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

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  • Beatrix Paal

    (University of Texas at Austin)

  • Bruce D. Smith

    (Department of Economics, University of Texas)

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.

Suggested Citation

  • Beatrix Paal & Bruce D. Smith, 2013. "The sub-optimality of the Friedman rule and the optimum quantity of money," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 911-948, November.
  • Handle: RePEc:cuf:journl:y:2013:v:14:i:3:paal:smith
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    References listed on IDEAS

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    Cited by:

    1. Bhattacharya, Joydeep & Singh, Rajesh, 2006. "On the Usefulness of the Constrained Planning Problem in a Model of Money," Staff General Research Papers Archive 12660, Iowa State University, Department of Economics.
    2. Joydeep Bhattacharya & Joseph Haslag & Antoine Martin & Rajesh Singh, 2008. "Who Is Afraid Of The Friedman Rule?," Economic Inquiry, Western Economic Association International, vol. 46(2), pages 113-130, April.
    3. Stacey Schreft & Bruce Smith, 2008. "The social value of risk-free government debt," Annals of Finance, Springer, vol. 4(2), pages 131-155, March.
    4. Joe Haslag & Joydeep Bhattacharya & Steven Russell, 2003. "Understanding the Roles of Money, or When is the Friedman Rule Optimal, and Why?," Working Papers 0301, Department of Economics, University of Missouri.
    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.
    6. Eisei Ohtaki, "undated". "Optimality of the Friedman rule under ambiguity," Working Papers e103, Tokyo Center for Economic Research.
    7. Ennis, Huberto M. & Keister, Todd, 2003. "Economic growth, liquidity, and bank runs," Journal of Economic Theory, Elsevier, vol. 109(2), pages 220-245, April.
    8. Boel, Paola & Camera, Gabriele, 2006. "Efficient monetary allocations and the illiquidity of bonds," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1693-1715, October.
    9. 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.
    10. Joydeep Bhattacharya & Joseph H. Haslag & Antoine Martin, 2005. "The Tobin effect and the Friedman rule," Staff Reports 224, Federal Reserve Bank of New York.
    11. Akyol, Ahmet, 2004. "Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk," Journal of Monetary Economics, Elsevier, vol. 51(6), pages 1245-1269, September.
    12. Bhattacharya, Joydeep & Haslag, Joseph & Martin, Antoine, 2009. "Optimal monetary policy and economic growth," European Economic Review, Elsevier, vol. 53(2), pages 210-221, February.
    13. Khan, Mohsin S. & Senhadji, Abdelhak S. & Smith, Bruce D., 2006. "Inflation And Financial Depth," Macroeconomic Dynamics, Cambridge University Press, vol. 10(02), pages 165-182, April.
    14. 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.
    15. Zhou, Ge, 2011. "Money and Long-run Growth," MPRA Paper 33765, University Library of Munich, Germany.
    16. Firouz Gahvari, 2009. "Friedman Rule in a Model with Endogenous Growth and Cash-in-advance Constraint," CESifo Working Paper Series 2708, CESifo Group Munich.
    17. Samuel Gil Martín, 2012. "Liquidity, Welfare and Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 59(2), pages 217-234, May.
    18. Bruce D. Smith & Beatrix Paal & Ke Wang, 2005. "Monopoly versus Competition in Banking: Some Implications for Growth and Welfare," 2005 Meeting Papers 435, Society for Economic Dynamics.
    19. Bhattacharya, Joydeep & Singh, Rajesh, 2005. "Optimal Choice of Monetary Instruments in an Economy with Real and Liquidity Shocks," Staff General Research Papers Archive 12355, Iowa State University, Department of Economics.
    20. Joseph H. Haslag & Antoine Martin, 2007. "Optimality of the Friedman Rule in an Overlapping Generations Model with Spatial Separation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1741-1758, October.
    21. KOBAYASHI Keiichiro, 2012. "Banking in the Lagos-Wright Monetary Economy," Discussion papers 12054, Research Institute of Economy, Trade and Industry (RIETI).

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