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Estimation of Markov regime-switching regression models with endogenous switching

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Author Info
Chang-Jin Kim
Jeremy M. Piger
Richard Startz

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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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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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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  2. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. 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.
  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. [Downloadable!]
  8. 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.
  9. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(1), pages 1-42.
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  10. Christopher Sims & Tao Zha, 2002. "Macroeconomic switching," Proceedings, Federal Reserve Bank of San Francisco, issue Mar. [Downloadable!]
  11. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70. [Downloadable!] (restricted)
  12. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March. [Downloadable!] (restricted)
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  1. Siddhartha Chib & Michael J. Dueker, 2004. "Non-Markovian regime switching with endogenous states and time-varying state strengths," Working Papers 2004-030, Federal Reserve Bank of St. Louis. [Downloadable!]
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