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The Optimum Quantity of Money: Theory and Evidence

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Author Info
Casey B. Mulligan
Xavier X. Sala-i-Martin

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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 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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Handle: RePEc:nbr:nberwo:5954

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Find related papers by JEL classification:
E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

References listed on IDEAS
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  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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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.
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  6. V. V. Chari & Lawrence J. Christiano & Patrick J. Kehoe, 1993. "Optimality of the Friedman Rule in Economies with Distorting Taxes," NBER Working Papers 4443, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
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  13. 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.
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  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. [Downloadable!] (restricted)
  15. Peter A. Diamond & J. A. Mirrlees, 1968. "Optimal Taxation and Public Production," Working papers 22, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. 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. [Downloadable!] (restricted)
  17. 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.
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  19. 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. [Downloadable!] (restricted)
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  20. 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. [Downloadable!] (restricted)
  21. Braun, R. Anton, 1994. "How large is the optimal inflation tax?," Journal of Monetary Economics, Elsevier, vol. 34(2), pages 201-214, October. [Downloadable!] (restricted)
  22. Martin Feldstein, 1997. "The Costs and Benefits of Going from Low Inflation to Price Stability," NBER Working Papers 5469, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  23. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-99, July. [Downloadable!] (restricted)
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  24. Sala-i-Martin, X. & Mulligan, C.B., 1992. "U.S. Money Demand: Surprising Cross-Sectional Estimates," Papers 671, Yale - Economic Growth Center.
    Other versions:
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Orazio Attanasio & Luigi Guiso & Tuillo Jappelli, 1998. "The Demand for Money, Financial Innovation, and the Welfare Cost of Inflation: An Analysis with Household Data," NBER Working Papers 6593, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Song Han & Casey B. Mulligan, 2008. "Inflation and the size of government," Review, Federal Reserve Bank of St. Louis, issue May, pages 245-267. [Downloadable!]
    Other versions:
  3. Gary S. Becker & Casey B. Mulligan, 1998. "Deadweight Costs and the Size of Government," NBER Working Papers 6789, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. Michael R. Pakko, 1998. "Dynamic shoe-leather costs in a shopping-time model of money," Working Papers 1998-007, Federal Reserve Bank of St. Louis. [Downloadable!]
  5. Beatrix Paal & Bruce D. Smith, 2001. "The sub-optimality of the Friedman rule and the optimum quantity of money," IEHAS Discussion Papers 0113, Institute of Economics, Hungarian Academy of Sciences. [Downloadable!]
  6. Joseph H. Haslag & Eric R. Young, 1998. "Money Creation, Reserve Requirements, and Seigniorage," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(3), pages 677-698, July. [Downloadable!] (restricted)
    Other versions:
  7. Michael R. Pakko, 1998. "Shoe-leather costs of inflation and policy credibility," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 37-50. [Downloadable!]
  8. Pedro Teles, 2003. "The optimal price of money," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q II, pages 29-39. [Downloadable!]
  9. Fiorella de Fiore, 2000. "Can indeterminacy explain the short-run non-neutrality of money?," Working Paper Series 32, European Central Bank. [Downloadable!]
  10. Matt Klaeffling & Victor Lopez Perez, 2003. "Inflation targets and the liquidity trap," Working Paper Series 272, European Central Bank. [Downloadable!]
  11. Boel, Paola & Camera, Gabriele, 2004. "Efficient Monetary Allocations and the Illiquidity of Bonds," Purdue University Economics Working Papers 1171, Purdue University, Department of Economics. [Downloadable!]
  12. Fiorella de Fiore, 2000. "The optimal inflation tax when taxes are costly to collect," Working Paper Series 38, European Central Bank. [Downloadable!]
  13. William T. Gavin & Finn E. Kydland, 1997. "Endogenous money supply and the business cycle," Working Papers 1995-010, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  14. Robert Dittmar & William T. Gavin & Finn E. Kydland, 2004. "Inflation persistence and flexible prices," Working Papers 2001-010, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  15. James McAndrews & William Roberds, 1999. "A general equilibrium analysis of check float," Staff Reports 84, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  16. Harashima, Taiji, 2007. "The Optimal Quantity of Money Consistent with Positive Nominal Interest Rates," MPRA Paper 1839, University Library of Munich, Germany, revised 19 Feb 2007. [Downloadable!]
  17. Joydeep Bhattacharya & Joseph H. Haslag, 2001. "On the Use of the Inflation Tax When Nondistortionary Taxes Are Available," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 823-841, October. [Downloadable!] (restricted)
    Other versions:
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