By Guido Menzio, Shouyong Shi and Hongfei Sun
We construct and analyze a tractable search model of money with a non-degenerate distribution of money holdings. Analytical tractability comes from modeling decentralized exchange as directed search, which makes the monetary steady state block recursive. 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 and provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate. Moreover, we analyze the properties of this distribution.
There are now several ways in which one can add non-degenerate distributions of money holdings to money search models, and all appear to be reasonably tractable. These are important theoretical developments, as they considerably expand the horizon of the questions that can be asked with money search model. It will be interesting to see what this literature will be able to bring in the next years. The Lagos-Wright model has certainly triggered quite a rush, we will see how this one fares.