An Extensive Study on Markov Switching Models with Endogenous Regressors
Xia Wang, Yuhuang Shang, Tingguo Zheng
Studies in Nonlinear Dynamics & Econometrics Volume 18, Issue 4, Pages 403–418
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This paper extends Kim’s (Kim, C.-J. 2004. “Markov-Switching Models with Endogenous Explanatory Variables.” Journal of Econometrics 122: 127–136; Kim, C.-J. 2009. “Markov-Switching Models with Endogenous Explanatory Variables II: A Two-Step MLE Procedure.” Journal of Econometrics 148: 46–55.) studies on Markov switching models with endogenous regressors by considering the time-varying relationship between endogenous regressors and instrumental variables. To deal with the endogenous problem, we introduce three estimation methods, e.g., a joint estimation procedure, a two-step estimation procedure and a MCMC estimation procedure. Although the joint estimation procedure provides us with a direct estimator via Kim’s (Kim, C.-J. 1994. “Dynamic Linear Models with Markov-Switching.” Journal of Econometrics 60: 1–22.) approximation, it is not always feasible due to the “curse of dimensionality” problem. In this case, we consider the two-step estimation procedure and the MCMC estimation procedure. Our Monte Carlo experiments show that three estimation procedures are in general feasible and robust. Although the two-step estimation procedure is not as efficient as the MCMC estimation procedure, they both perform better than the joint estimation procedure. In an application to the Campbell and Mankiw’s (1989) consumption model, we document the robustness of our three estimation procedures and verify the significant regime switching behavior of this model.
JEL-Codes: C13; C32
Keywords: endogeneity; Markov switching model; joint estimation procedure; two-step estimation procedure; MCMC estimation procedure; consumption model

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