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Estimation of Markov regime-switching regression models with endogenous switching

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  • Chang-Jin Kim
  • Jeremy M. Piger
  • Richard Startz

Abstract

Following Hamilton (1989), estimation of Markov regime-switching regressions nearly always relies on the assumption that the latent state variable controlling the regime change is exogenous. We incorporate endogenous switching into a Markov-switching regression and develop strategies for identification and estimation. Identification requires instruments, which can be found in observed exogenous variables that influence the transition probabilities of the regime-switching process, as in the so-called time-varying transition probability case. However, even with fixed transition probabilities, the lagged state variable can serve as an instrument provided it is exogenous and the state process is serially dependent. This is true even though the lagged state is unobserved. A straightforward test for endogeneity is also presented. Monte Carlo experiments confirm that the estimation procedures perform quite well in practice. We apply the endogenous switching model to the volatility feedback model of equity returns given in Turner, Startz and Nelson (1989).

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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2003-015.

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Date of creation: 2004
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Handle: RePEc:fip:fedlwp:2003-015

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Keywords: Econometric models;

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  1. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
  2. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
  3. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  4. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
  5. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  6. Kazumitsu Nawata & Michael McAleer, 2001. "Size Characteristics Of Tests For Sample Selection Bias: A Monte Carlo Comparison And Empirical Example," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 105-112.
  7. Michael T. Owyang, 2002. "Modeling Volcker as a non-absorbing state: agnostic identification of a Markov-switching VAR," Working Papers 2002-018, Federal Reserve Bank of St. Louis.
  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  9. Turner, C.M. & Startz, R. & Nelson, C.R., 1989. "The Markov Model Of Heteroskedasticity, Risk And Learning In The Stock Market," Discussion Papers in Economics at the University of Washington 89-01, Department of Economics at the University of Washington.
  10. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  11. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
  12. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
  13. Christopher M. Turner & Richard Startz & Charles R. Nelson, 1989. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," NBER Working Papers 2818, National Bureau of Economic Research, Inc.
  14. Chang-Jin Kim & James C. Morley & Charles Nelson, 2000. "Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?," Discussion Papers in Economics at the University of Washington 0023, Department of Economics at the University of Washington.
  15. Christopher Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  16. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
  17. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 11(1), pages 7-54, June.
  18. Francis X. Diebold & Joon-Haeng Lee & Gretchen C. Weinbach, 1993. "Regime switching with time-varying transition probabilities," Working Papers 93-12, Federal Reserve Bank of Philadelphia.
  19. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
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