Frequency Dependence in Regression Model Coefficients: An Alternative Approach for Modeling Nonlinear Dynamic Relationships in Time Series
This article proposes a new class of nonlinear time series models in which one of the coefficients of an existing regression model is frequency dependent—that is, the relationship between the dependent variable and this explanatory variable varies across its frequency components. We show that such frequency dependence implies that the relationship between the dependent variable and this explanatory variable is nonlinear. Past efforts to detect frequency dependence have not been satisfactory; for example, we note that the two-sided bandpass filtering used in such efforts yields inconsistent estimates of frequency dependence where there is feedback in the relationship. Consequently, we provide an explicit procedure for partitioning an explanatory variable into frequency components using one-sided bandpass filters. This procedure allows us to test for and quantify frequency dependence even where feedback may be present. A distinguishing feature of these new models is their potentially tight connection to macroeconomic theory; indeed, they are perhaps best introduced by reference to the frequency dependence in the marginal propensity to consume posited by the Permanent Income Hypothesis (PIH) of consumption theory. An illustrative empirical application is given, in which the Phillips Curve relationship between inflation and unemployment is found to be negligible at low frequencies, corresponding to periods ≥ 18 months, but inverse at higher frequencies, just as predicted by Friedman and Phelps in the 1960s.
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- Jushan Bai, 1995.
"Estimating Multiple Breaks One at a Time,"
95-18, Massachusetts Institute of Technology (MIT), Department of Economics.
- Diego Comin & Mark Gertler, 2003.
"Medium Term Business Cycles,"
NBER Working Papers
10003, National Bureau of Economic Research, Inc.
- Robert J. Hodrick & Edward Prescott, 1981.
"Post-War U.S. Business Cycles: An Empirical Investigation,"
451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
- Perron, P. & Bai, J., 1995.
"Estimating and Testing Linear Models with Multiple Structural Changes,"
Cahiers de recherche
9552, Universite de Montreal, Departement de sciences economiques.
- Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
- Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- R. F. Engle, 1972.
"Band Spectrum Regressions,"
96, Massachusetts Institute of Technology (MIT), Department of Economics.
- Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "Inflation and monetary policy in the twentieth century," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q I, pages 22-45.
- BAI, Jushan & PERRON, Pierre, 1998.
"Computation and Analysis of Multiple Structural-Change Models,"
Cahiers de recherche
9807, Universite de Montreal, Departement de sciences economiques.
- Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
- Lawrence J. Christiano & Terry J. Fitzgerald, 2003.
"The Band Pass Filter,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, 05.
- Tom Doan, . "CFFILTER: RATS procedure to perform band pass filter using Christiano-Fitzgerald method," Statistical Software Components RTS00034, Boston College Department of Economics.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
- Engle, Robert F, 1978. "Testing Price Equations for Stability across Spectral Frequency Bands," Econometrica, Econometric Society, vol. 46(4), pages 869-81, July.
- Ashley, Richard, 1984. "A Simple Test for Regression Parameter Instability," Economic Inquiry, Western Economic Association International, vol. 22(2), pages 253-68, April.
- Marianne Baxter & Robert G. King, 1995.
"Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series,"
NBER Working Papers
5022, National Bureau of Economic Research, Inc.
- Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
- den Haan, Wouter J. & Sumner, Steven W., 2004.
"The comovement between real activity and prices in the G7,"
European Economic Review,
Elsevier, vol. 48(6), pages 1333-1347, December.
- Wouter J. Den Haan & Steven Sumner, 2001. "The Comovements between Real Activity and Prices in the G7," NBER Working Papers 8195, National Bureau of Economic Research, Inc.
- Den Haan, Wouter & Sumner, Steven, 2001. "The Comovements between Real Activity and Prices in the G7," CEPR Discussion Papers 2801, C.E.P.R. Discussion Papers.
- Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678.
- Farley, John U. & Hinich, Melvin & McGuire, Timothy W., 1975. "Some comparisons of tests for a shift in the slopes of a multivariate linear time series model," Journal of Econometrics, Elsevier, vol. 3(3), pages 297-318, August.
- repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
- Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002.
"Band Spectral Regression with Trending Data,"
Econometric Society, vol. 70(3), pages 1067-1109, May.
- Dean Corbae & Sam Ouliaris & Peter C.B. Phillips, 1997. "Band Spectral Regression with Trending Data," Cowles Foundation Discussion Papers 1163, Cowles Foundation for Research in Economics, Yale University.
- Corbae, D. & Ouliaris, S. & Phillips, P.C.B., 1997. "Band Spectral Regression with Trending Data," Working Papers 97-09, University of Iowa, Department of Economics.
- Stock, James H. & Watson, Mark W., 1999.
"Business cycle fluctuations in us macroeconomic time series,"
Handbook of Macroeconomics,
in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64
- James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc.
- Richard A. Ashley & Randall J. Verbrugge., 2006. "Mis-Specification in Phillips Curve Regressions: Quantifying Frequency Dependence in This Relationship While Allowing for Feedback," Working Papers e06-11, Virginia Polytechnic Institute and State University, Department of Economics.
- Tan, Hui Boon & Ashley, Richard, 1999. "Detection And Modeling Of Regression Parameter Variation Across Frequencies," Macroeconomic Dynamics, Cambridge University Press, vol. 3(01), pages 69-83, March.
- repec:cup:macdyn:v:3:y:1999:i:1:p:69-83 is not listed on IDEAS
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