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Estimation of Markov regime-switching regression models with endogenous switching

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

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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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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  1. 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;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
  2. 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.
  3. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  4. Andrew J. Filardo, 1993. "Business cycle phases and their transitional dynamics," Research Working Paper 93-14, Federal Reserve Bank of Kansas City.
  5. Turner, C.M. & Startz, R. & Nelson, C.R., 1989. "The Markov Model Of Heteroskedasticity, Risk And Learning In The Stock Market," Working Papers 89-01, University of Washington, Department of Economics.
  6. 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.
  7. 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.
  8. 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.
  9. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
  10. Christopher A. Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  11. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  12. Kim, Chang-Jin & Morley, James C & Nelson, Charles R, 2004. "Is There a Positive Relationship between Stock Market Volatility and the Equity Premium?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(3), pages 339-60, June.
  13. 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.
  14. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," FRB Atlanta Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  15. 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.
  16. 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.
  17. 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.
  18. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
  19. 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.
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