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The Optimum Quantity of Money: Theory and Evidence

  • Casey B. Mulligan
  • 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. 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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5954.

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Date of creation: Mar 1997
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Publication status: published as Journal of Money, Credit and Banking, Vol. 29, no. 4, part 2 (November 1997): 687-715
Handle: RePEc:nbr:nberwo:5954
Note: EFG ME
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  1. Braun, R. Anton, 1994. "How large is the optimal inflation tax?," Journal of Monetary Economics, Elsevier, vol. 34(2), pages 201-214, October.
  2. 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.
  3. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
  4. 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.
  5. 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.
  6. 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.
  7. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Casey B. Mulligan, 1997. "The demand for money by firms: some additional empirical results," Discussion Paper / Institute for Empirical Macroeconomics 125, Federal Reserve Bank of Minneapolis.
  13. Barro, Robert J., 1979. "On the Determination of the Public Debt," Scholarly Articles 3451400, Harvard University Department of Economics.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. Peter A. Diamond & J. A. Mirrlees, 1968. "Optimal Taxation and Public Production," Working papers 22, Massachusetts Institute of Technology (MIT), Department of Economics.
  22. Martin Feldstein, 1996. "The Costs and Benefits of Going from Low Inflation to Price Stability," NBER Working Papers 5469, National Bureau of Economic Research, Inc.
  23. Mulligan, Casey B & Sala-i-Martin, Xavier, 1996. "Adoption of Financial Technologies: Implications for Money Demand and Monetary Policy," CEPR Discussion Papers 1358, C.E.P.R. Discussion Papers.
  24. 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.
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