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Econometric Analysis of Fisher's Equation

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  • Peter C. B. Phillips

Abstract

. Fisher's equation for the determination of the real rate of interest is studied from a fresh econometric perspective. Some new methods of data description for nonstationary time series are introduced. The methods provide a nonparametric mechanism for modelling the spatial densities of a time series that displays random wandering characteristics, like interest rates and inflation. Hazard rate functionals are also constructed, an asymptotic theory is given, and the techniques are illustrated in some empirical applications to real interest rates for the United States. The paper ends by calculating semiparametric estimates of long‐range dependence in U.S. real interest rates, using a new estimation procedure called modified log periodogram regression and new asymptotics that covers the nonstationary case. The empirical results indicate that the real rate of interest in the United States is (fractionally) nonstationary over 1934–1997 and over the more recent subperiods 1961–1985 and 1961–1997. Unit root nonstationarity and short memory stationarity are both strongly rejected for all these periods.

Suggested Citation

  • Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    • Handle: RePEc:bla:ajecsc:v:64:y:2005:i:1:p:125-168
    DOI: 10.1111/j.1536-7150.2005.00355.x
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    1. Rose, Andrew Kenan, 1988. " Is the Real Interest Rate Stable?," Journal of Finance, American Finance Association, vol. 43(5), pages 1095-1112, December.
    2. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    3. Carl E. Walsh, 1987. "Three questions concerning nominal and real interest rates," Economic Review, Federal Reserve Bank of San Francisco, issue Fall, pages 5-19.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    5. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    6. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    7. David E.W. Laidler, 2016. "The Golden Age of the Quantity Theory," Economics Books, Princeton University Press, edition 1, number 4959.
    8. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-125, February.
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    10. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
    11. Fama, Eugene F, 1975. "Short-Term Interest Rates as Predictors of Inflation," American Economic Review, American Economic Association, vol. 65(3), pages 269-282, June.
    12. Mishkin, Frederic S., 1981. "The real interest rate: An empirical investigation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 15(1), pages 151-200, January.
    13. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708.
    14. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    15. Mishkin, Frederic S., 1992. "Is the Fisher effect for real? : A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 195-215, November.
    16. Lawrence H. Summers, 1982. "The Nonadjustment of Nominal Interest Rates: A Study of the Fisher Effect," NBER Working Papers 0836, National Bureau of Economic Research, Inc.
    17. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    18. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    19. Phillips, Peter, 1999. "Discrete Fourier Transforms of Fractional Processes August," Working Papers 149, Department of Economics, The University of Auckland.
    20. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
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