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Econometric Analysis of Fisher's Equation

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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 US. The paper ends by calculating Gaussian semiparametric estimates of long range dependence in US real interest rates, using a new asymptotic theory that covers the nonstationary case. The empirical results indicate that the real rate of interest in the US 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, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1180
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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. 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.
    4. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
    5. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
    6. 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.
    7. 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.
    8. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    9. Ross Williams, 2013. "Introduction," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 46(4), pages 460-461, December.
    10. 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.
    11. 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.
    12. 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.
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    Cited by:

    1. Alfred A. Haug, 2014. "On real interest rate persistence: the role of breaks," Applied Economics, Taylor & Francis Journals, vol. 46(10), pages 1058-1066, April.
    2. Lieberman, Offer & Phillips, Peter C.B., 2008. "A complete asymptotic series for the autocovariance function of a long memory process," Journal of Econometrics, Elsevier, vol. 147(1), pages 99-103, November.
    3. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    4. Jumah, Adusei & Kunst, Robert M., 2002. "On Mean Reversion in Real Interest Rates: An Application of Threshold Cointegtation," Economics Series 109, Institute for Advanced Studies.
    5. Guglielmo Maria Caporale & Luis Alberiko Gil-Alaña, 2011. "Interest rate dynamics in Kenya," NCID Working Papers 10/2011, Navarra Center for International Development, University of Navarra.
    6. Kanas, Angelos, 2008. "On real interest rate dynamics and regime switching," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2089-2098, October.
    7. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
    8. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    9. Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    10. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
    11. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    12. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2016. "Persistence and cyclical dependence in the monthly euribor rate," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 40(1), pages 157-171, January.
    13. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    14. Marc-André Gosselin & René Lalonde, 2006. "An Eclectic Approach to Estimating U.S. Potential GDP," Empirical Economics, Springer, vol. 31(4), pages 951-975, November.
    15. Zisimos Koustas & Jean-Francois Lamarche, 2005. "Policy-Induced Mean Reversion in the Real Interest Rate?," Working Papers 0503, Brock University, Department of Economics, revised Jul 2005.
    16. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
    17. Basma Bekdache & Christopher F. Baum, 1999. "A re-evaluation of empirical tests of the Fisher hypothesis," Computing in Economics and Finance 1999 944, Society for Computational Economics, revised 18 Sep 2000.
    18. Dimitrios D. Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Paper series 14_08, Rimini Centre for Economic Analysis.
    19. Nicolas Million, 2003. "The Fisher Effect revisited through an efficient non linear unit root testing procedure," Applied Economics Letters, Taylor & Francis Journals, vol. 10(15), pages 951-954.
    20. repec:eee:jpolmo:v:39:y:2017:i:5:p:775-789 is not listed on IDEAS
    21. Jerry Coakley & Ana-Maria Fuertes, 2002. "Asymmetric dynamics in UK real interest rates," Applied Financial Economics, Taylor & Francis Journals, vol. 12(6), pages 379-387.
    22. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
    23. Cheng-Feng Lee & Ching-Chuan Tsong, 2012. "A revisit on real interest rate parity hypothesis -- simulation evidence from efficient unit root tests," Applied Economics, Taylor & Francis Journals, vol. 44(24), pages 3089-3099, August.
    24. Anari, Ali & Kolari, James, 2016. "Dynamics of interest and inflation rates," Journal of Empirical Finance, Elsevier, vol. 39(PA), pages 129-144.

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