Ebook A Model of Dynamic Liquidity Contracts
The level of resources of lenders have significant and positive effects on lending and economic activity. As their capital levels fall, banks become more conservative in their lending. During the credit crunch of 1990, banks started cutting back on lending immensely. Limited bank capital relative to the loan demand contributed to restrictive bank lending during the recession of 1990/91. There is a large empirical literature that examines the link between bank capital and lending (see Sharpe for an extensive survey).
There is also a theoretical literature that suggests that higher bank capital tends to increase lending (see Besanko and Kanatas, Thakor, Holmström and Tirole, and Diamond and Rajan). The analyses in Thakor and Holmström and Tirole are most consistent with the findings of the empirical literature. Yet, a proper investigation of these issues necessitates a genuinely dynamic model with endogenous capital constraints on financial intermediaries.
There is also empirical evidence that dynamic bank relationships help borrowers through implicit contracting (see Petersen and Rajan [28], Berger and Udell, Hoshi, Kashyap and Sharsftein). On the theoretical side, Haubrich, Boot, Greenbaum and Thakor are early examples of works to recognize the potential gains from long-term interactions between banks and borrowers. What is missing though is an explicitly dynamic model of liquidity provision generating interesting credit dynamics and rationing which could capture the stylized facts observed in the data.
This paper aims at filling these gaps. We study the nature of long-term liquidity provision between lenders and borrowers in the absence of perfect enforceability and when both parties are financially constrained. To this end, we build an infinite horizon model of long-term lending and borrowing and analyze in what ways liquidity shortages on both sides affect the evolution of the economy and investment activity in particular.
An infinitely-lived, risk neutral borrower (firm or entrepreneur) receives a project every period with some probability. The project requires a certain amount of funds to be invested and has a stochastic return structure. Projects have positive net present value which make them socially desirable to undertake. Moreover, the projects are indivisible and although the borrower has a given endowment every period, it is not sufficient to cover the required investment level.
There is limited liability on the part of the borrower; net payments need to be nonnegative. All these in turn generate a demand for liquidity from the borrower. The problem is that this demand is not always matched by an associated supply of credit since the contracts are not perfectly enforceable. It is possible for the borrower to renege on the contractual clauses and run away with the return on investment. There is no commitment mechanism to prevent the borrower from defaulting. As a consequence, at the optimum, the lender offers incentive-compatible contracts and the borrower is credit constrained.
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