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The optimum quantity of money: theory and evidence

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  • Casey B. Mulligan
  • Xavier X. Sala-i-Martin
  • Frederic S. Mishkin
  • Jonas D. M. Fisher

Abstract

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 {\it 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 a optimal nominal interest rate of less than 1\%/year, although that finding is sensitive to the calibration.

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Bibliographic Info

Article provided by Federal Reserve Bank of Cleveland in its journal Proceedings.

Volume (Year): (1997)
Issue (Month): ()
Pages: 687-724

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Handle: RePEc:fip:fedcpr:y:1997:p:687-724

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Keywords: Monetary theory;

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  1. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-71, October.
  2. Faig, Miquel, 1988. "Characterization of the optimal tax on money when it functions as a medium of exchange," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 137-148, July.
  3. V.V. Chari & Lawrence J. Christiano & Patrick J. Kehoe, 1993. "Optimality of the Friedman rule in economies with distorting taxes," Staff Report 158, Federal Reserve Bank of Minneapolis.
  4. Woodford, Michael, 1990. "The optimum quantity of money," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 2, chapter 20, pages 1067-1152 Elsevier.
  5. Casey B. Mulligan, . "The Intertemporal Substitution of Work--What Does the Evidence Say?," University of Chicago - Population Research Center 95-11, Chicago - Population Research Center.
  6. Allan H. Meltzer, 1963. "The Demand for Money: The Evidence from the Time Series," Journal of Political Economy, University of Chicago Press, vol. 71, pages 219.
  7. Robert J. Barro & David B. Gordon, 1984. "Rules, Discretion and Reputation in a Model of Monetary Policy," NBER Working Papers 1079, National Bureau of Economic Research, Inc.
  8. Casey B. Mulligan & Xavier Sala-I-Martin, 1992. "U.S. Money Demand: Surprising Cross-Sectional Estimates," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(2), pages 285-343.
  9. Robert E. Lucas Jr. & Nancy L. Stokey, 1984. "Money and Interest in Cash-In-Advance Economy," Discussion Papers 628, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Casey B. Mulligan & Xavier Sala-i-Martin, 1996. "Adoption of Financial Technologies: Implications for Money Demand and Monetary Policy," NBER Working Papers 5504, National Bureau of Economic Research, Inc.
  11. Robert E. Lucas Jr. & Nancy L. Stokey, 1982. "Optimal Fiscal and Monetary Policy in an Economy Without Capital," Discussion Papers 532, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. King, Robert G., 1988. "Money demand in the United States: A quantitative review," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 29(1), pages 169-172, January.
  13. Karni, Edi, 1973. "The Transactions Demand for Cash: Incorporation of the Value of Time into the Inventory Approach," Journal of Political Economy, University of Chicago Press, vol. 81(5), pages 1216-25, Sept.-Oct.
  14. Kimbrough, Kent P., 1986. "The optimum quantity of money rule in the theory of public finance," Journal of Monetary Economics, Elsevier, vol. 18(3), pages 277-284, November.
  15. Casey B. Mulligan, . "The Demand for Money by Firms: Some Additional Empirical Results," University of Chicago - Population Research Center 97-1, Chicago - Population Research Center.
  16. Lucas, Robert E., 1988. "Money demand in the United States: A quantitative review," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 29(1), pages 137-167, January.
  17. Thomas Mroz, . "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," University of Chicago - Population Research Center 84-8, Chicago - Population Research Center.
  18. Peter A. Diamond & J. A. Mirrlees, 1968. "Optimal Taxation and Public Production," Working papers 22, Massachusetts Institute of Technology (MIT), Department of Economics.
  19. Karni, Edi, 1974. "The Value of Time and the Demand for Money," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 6(1), pages 45-64, February.
  20. Mulligan, Casey B, 1997. "Scale Economies, the Value of Time, and the Demand for Money: Longitudinal Evidence from Firms," Journal of Political Economy, University of Chicago Press, vol. 105(5), pages 1061-79, October.
  21. Martin S. Feldstein, 1997. "The Costs and Benefits of Going from Low Inflation to Price Stability," NBER Chapters, in: Reducing Inflation: Motivation and Strategy, pages 123-166 National Bureau of Economic Research, Inc.
  22. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
  23. Guidotti, Pablo E. & Vegh, Carlos A., 1993. "The optimal inflation tax when money reduces transactions costs : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 31(2), pages 189-205, April.
  24. Braun, R. Anton, 1994. "How large is the optimal inflation tax?," Journal of Monetary Economics, Elsevier, vol. 34(2), pages 201-214, October.
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