By Guido Menzio, Shouyong Shi and Hongfei Sun
Dispersion of money balances among individuals is the basis for a range of policies but it has been abstracted from in monetary theory for tractability reasons. In this paper, we fill in this gap by constructing a tractable search model of money with a non-degenerate distribution of money holdings. We assume search to be directed in the sense that buyers know the terms of trade before visiting particular sellers. Directed search makes the monetary steady state block recursive in the sense that individuals’ policy functions, value functions and the market tightness function are all independent of the distribution of individuals over money balances, although the distribution affects the aggregate activity by itself. Block recursivity enables us to characterize the equilibrium analytically. By adapting lattice-theoretic techniques, we characterize individuals’ policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists. Moreover, we provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate and analyze the properties of this distribution.
There have been several papers in money search that I have featured here recently. This is because this field is evolving fast lately, and this paper is a fine example of that. All models so far do not allow any non-trivial dispersion in money holdings, except for a short period. This paper overcomes this elegantly, and this promises to be very useful for future models.