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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.
Monetary theorists have advanced an intriguing notion: we exchange money to make up for a lack of enforcement, when it is difficult to monitor and sanction opportunistic behaviors. We demonstrate that, in fact, monetary equilibrium cannot generally be sustained when monitoring and punishment limitations preclude enforcement — external or not. Simply put, monetary systems cannot operate independently of institutions — formal or informal — designed to monitor behaviors and sanction undesirable ones. This fundamental result is derived by integrating monetary theory with the theory of repeated games, studying monetary equilibrium as the outcome of a matching game with private monitoring.