NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

The Optimum Quantity of Money: Theory and Evidence

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

NBER Working Paper No. 5954
Issued in March 1997
NBER Program(s):   EFG   ME

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. The Friedman rule is optimal or not, depending 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 find that it tends to be optimal to tax money more heavily when the interest elasticity of money demand is small. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields an optimal nominal interest rate of less than 1% per year, although that finding is sensitive to the calibration.

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Document Object Identifier (DOI): 10.3386/w5954

Published:

  • Journal of Money, Credit and Banking, Vol. 29, no. 4, part 2 (November 1997): 687-715 ,
  • Casey B. Mulligan & Xavier X. Sala-i-Martin & Frederic S. Mishkin & Jonas D. M. Fisher, 1997. "The optimum quantity of money: theory and evidence," Proceedings, Federal Reserve Bank of Cleveland, pages 687-724.

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