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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 21, Issue 3 (Apr 2017)

Issues

Changes in persistence, spurious regressions and the Fisher hypothesis

Robinson Kruse
  • Corresponding author
  • CREATES, Aarhus University, Department of Economics and Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
  • Hendyplan, Uitbreidingstraat 84/3, 2600 Berchem, Belgium
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Daniel Ventosa-Santaulària
  • Centro de Investigación y Docencia Económicas, CIDE , Carretera México-Toluca 3655, Col. Lomas de Sta Fe, Del. Álvaro Obregón, México D.F, C.P. 01210, México
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Antonio E. Noriega
  • Banco de México, Dirección General de Emisión, Legaria 691, Col. irrigación, México D.F., México
  • Universidad de Guanajuato, Department of Economics and Finance, Cerro El Establo S/N, Guanajuato, Gto. México
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Published Online: 2017-04-07 | DOI: https://doi.org/10.1515/snde-2015-0062

Abstract

Declining inflation persistence has been documented in numerous studies. We show that when time series with changes in persistence are analyzed in a regression framework with other persistent time series like interest rates, spurious regressions are likely to occur. We propose the coefficient of determination R2 as a simple test statistic to distinguish between spurious and genuine regressions in situations where time series possibly exhibit changes in persistence. We extend the analysis towards fractional (co-)integration as well. To this end, we establish the limit theory for the R2 statistic and conduct a Monte Carlo study where we investigate its finite-sample properties. The test performs remarkably well in terms of size and power and is robust to level shifts and multiple changes in persistence. Finally, we apply the test to the Fisher equation for the United States. The newly proposed R2-based test offers robust evidence favourable to the Fisher hypothesis.

This article offers supplementary material which is provided at the end of the article.

Keywords: Fisher hypothesis; inflation; spurious regression; structural breaks

JEL Classification: C12; C22; E31; E43

References

  • Barsky, R. B. 1987. “The Fisher Hypothesis and the Forecastability and Persistence of Inflation.” Journal of Monetary Economics 19: 3–24.CrossrefGoogle Scholar

  • Busetti, F., and A. Taylor. 2004. “Tests of Stationarity Against a Change in Persistence.” Journal of Econometrics 123: 33–66.CrossrefGoogle Scholar

  • Christopoulos, D. K., and M. A. León-Ledesma. 2007. “A Long-Run Non-Linear Approach to the Fisher Effect.” Journal of Money, Credit and Banking 39: 543–559.CrossrefGoogle Scholar

  • de Jong, R. 2003. “Logarithmic Spurious Regressions.” Economics Letters 81: 13–21.CrossrefGoogle Scholar

  • Entorf, H. 1997. “Random Walks with Drifts: Nonsense Regression and Spurious Fixed-Effect Estimation.” Journal of Econometrics 80: 287–296.CrossrefGoogle Scholar

  • Ferson, W. E., S. Sarkissian, and T. T. Simin. 2003. “Spurious Regressions in Financial Economics?” The Journal of Finance 58: 1393–1414.CrossrefGoogle Scholar

  • Gan, L., C. Hsiao, and S. Xu. 2014. “Model Specification Test with Correlated But Not Cointegrated Variables.” Journal of Econometrics 178: 80–85.Google Scholar

  • Garcia, R., and P. Perron. 1996. “An Analysis of the Real Interest Rate Under Regime Shifts.” The Review of Economics and Statistics 78: 111–125.CrossrefGoogle Scholar

  • Granger, C. and P. Newbold. 1974. “Spurious Regressions in Econometrics.” Journal of Econometrics 2: 11–20.CrossrefGoogle Scholar

  • Granger, C., N. Hyung, and Y. Jeon. 2001. “Spurious Regressions with Stationary Series.” Applied Economics 33: 899–904.CrossrefGoogle Scholar

  • Haldrup, N., R. Kruse, T. Terasvirta, and R. Varneskov. 2013. “Unit Roots, Nonlinearities and Structural Breaks.” In Handbook of Research Methods and Applications in Empirical Macroeconomics, 61–94. Cheltenham: Edward Elgar Publishing.Google Scholar

  • Halunga, A., D. R. Osborn, and M. Sensier. 2008. “Changes in the Order of Integration of US and UK Inflation.” Economics Letters 102: 30–32.CrossrefGoogle Scholar

  • Harvey, D., S. Leybourne, and A. Taylor. 2006. “Modified Tests for a Change in Persistence.” Journal of Econometrics 134: 441–469.Google Scholar

  • Hassler, U. 1998. “A Note on Correlation in Regressions Without Cointegration.” Jahrbücher für Nationalökonomie und Statistik 217: 518–523.Google Scholar

  • Hassler, U., and J. Breitung. 2006. “A Residual-Based LM-Type Test Against Fractional Cointegration.” Econometric Theory 22: 1091–1111.CrossrefGoogle Scholar

  • Hassler, U. and J. Scheithauer. 2011. “Detecting Changes from Short to Long Memory.” Statistical Papers 52: 847–870.CrossrefGoogle Scholar

  • Hassler, U., and B. Meller. 2014. “Detecting Multiple Breaks in Long Memory the Case of US Inflation.” Empirical Economics 46: 653–680.CrossrefGoogle Scholar

  • Haug, A., A. Beyer, and W. Dewald. 2011. “Structural Breaks and the Fisher Effect.” The BE Journal of Macroeconomics 11: 1–29.Google Scholar

  • Jensen, M. J. 2009. “The Long-Run Fisher Effect: Can It Be Tested?” Journal of Money, Credit and Banking 41: 221–231.CrossrefGoogle Scholar

  • Kang, K. H., C.-J. Kim, and J. Morley. 2009. “Changes in US Inflation Persistence.” Studies in Nonlinear Dynamics & Econometrics 13: 1–21.Google Scholar

  • Kejriwal, M. 2009. “The Nature of Persistence in Euro Area Inflation: A Reconsideration.” Purdue University Working Paper 1218: 1–28.Google Scholar

  • Kejriwal, M., and P. Perron. 2012. “A Note on Estimating a Structural Change in Persistence.” Economics Letters 117: 932–935.CrossrefGoogle Scholar

  • Kejriwal, M., P. Perron, and J. Zhou. 2013. “Wald Tests for Detecting Multiple Structural Changes in Persistence.” Econometric Theory 29: 289–323.CrossrefGoogle Scholar

  • Kim, J. 2000. “Detection of Change in Persistence of a Linear Time Series.” Journal of Econometrics 95: 97–116.CrossrefGoogle Scholar

  • Kouretas, G. P., and M. E. Wohar. 2012. “The Dynamics of Inflation: A Study of a Large Number of Countries.” Applied Economics 44: 2001–2026.CrossrefGoogle Scholar

  • Koustas, Z., and A. Serletis. 1999. “On the Fisher Effect.” Journal of Monetary Economics 44: 105–130.CrossrefGoogle Scholar

  • Kruse, R., and P. Sibbertsen. 2012. “Long Memory and Changing Persistence.” Economics Letters 114: 268–272.CrossrefGoogle Scholar

  • Kumar, M. S., and T. Okimoto. 2007. “Dynamics of Persistence in International Inflation Rates.” Journal of Money, Credit and Banking 39: 1457–1479.CrossrefGoogle Scholar

  • Kurozumi, E. 2005. “Detection of Structural Change in the Long-Run Persistence in a Univariate Time Series.” Oxford Bulletin of Economics and Statistics 67: 181–206.CrossrefGoogle Scholar

  • Lai, K. S. 2008. “The Puzzling Unit Root in the Real Interest Rate and Its Inconsistency with Intertemporal Consumption Behavior.” Journal of International Money and Finance 27: 140–155.CrossrefGoogle Scholar

  • Lanne, M. 2006. “Nonlinear Dynamics of Interest Rate and Inflation.” Journal of Applied Econometrics 21: 1157–1168.CrossrefGoogle Scholar

  • Leybourne, S., and A. R. Taylor. 2004. “On Tests for Changes in Persistence.” Economics Letters 84: 107–115.CrossrefGoogle Scholar

  • Leybourne, S., T.-H. Kim, V. Smith, and P. Newbold. 2003. “Tests for a Change in Persistence Against the Null of Difference-Stationarity.” The Econometrics Journal 6: 291–311.CrossrefGoogle Scholar

  • Leybourne, S., T. Kim, and A. Taylor. 2007a. “Detecting Multiple Changes in Persistence.” Studies in Nonlinear Dynamics & Econometrics 11: 1370–1370.Google Scholar

  • Leybourne, S., R. Taylor, and T.-H. Kim. 2007b. “Cusum of Squares-Based Tests for a Change in Persistence.” Journal of Time Series Analysis 28: 408–433.CrossrefGoogle Scholar

  • Malliaropulos, D. 2000. “A Note on Nonstationarity, Structural Breaks, and the Fisher Effect.” Journal of Banking & Finance 24: 695–707.CrossrefGoogle Scholar

  • Marmol, F. 1995. “Spurious Regressions Between i(d) Processes.” Journal of Time Series Analysis 16: 313–321.CrossrefGoogle Scholar

  • Marmol, F. 1996. “Nonsense Regressions Between Integrated Processes of Different Orders.” Oxford Bulletin of Economics & Statistics 58: 525–36.CrossrefGoogle Scholar

  • Marmol, F. 1998. “Spurious Regression Theory with Nonstationary Fractionally Integrated Processes.” Journal of Econometrics 84: 233–250.CrossrefGoogle Scholar

  • Martins, L. F., and P. M. Rodrigues. 2014. “Testing for Persistence Change in Fractionally Integrated Models: An Application to World Inflation Rates.” Computational Statistics & Data Analysis 76: 502–522.CrossrefGoogle Scholar

  • Maynard, A., A. Smallwood, and M. E. Wohar. 2013. “Long Memory Regressors and Predictive Testing: A Two-Stage Rebalancing Approach.” Econometric Reviews 32: 318–360.CrossrefGoogle Scholar

  • Neely, C. J., and D. E. Rapach. 2008. “Real Interest Rate Persistence: Evidence and Implications.” Federal Reserve Bank of St. Louis Working Paper Series.Google Scholar

  • Noriega, A., and D. Ventosa-Santaulària. 2007. “Spurious Regression and Trending Variables.” Oxford Bulletin of Economics and Statistics 7: 4–7.Google Scholar

  • Noriega, A., and M. Ramos-Francia. 2009. “The Dynamics of Persistence in US Inflation.” Economics Letters 105 (2): 168–172.Google Scholar

  • Noriega, A., C. Capistrán, and M. Ramos-Francia. 2012. “On the Dynamics of Inflation Persistence Around the World.” Empirical Economics 1–23.Google Scholar

  • O’Reilly, G., and K. Whelan. 2005. “Has Euro-area Inflation Persistence Changed over Time?” Review of Economics and Statistics 87: 709–720.CrossrefGoogle Scholar

  • Perron, P. 2006. “Dealing with Structural Breaks.” Palgrave Handbook of Econometrics 1: 278–352.Google Scholar

  • Phillips, P. 1986. “Understanding Spurious Regressions in Econometrics.” Journal of Econometrics 33: 311–340.CrossrefGoogle Scholar

  • Phillips, P. 2005. “Econometric Analysis of Fisher’s Equation.” American Journal of Economics and Sociology 64: 125–168.CrossrefGoogle Scholar

  • Rapach, D. E., and C. E. Weber. 2004. “Are Real Interest Rates Really Nonstationary? New Evidence from Tests with Good Size and Power.” Journal of Macroeconomics 26: 409–430.CrossrefGoogle Scholar

  • Rapach, D. E., and M. E. Wohar. 2005. “Regime Changes in International Real Interest Rates: Are They a Monetary Phenomenon?” Journal of Money, Credit, and Banking 37: 887–906.CrossrefGoogle Scholar

  • Rose, A. K. 1988. “Is the Real Interest Rate Stable?” The Journal of Finance 43: 1095–1112.CrossrefGoogle Scholar

  • Shimotsu, K. 2006. “Simple (But Effective) Tests of Long Memory Versus Structural Breaks.” Queen’s Economics Department Working Paper No. 1101.Google Scholar

  • Sibbertsen, P., and R. Kruse. 2009. “Testing for a Break in Persistence Under Long-Range Dependencies.” Journal of Time Series Analysis 30: 263–285.CrossrefGoogle Scholar

  • Sun, Y., C. Hsiao, and Q. Li. 2011. “Measuring Correlations of Integrated But Not Cointegrated Variables: A Semiparametric Approach.” Journal of Econometrics 164: 252–267.Google Scholar

  • Sun, Y., C. Hsiao, and Q. Li. 2015. “Volatility Spillover Effect: A Semiparametric Analysis of Non-Cointegrated Process.” Econometric Reviews 34: 127–145.CrossrefGoogle Scholar

  • Tsay, W., and C. Chung. 2000. “The Spurious Regression of Fractionally Integrated Processes.” Journal of Econometrics 96: 155–182.CrossrefGoogle Scholar

  • Tsong, C.-C., and C.-F. Lee. 2013. “Quantile Cointegration Analysis of the Fisher Hypothesis.” Journal of Macroeconomics 35: 186–198.CrossrefGoogle Scholar

  • Ventosa-Santaulària, D. 2009. “Spurious Regression.” Journal of Probability and Statistics 2009: 1–27.Google Scholar

  • Westerlund, J. 2008. “Panel Cointegration Tests of the Fisher Effect.” Journal of Applied Econometrics 23: 193–233.CrossrefGoogle Scholar

  • Wolters, M., and P. Tillmann. 2015. “The Changing Dynamics of US Inflation Persistence a Quantile Regression Approach.” Studies in Nonlinear Dynamics & Econometrics 19: 161–182.Google Scholar

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Published Online: 2017-04-07


Citation Information: Studies in Nonlinear Dynamics & Econometrics, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2015-0062.

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