Wright, together with co-author Nobuhiro Kiyotaki, pioneered the use of search theory in monetary economics. The application of search theory to macroeconomics would later be known as matching theory. Search-theoretic models of monetary exchange are based on explicit descriptions of the frictions that make money essential, which contrasts with earlier reduced form approaches to money in macroeconomics, such as putting money in the utility function or imposing cash-in-advance constraints. These earlier ways of modeling money's role did not show explicitly how it helps overcome informational, spatial, or temporal frictions. Search-theoretic models, on the other hand, are based on explicit descriptions of specialization, the pattern of meetings, and the information structure.
Kiyotaki and Wright (1989) was the first attempt to use a search-theoretic model to endogenously determine which commodities would become media of exchange, i.e. commodity money. Later, Kiyotaki and Wright (1991) constructed an alternative search-based model to prove that fiat money can be valued as a medium of exchange even if it has a rate of return that is inferior to other available assets. The application of these theories emerged in Kiyotaki and Wright (1993), when the authors developed a tractable model of the exchange process that captures the "double coincidence of wants problem" in a pure barter setup. In this model, the essential function of money is its role as a medium of exchange. The model can be used to address issues in monetary economics, such as the interaction between specialization and monetary exchange, and the possibility of equilibria with multiple fiat currencies.
A shortcoming of search-theoretic models of money is that these models becomes intractable without very strong assumptions, and are therefore impractical for the analysis of monetary policy. Wright and Ricardo Lagos (2005) attempt to overcome this shortcoming by proposing a more general, yet still tractable, framework for the analysis of monetary policy.