| Content | 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. |
