantageous option involving fast repayment, and a “penalty” for deviating and repaying later. These predictions seem to resemble some salient features of many credit-card and mortgage contracts. For fully sophisticated borrowers (β̂ = β), the discontinuity acts as a commitment device and yields fast repayment. But all other borrowers (β̂ > β), even those with an arbitrarily small amount of naivete, end up delaying repayment despite the penalty, and receive little benefit from commitment. Furthermore, because they believe they will repay early, they underestimate the cost of credit, and hence borrow too much. Non-sophisticated borrowers cross-subsidize sophisticated borrowers, while sophisticated borrowers “discipline” firms by preventing very exploitative contracts. We identify natural conditions under which the above results obtain even if firms observe neither β nor β̂—because all non-sophisticated consumers endogenously choose contracts for which they mispredict their future behavior. Because linear contracts prevent borrowers from discretely misestimating their behavior, requiring credit contracts to have a linear structure can raise social welfare. ∗Preliminary Draft—Exclusively for Circulation at Yale IO Seminar on October 25, 2007. Not for Web Posting! We apologize for the underpolished nature of many parts of this paper, and for missing proofs.