*Michael Woodford*

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Michael Woodford: Department of Economics, Princeton University, Postal: Princeton University , Princeton, NJ 08544 , USA

**Abstract:** Central banks now generally agree that conventional monetary aggregates are of little use as targets or even indicators for monetary policy, owing to the instability of money demand relations in economies with well-developed financial markets. But monetary theory has provided little guidance for the analysis of policies that are not formulated in terms of a path for the money supply, and a stable money demand relation is generally assumed as a central element of a theoretical analysis. This paper, instead, shows that it is possible to analyze equilibrium inflation determination without any reference to either money supply or demand, as long as one specifies policy in terms of a 'Wicksellian' interest-rate feedback rule. The paper's central result is an approximation theorem, showing the existence, for a simple monetary model, of a well-behaved 'cashless limit' in which the money balances held to facilitate transactions become negligible. The relations that determine equilibrium inflation in the cashless limit also provide a useful approximate account in the case of an economy in which monetary frictions are present, but small. The approximation remains valid in the case of time variation in the monetary frictions, including variation of a kind that may result in substantial instability of money demand in percentage terms. Inflation in the cashless limit is shown to be a function of the gap between the 'natural rate' of interest, determined by the supply of goods and opportunities for intertemporal substitution, and a time-varying parameter of the interest-rate rule indicating the tightness of monetary policy. Inflation can be completely stabilized, in principle, by adjusting the policy parameter so as to track variation in the natural rate. Under such a regime, instability of money demand has little effect upon equilibrium inflation, and need not be monitored by the central bank.

**Keywords:**
interest-rate feedback; cashless limit

62 pages, November 6, 1997

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