This paper studies the effects of monetary policy, in the sense of fully anticipated inflation, on capital formation. The relation between money and capital is a classic issue, going back to Tobin (1965), Sidrauski (1967a,1967b), Stockman (1981), Cooley and Hansen (1989,1991), Gomme (1993), Ireland (1994) and many others. All of these papers adopt reduced$form approaches: they either put money in the utility function or impose cash$in$advance con$ straints, in an attempt to capture implicitly the role of money in the exchange process, but in other respects use frictionless models. An alternative literature on money, going back to Kiy$ otaki and Wright (1989,1993), Aiyagari and Wallace (1991), Shi (1995), Trejos and Wright (1995), Kocherlakota (1998), Wallace (2001) and others, is more explicit about the frictions that make money essential, and in doing so has introduced some new elements into monetary economics, including detailed descriptions of specialization, information, matching, pricing, etc. Our goal is to see how these elements matter for the impact of inflation on investment, and other variables, including welfare. It turns out that modeling microfoundations in more detail does indeed make a difference for the quantitative results.
We build on the two$sector model in Lagos and Wright (2005), where some economic activity takes place in centralized markets and some in decentralized markets. This is useful because, in addition to providing microfoundations for the role of a medium of exchange, decentralized markets allow us to introduce ingredients like stochastic trading opportunities and bargaining, while centralized markets allow us to incorporate capital as in standard growth theory. This contrasts sharply with other attempts to study money and capital in models with frictions, including Shi (1999), Shi and Wang (2006), and Menner (2006), who build on Shi (1997), and Molico and Zhang (2005), who build on Molico (2006). Those models have only decentralized markets. It is much easier to connect with mainstream macro and to incorporate not only capital but other ingredients, like fiscal policy, in a model with some centralized trade. In particular, as a special case, in nonmonetary equilibrium, our model reduces to the textbook growth model, while those mentioned above reduce to something quite different pautarky.