Estimation of Markov regime-switching regression models with endogenous switching

Abstract

Following Hamilton (1989), estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters. The model nests the exogenous switching model, yielding straightforward tests for endogeneity. In Monte Carlo experiments, maximum likelihood estimates of the endogenous switching model parameters were quite accurate, even in the presence of certain model misspecifications. As an application, we extend the volatility feedback model of equity returns given in Turner, Startz and Nelson (1989) to allow for endogenous switching.Keywords: Endogeneity, Regime-Switching JEL Classification: C13, C22, G12 * Kim: Dept. of Economics, Korea University, Seoul, Korea, (cjkim@korea.ac.kr 1Recent decades have seen extensive interest in time-varying parameter models of macroeconomic and financial time series. One notable set of models are regime-switching regressions, which date to at least Quandt (1958). Goldfeld and Quandt (1973) introduced a particularly useful version of these models, referred to in the following as a Markov-switching model, in which the latent state variable controlling regime shifts follows a Markov-chain, and is thus serially dependent. In an influential article, Hamilton (1989) extended Markov-switching models to the case of dependent data, specifically an autoregression.The vast literature generated by Hamilton (1989) typically assumes that the regime shifts are exogenous with respect to all realizations of the regression disturbance. In this paper we work with Markov-switching regressions of the type considered by Hamilton (1989) and various extensions, but relax the exogenous switching assumption. We develop a model of endogenous Markov regime-switching that is based on a probit specification for the realization of the latent state. The model is quite parsimonious, and admits a test for endogenous switching as a simple parameter restriction. The model parameters can be estimated via maximum likelihood with relatively minor modifications to the recursive filter in Hamilton (1989).Why are we motivated to investigate Markov-switching regressions with endogenous switching? Many of the model's applications are in macroeconomics or finance in situations where it is natural to assume the state is endogenous. As an example, it is often the case that the estimated state variable has a strong business cycle correlation. This can be seen in recent applications of the regime-switching model to identified monetary VARs, such as Sims andZha (2002) andOwyang (2002). It is not hard to imagine that the shocks to the regression, such as the macroeconomic shocks to the VAR, would be correlated with the business cycle. As another example, some applications of the model contain parameters that represent the reaction...

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