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The sub-optimality of the Friedman rule and the optimum quantity of money

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Author Info
Beatrix Paal () (Department of Economics, Landau Building Stanford University, Stanford)
Bruce D. Smith () (Department of Economics,University of Texas, Austin)

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Abstract

According to the logic of the Friedman rule, the opportunity cost of holding money faced by private agents should equal the social cost of creating additional fiat money. Thus nominal rates of interest should be zero. This logic has been shown to be correct in a number of contexts, with and without various distortions. In practice, however, economies that have confronted very low nominal rates of interest over extended periods have been viewed as performing very poorly rather than as performing very well. Examples include the U.S. during the Great Depression, or Japan during the last decade. Indeed economies experiencing low nominal interest rates have often suffered severe and long-lasting recessions. This observation suggests that the logic of the Friedman rule needs to be reassessed. We consider the possibility that low nominal rates of interest imply that fiat money is a good asset. As a result, agents are induced to hold an excessive amount of savings in the form of money, and a suboptimal amount of savings in other, more productive forms. Hence low nominal interest rates can lead to low rates of investment and, in an endogenous growth model, to low rates of real growth. This is a cost of following the Friedman rule. Benefits of following the Friedman rule include the possibility that banks will provide considerable liquidity, reducing the cost of transactions that require cash. With this trade-off, we describe conditions under which the Friedman rule is and is not optimal. Finally, our model predicts that excessively high rates of inflation, and nominal rates of interest, are detrimental to growth. This implication of the model, which is consistent with observation, in turn implies that there is a nominal rate of interest that maximizes an economy’s real growth rate. We characterize this interest rate, and we describe when it is and is not optimal to drive the nominal rate of interest to its growth maximizing level.

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Paper provided by Institute of Economics, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 0113.

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Length: 38 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:has:discpr:0113

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References listed on IDEAS
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. Smith, Bruce D, 1991. "Interest on Reserves and Sunspot Equilibria: Friedman's Proposal Reconsidered," Review of Economic Studies, Blackwell Publishing, vol. 58(1), pages 93-105, January. [Downloadable!] (restricted)
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  2. David K. Levine, 1991. "Asset Trading Mechanisms and Expansionary Policy," Levine's Working Paper Archive 43, David K. Levine. [Downloadable!]
  3. Bruno, Michael & Easterly, William, 1998. "Inflation crises and long-run growth," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 3-26, February. [Downloadable!] (restricted)
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  4. Correia, Maria Isabel Horta & Teles, Pedro, 1996. "Is the Friedman Rule Optimal When Money is an Intermediate Good?," CEPR Discussion Papers 1287, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  5. Schreft, Stacey L & Smith, Bruce D, 1998. "The Effects of Open Market Operations in a Model of Intermediation and Growth," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 519-50, July. [Downloadable!] (restricted)
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  6. Bhattacharya, Joydeep, et al, 1997. "Monetary, Fiscal, and Reserve Requirement Policy in a Simple Monetary Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 321-50, May.
  7. Azariadis, Costas & Smith, Bruce D, 1996. " Private Information, Money, and Growth: Indeterminacy, Fluctuations, and the Mundell-Tobin Effect," Journal of Economic Growth, Springer, vol. 1(3), pages 309-32, September.
  8. Schreft, Stacey L. & Smith, Bruce D., 1997. "Money, Banking, and Capital Formation," Journal of Economic Theory, Elsevier, vol. 73(1), pages 157-182, March. [Downloadable!] (restricted)
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  9. Bruce Champ & Bruce D. Smith & Stephen D. Williamson, 1996. "Currency Elasticity and Banking Panics: Theory and Evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 29(4), pages 828-64, November. [Downloadable!] (restricted)
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  10. Mitsui, Toshihide & Watanabe, Shinichi, 1989. "Monetary growth in a turnpike environment," Journal of Monetary Economics, Elsevier, vol. 24(1), pages 123-137, July. [Downloadable!] (restricted)
  11. Levine, David K., 1991. "Asset trading mechanisms and expansionary policy," Journal of Economic Theory, Elsevier, vol. 54(1), pages 148-164, June. [Downloadable!] (restricted)
  12. Williamson, Stephen D., 1996. "Sequential markets and the suboptimality of the Friedman rule," Journal of Monetary Economics, Elsevier, vol. 37(3), pages 549-572, June. [Downloadable!] (restricted)
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  13. Townsend, Robert M, 1987. "Economic Organization with Limited Communication," American Economic Review, American Economic Association, vol. 77(5), pages 954-71, December. [Downloadable!] (restricted)
  14. Mulligan, Casey B & Sala-I-Martin, Xavier X, 1997. "The Optimum Quantity of Money: Theory and Evidence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 687-715, November.
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  15. Bencivenga, Valerie R & Smith, Bruce D, 1992. "Deficits, Inflation, and the Banking System in Developing Countries: The Optimal Degree of Financial Repression," Oxford Economic Papers, Oxford University Press, vol. 44(4), pages 767-90, October. [Downloadable!] (restricted)
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  16. Hornstein, Andreas & Krusell, Per, 1993. "Money and Insurance in a Turnpike Environment," Economic Theory, Springer, vol. 3(1), pages 19-34, January.
  17. Bullard, James & Keating, John W., 1995. "The long-run relationship between inflation and output in postwar economies," Journal of Monetary Economics, Elsevier, vol. 36(3), pages 477-496, December. [Downloadable!] (restricted)
  18. Bryant, John & Wallace, Neil, 1984. "A Price Discrimination Analysis of Monetary Policy," Review of Economic Studies, Blackwell Publishing, vol. 51(2), pages 279-88, April. [Downloadable!] (restricted)
  19. Ireland, Peter N, 1996. "The Role of Countercyclical Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 104(4), pages 704-23, August. [Downloadable!] (restricted)
  20. Bhattacharya, Joydeep & Huybens, E. & Guzman, M. & Smith, B.D., 2002. "Monetary, Fiscal, and Bank Regulatory Policy in a Simple Monetary Growth Model," Staff General Research Papers 5136, Iowa State University, Department of Economics.
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  21. Marco Espinosa & Chong K. Yip, 2000. "Government Financing in an Endogenous Growth Model with Financial Market Restrictions," Departmental Working Papers _118, Chinese University of Hong Kong, Department of Economics.
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  22. Sangmok Choi & Bruce D. Smith & John H. Boyd, 1996. "Inflation, financial markets and capital formation," Proceedings, Federal Reserve Bank of St. Louis, issue May, pages 9-35. [Downloadable!]
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  23. Chari, V. V. & Christiano, Lawrence J. & Kehoe, Patrick J., 1996. "Optimality of the Friedman rule in economies with distorting taxes," Journal of Monetary Economics, Elsevier, vol. 37(2-3), pages 203-223, April. [Downloadable!] (restricted)
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  24. Diamond, Douglas W & Dybvig, Philip H, 1983. "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 401-19, June. [Downloadable!] (restricted)
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  25. Mohsin S. Khan & A. Senhadji Semlali, 2000. "Threshold Effects in the Relationship Between Inflation and Growth," IMF Working Papers 00/110, International Monetary Fund.
  26. King, Robert G & Levine, Ross, 1993. "Finance and Growth: Schumpeter Might Be Right," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 717-37, August. [Downloadable!] (restricted)
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  27. Greenwood, Jeremy & Smith, Bruce D., 1997. "Financial markets in development, and the development of financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 21(1), pages 145-181, January. [Downloadable!] (restricted)
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  28. 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. [Downloadable!] (restricted)
Full references

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. Bruce D. Smith & Mohsin S. Khan & A. Senhadji Semlali, . "Inflation and Financial Depth," IMF Working Papers 01/44, International Monetary Fund. [Downloadable!]
    Other versions:
  2. Joseph H. Haslag & Antoine Martin, 2005. "Optimality of the Friedman rule in an overlapping generations model with spatial separation," Staff Reports 225, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  3. Joydeep Bhattacharya & Joseph Haslag & Antoine Martin & Rajesh Singh, 2005. "Who is afraid of the Friedman rule?," Staff Reports 208, Federal Reserve Bank of New York. [Downloadable!]
    Other versions:
  4. Stacey L. Schreft & Bruce D. Smith, 2003. "The social value of risk-free government debt," Research Working Paper RWP 03-02, Federal Reserve Bank of Kansas City. [Downloadable!]
    Other versions:
  5. Joe Haslag & Antoine Martin, 2003. "Optimality of the Friedman Rule in Overlapping Generations Model with Spatial Separation," Working Papers 0306, Department of Economics, University of Missouri. [Downloadable!]
    Other versions:
  6. Bhattacharya, Joydeep & Singh, Rajesh, 2006. "On the Usefulness of the Constrained Planning Problem in a Model of Money," Staff General Research Papers 12660, Iowa State University, Department of Economics. [Downloadable!]
  7. Bhattacharya, Joydeep & Singh, Rajesh, 2005. "Optimal Choice of Monetary Instruments in an Economy with Real and Liquidity Shocks," Staff General Research Papers 12355, Iowa State University, Department of Economics. [Downloadable!]
  8. Max Gillman & Mark N Harris & Michal Kejak, 2007. "The Interaction of Inflation and Financial Development with Endogenous Growth," Money Macro and Finance (MMF) Research Group Conference 2006 29, Money Macro and Finance Research Group. [Downloadable!]
  9. Joydeep Bhattacharya & Joseph Haslag & Antoine Martin, 2005. "The Tobin effect and the Friedman rule," Staff Reports 224, Federal Reserve Bank of New York. [Downloadable!]
  10. Joseph H. Haslag & Joydeep Bhattacharya & Antoine Martin, 2004. "Sub-Optimality of the Friedman Rule in Townsends Turnpike and Limited Communication Models of money: Do finite lives and initial dates matter?," Working Papers 0415, Department of Economics, University of Missouri, revised 21 Dec 2004. [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. Huberto M. Ennis & Todd Keister, 2003. "Economic growth, liquidity, and bank runs," Working Paper 03-01, Federal Reserve Bank of Richmond. [Downloadable!]
    Other versions:
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