The Optimum Quantity of Money: Theory and Evidence

Casey B. Mulligan and Xavier X. Sala-i-Martin


In this paper we propose a simple and general model for computing the Ramsey optimal inflation tax, which includes several models from the previous literature as special cases. We show that it cannot be claimed that the Friedman rule is always optimal (or always non-optimal) on theoretical grounds. For example, we show that Kimbrough's (1986) result in favor of the Friedman rule depends on the particular functional form of his transaction technology. We show that, far from being general, the result in Chari, Christiano and Kehoe (1996) in favor of the Friedman rule and the irrelevance of the interest elasticity depends crucially on their assumptions that there cannot be "scale economies" in the holding of money, that money holdings are infinite when the Friedman rule is followed, and that taxes are not paid with money. On the other hand, we show that Guidotti and Végh's (1993) strong results in favor of the taxation of money come from neglecting the possibility of corner solutions.

The optimality of the Friedman rule depends on conditions related to the shape of various relevant functions. One contribution of this paper is to relate these conditions to measurable variables such as the interest rate or the consumption elasticity of money demand. We find that it tends to be optimal to tax money when there are economies of scale in the demand for money (the scale elasticity is smaller than one) and/or when money is required for the payment of consumption or wage taxes. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields a optimal nominal interest rate of less than 1%/year, although that finding is sensitive to the calibration.

This paper is also circulated as: NBER Working Paper No. 5504, March 1996.

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