Two monetary models with alternating markets

We present a thought-provoking study of two monetary models: the cash-in-advance and the Lagos and Wright (2005) models. The different approaches to modeling money-reduced form versus explicit role-induce neither fundamental theoretical nor quantitative differences in results. Given conformity of preferences, technologies, and shocks, both models reduce to equilibrium difference equations that coincide unless price distortions are differentially imposed on cash prices, across models. Equal distortions support equally large welfare costs of inflation. Performance differences stem from unequal assumptions about the pricing mechanism that governs cash transactions, not the differential modeling of the monetary exchange process.