Clearinghouses support financial trades by keeping records of transactions and by providing liquidity through short-term credit that participants clear periodically. We study efficient clearing arrangements for exchanges, where traders must clear with a clearinghouse, and for over-the-counter (OTC) markets, where traders can clear bilaterally. When clearing is costly, it can be efficient to subsidize OTC clearing by charging a higher clearing price for transactions conducted on exchanges. The clearinghouse then operates across both markets. Since clearinghouses offer credit, intertemporal incentives are needed to ensure settlement. When liquidity costs increase, concerns about default lead to a tightening of liquidity provision.

We develop a model of monetary exchange where, as in the random matching literature, agents trade bilaterally and not through centralized markets. Rather than assuming they match exogenously and at random, however, we determine who meets whom as part of the equilibrium. We show how to formalize this process of directed matching in dynamic models with double coincidence problems, and present several examples and applications that illustrate how the approach can be used in monetary theory. Some of our results are similar to those in the random matching literature; others differ significantly. Copyright Econometric Society, 2002.

In Corbae, Temzelides, and Wright (2001) (hereafter, CTW) we proposed a new version of the framework that uses bilateral matching to model the exchange process, and in particular to model the use of money as a medium of exchange. Our version does not have agents meeting exogenously and at random, but rather has agents meeting endogenously. That is, agents are matched at each date subject to a stability condition that requires, roughly, that no agents prefer to be paired with each other or to be unmatched, rather than to be paired with the partners they get along the equilibrium path. While similar in spirit to the cooperative matching concept introduced by David Gale and Lloyd Shapley (1962), we had to generalize their framework to dynamic models because we are interested in monetary economics. Here we present a version of the solution concept in CTW, specialized in some ways but also generalized to include extrinsic uncertainty (sunspots). We then discuss some applications of endogenous matching models to issues that have previously been addressed using random matching, including the existence of sunspot equilibria and the efficiency of inside versus outside money. One of our main goals is to show how endogenous matching is a useful alternative to random matching. This may be interesting to those who think that bilateral trade is a reasonable friction upon which to build a theoretical foundation for monetary economics but perhaps think that random matching is an extreme and unrealistic simplification. Another goal is to provide examples where it makes a difference for substantive results how we model the matching process, and also examples where it does not. I. Endogenous Matching

In this paper, we develop a model of money and reserve‐holding banks. We allow for private liabilities to circulate as media of exchange in a random‐matching framework. Some individuals, which we identify as banks, are endowed with a technology to issue private notes and to keep reserves with a clearinghouse. Bank liabilities are redeemed according to a stochastic process that depends on the endogenous trades. We find conditions under which note redemptions act as a force that is sufficient to stabilize note issue by the banking sector.