IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v22y2016i14p1414-1434.html
   My bibliography  Save this article

The Friedman rule and inflation targeting

Author

Listed:
  • Qian Guo
  • Huw Rhys
  • Xiaojing Song
  • Mark Tippett

Abstract

We use concepts from the financial economics discipline – and in particular the methods of continuous time finance – to develop a monetarist model under which the rate of inflation evolves in terms of a first-order mean reversion process based on a ‘white noise’ error structure. The Fokker–Planck (i.e. the Chapman–Kolmogorov) equation is then invoked to retrieve the steady-state (i.e. unconditional) probability distribution for the rate of inflation. Monthly data for the UK Consumer Price Index (CPI) covering the period from 1988 until 2012 are then used to estimate the parameters of the probability distribution for the UK inflation rate. The parameter estimates are compatible with the hypothesis that the UK inflation rate evolves in terms of a slightly skewed and highly leptokurtic probability distribution that encompasses non-convergent higher moments. We then determine the Hamilton–Jacobi–Bellman fundamental equation of optimality corresponding to a monetary policy loss function defined in terms of the squared difference between the targeted rate of inflation and the actual inflation rate. Optimising and then solving the Hamilton–Jacobi–Bellman equation shows that the optimal control for the rate of increase in the money supply will be a linear function of the difference between the current rate of inflation and the targeted inflation rate. The conditions under which the optimal control will lead to the Friedman rule are then determined. These conditions are used in conjunction with the Fokker–Planck equation and the mean reversion process describing the evolution of the inflation rate to determine the probability distribution for the inflation rate under the Friedman rule. This shows that whilst the empirically determined probability distribution for the UK inflation rate meets some of the conditions required for the application of the Friedman rule, it does not meet them all.

Suggested Citation

  • Qian Guo & Huw Rhys & Xiaojing Song & Mark Tippett, 2016. "The Friedman rule and inflation targeting," The European Journal of Finance, Taylor & Francis Journals, vol. 22(14), pages 1414-1434, November.
    • Handle: RePEc:taf:eurjfi:v:22:y:2016:i:14:p:1414-1434
    DOI: 10.1080/1351847X.2014.953700
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1351847X.2014.953700
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1351847X.2014.953700?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1586-1609, November.
    2. Friedman, Milton, 1988. "Money and the Stock Market," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 221-245, April.
    3. Chang, Tsangyao & Ranjbar, Omid & Tang, D.P., 2013. "Revisiting the mean reversion of inflation rates for 22 OECD countries," Economic Modelling, Elsevier, vol. 30(C), pages 245-252.
    4. McCallum, Bennett T. & Nelson, Edward, 2010. "Money and Inflation: Some Critical Issues," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 3, pages 97-153, Elsevier.
    5. Milton Friedman, 1971. "A Theoretical Framework for Monetary Analysis," NBER Books, National Bureau of Economic Research, Inc, number frie71-1, March.
    6. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    7. Fama, Eugene F, 1981. "Stock Returns, Real Activity, Inflation, and Money," American Economic Review, American Economic Association, vol. 71(4), pages 545-565, September.
    8. Chien-Chiang Lee & Chun-Ping Chang, 2007. "Mean reversion of inflation rates in 19 OECD countries: Evidence from panel Lm unit root tests with structural breaks," Economics Bulletin, AccessEcon, vol. 3(23), pages 1-15.
    9. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3-4), pages 379-405.
    10. Joseph E. Stiglitz, 1988. "On the Relevance or Irrelevance of Public Financial Policy," International Economic Association Series, in: Kenneth J. Arrow & Michael J. Boskin (ed.), The Economics of Public Debt, chapter 2, pages 41-76, Palgrave Macmillan.
    11. repec:ebl:ecbull:v:3:y:2007:i:23:p:1-15 is not listed on IDEAS
    12. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3‐4), pages 379-405, April.
    13. Lee, Hsiu-Yun & Wu, Jyh-Lin, 2001. "Mean Reversion of Inflation Rates: Evidence from 13 OECD Countries," Journal of Macroeconomics, Elsevier, vol. 23(3), pages 477-487, July.
    14. Friedman, Milton, 1971. "Government Revenue from Inflation," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 846-856, July-Aug..
    15. Nelson, Edward, 2013. "Friedman's monetary economics in practice," Journal of International Money and Finance, Elsevier, vol. 38(C), pages 59-83.
    16. Joseph E. Stiglitz, 1983. "On the Relevance or Irrelevance of Public Financial Policy: Indexation,Price Rigidities and Optimal Monetary Policy," NBER Working Papers 1106, National Bureau of Economic Research, Inc.
    17. Edward Nelson, 2007. "Milton Friedman and U.S. monetary history: 1961-2006," Review, Federal Reserve Bank of St. Louis, vol. 89(May), pages 153-182.
    18. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    19. Merton H. Miller & Franco Modigliani, 1961. "Dividend Policy, Growth, and the Valuation of Shares," The Journal of Business, University of Chicago Press, vol. 34, pages 411-411.
    20. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    21. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    22. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1586-1609.
    23. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. F. Pizzutilo, 2012. "The behaviour of the distributions of stock returns: an analysis of the European market using the Pearson system of continuous probability distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(20), pages 1743-1752, October.
    2. Xiaojing Song & Thu Phuong Truong & Mark Tippett & John van der Burg, 2022. "The quantity theory of stock prices," The European Journal of Finance, Taylor & Francis Journals, vol. 28(17), pages 1685-1707, November.
    3. Ditimi Amassoma & O. Adeleke, 2018. "Testing for the Causality between Interest Rate and Stock Market Performance in Nigeria," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 3, pages 109-124.
    4. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1586-1609, November.
    5. Lothian, James R., 2009. "Milton Friedman's monetary economics and the quantity-theory tradition," Journal of International Money and Finance, Elsevier, vol. 28(7), pages 1086-1096, November.
    6. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, January.
    7. Mark Tippett, 2004. ""Discussion of" Interim Reporting Frequency and Financial Analysts' Expenditures," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(1-2), pages 199-207.
    8. Mark Tippett, 2004. "Discussion of Interim Reporting Frequency and Financial Analysts’ Expenditures," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(1‐2), pages 199-207, January.
    9. Luis A. Gil-Alana & Andrea Mervar & James E. Payne, 2017. "The stationarity of inflation in Croatia: anti-inflation stabilization program and the change in persistence," Economic Change and Restructuring, Springer, vol. 50(1), pages 45-58, February.
    10. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    11. Sellin, Peter, 1998. "Monetary Policy and the Stock Market: Theory and Empirical Evidence," Working Paper Series 72, Sveriges Riksbank (Central Bank of Sweden).
    12. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    13. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    14. Julien Pinter, 2022. "Monetarist arithmetic at COVID‐19 time: A take on how not to misapply the quantity theory of money," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(2), July.
    15. José Santiago Fajardo Barbachan & Aquiles Rocha de Farias & José Renato Haas Ornelas, 2008. "A Goodness-of-Fit Test with Focus on Conditional Value at Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 6(2), pages 139-155.
    16. Frauke Dobnik, 2013. "Long-run money demand in OECD countries: what role do common factors play?," Empirical Economics, Springer, vol. 45(1), pages 89-113, August.
    17. Till Massing, 2019. "What is the best Lévy model for stock indices? A comparative study with a view to time consistency," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(3), pages 277-344, September.
    18. Shiller, Robert J., 1999. "Social security and institutions for intergenerational, intragenerational, and international risk-sharing," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 50(1), pages 165-204, June.
    19. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    20. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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:taf:eurjfi:v:22:y:2016:i:14:p:1414-1434. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.