Moral Hazard and Secured Lending in an Infinitely Repeated Credit Market Game

Abstract

We analyze repeated moral hazard with discounting in a competitive credit market with risk neutrality. Even without learning or risk aversion, long-term bank-borrower relationships are welfare enhancing. The main result is that the borrower obtains an infinite sequence of unsecured loans at below spot market cost following the first good project realization. This contract produces first-best action choices. Prior to this stage, the borrower gets secured loans with above-market borrowing cost. The optimal contract thus displays a selective memory feature, taking only one of two forms at any given point in time, depending on prior history. We consider an infinitely repeated bank-borrower relationship with moral hazard and universal risk neutrality, and explore the ramifications of credit contract duration when the two well-known benefits of long-term contracting-learning and improved risk sharing-are absent. Our objectives are twofold. The first is to analyze an infinitely repeated game with discounting in a credit market context. We thus relate the theory of repeated games to financial intermediation theory, particularly to issues of moral hazard and collateral-related distortions. The second objective is to understand noteworthy stylized facts of credit markets, such as durability in credit relationships, lower borrowing costs for established borrowers, and unsecured loans for established borrowers versus secured loans for newer borrowers. While these practices may be partly due to learning, we show that learning is not essential to rationalize them. Even if information decays rapidly and banks learn nothing about borrowers through time, these aspects of credit contracting arise in a repeated-game context. Our main results are as follows. First, despite universal risk neutrality and the absence of learning, a durable bank relationship benefits the borrower.2 The intuition is that the long-term contracting permitted by a durable relationship enables the bank to efficiently tax and subsidize the borrower through time to reduce the use of (costly) collateral. Second, the average welfare loss (due to moral hazard) per period is positive even as the time horizon goes to infinity. Third, the optimal infinite-horizon contract has the striking property that, following the period