Journal of Money, Credit, and Banking

1. Evolution Of Money Search Models

Before giving my general comments on the paper, I think that it would be useful to describe the evolution of monetary search models for those who have not followed recent developments in the literature. In this way, one has a better sense of the contribution made by Aruoba and Wright (2003, this issue of JMCB ).

Most people are familiar with the basic monetary search model developed by Kiyotaki and Wright (1989, 1993), and for many this may be the extent of their knowledge of money search models. In this first generation of models, goods and money are indivisible and agents can only hold one unit of goods or money. The key contribution of the models was to carefully describe the decentralized trading environment that gives rise to a double coincidence of wants problem and to endogenize the decision to accept money as payment for goods and services. In all search models, assumptions regarding anonymity of trading histories and imperfect record keeping mean that credit is not feasible, thus money is "essential" for trade, i.e., better allocations can be achieved through the use of money than without it.

While analyzing the decision to accept money as a medium of exchange does not hinge on indivisibilities or inventory restrictions, other questions such as how [End Page 1111] changes in the money stock affect prices do hinge on these extreme modeling assumptions. Subsequent work by Trejos and Wright (1995) and Shi (1995) loosened the indivisibility restriction on goods but maintained the assumptions on money holdings and decentralized trading. In these second-generation models, goods are perishable and perfectly divisible. Prices will be determined endogenously, and this allows us to analyze how changes in the money stock affect the value of money.

Generation three models loosened the inventory restrictions on money holdings and divisibility of money. The fundamental problem in doing so is that, due to the decentralized nature of exchange, trading histories differ across agents, resulting in heterogeneous money holdings. This means the distribution of money holdings is endogenous and nondegenerate. The standard "representative agent" assumption that all agents hold the same amount of currency cannot be imposed. While some models studied the distribution of money holdings (see Camera and Corbae, 1999, Green and Zhou, 1998, Molico, 1999), Shi (1997) introduced the use of large households composed of a continuum of workers and shoppers to make the distribution degenerate. Household agents go out and trade but at the end of the day come back, pool their money holdings, and divide them up equally among buyers. In his model, trade is still decentralized, but goods and money are perfectly divisible, and there are no arbitrary upper bounds on money holdings for the households. The key contribution is that monetary policy analysis can be carried out in the standard fashion to see how changes in the money growth rate affect equilibrium output, consumption, and welfare.

More recently, Lagos and Wright (2003) have developed an alternative framework to Shi's that also makes the distribution of money holdings degenerate. There are no households, only individuals. In this model, agents spend or acquire money by trading specialized goods in a decentralized search market, then go to a centralized market and trade money for general goods or sell goods for money. An appealing aspect of this model is that Lagos and Wright reintroduce centralized competitive markets for some part of economic activity—an institution near and dear to most economists' hearts. Also, the goods price of money is determined in this market rather than simply being the household's shadow value of money as in Shi. Finally, price formation in their model leads to holdup problems, which significantly affect the quantitative impact of monetary policy.

Aruoba and Wright is the newest generation of money search models. It exploits the centralized market introduced in Lagos-Wright to make...