IDEAS home Printed from
   My bibliography  Save this paper

The Harmonic Fisher Equation and the Inflationary Bias of Real Uncertainty




The classical Fisher equation asserts that in a nonstochastic economy, the inflation rate must equal the difference between the nominal and real interest rates. We extend this equation to a representative agent economy with real uncertainty in which the central bank sets the nominal rate of interest. The Fisher equation still holds, but with the rate of inflation replaced by the harmonic mean of the growth rate of money. Except for logarithmic utility, we show that on almost every path the long-run rate of inflation is strictly higher than it would be in the nonstochastic world obtained by replacing output with expected output in every period. If the central bank sets the nominal interest rate equal to the discount rate of the representative agent, then the long-run rate of inflation is positive (and the same) on almost every path. By contrast, the classical Fisher equation asserts that inflation should then be zero. In fact, no constant interest rate will stabilize prices, even if the economy is stationary with bounded i.d.d. shocks. The central bank must actively manage interest rates if it wants to keep prices bounded forever. However, not even an active central bank can keep prices exactly constant.

Suggested Citation

  • Ioannis Karatzas & Martin Shubik & William D. Sudderth & John Geanakoplos, 2003. "The Harmonic Fisher Equation and the Inflationary Bias of Real Uncertainty," Cowles Foundation Discussion Papers 1424, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1424

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Orus, Juan & González, Manuel, 2004. "Inflation-Proof Credits and Financial Instruments. Making the Fisher Hypothesis a Reality," MPRA Paper 343, University Library of Munich, Germany.
    2. James R. Rhodes, 2006. "DEVOLUTION OF THE FISHER EQUATION: Rational Appreciation to Money Illusion," GRIPS Discussion Papers 07-05, National Graduate Institute for Policy Studies, revised Sep 2007.

    More about this item


    Inflation; equilibrium; Control; Interest rate; Central bank; Harmonic Fisher equation;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1424. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Regan). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.