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. We report that the different approach to modeling money - reduced-form vs. explicit role - neither induces theoretical nor quantitative differences in results. Given conformity of preferences, technologies and shocks, both models reduce to one difference equation. The equations do not coincide only if price distortions are differentially imposed across models. To illustrate, when cash prices are equally distorted in both models equally large welfare costs of inflation are obtained in each model. Our insight is that if results differ, then this is due to differential assumptions about the pricing mechanism that governs cash transactions, not the explicit microfoundation of money.