Markov-Switching Models with Endogenous Explanatory Variables II: A Two-Step MLE Procedure with Standard-Error Correction

Abstract

This paper provides a unified framework for a two-step MLE procedure to deal with the problem of endogeneity in Markov-switching regression models. Two important issues are considered. First, a consistent estimation of the Markov-switching regression equation of interest is considered. Second, obtaining correct standard errors of the coefficients estimates in the second step is considered, in light of Pagan's (1984) 'generated regressors.' Our Monte Carlo experiments provide the validity of the proposed methods in small samples. The model and the proposed methods are applied to Campbell and Mankiw's (1989) consumption function, by allowing for possibilities of structural breaks in the sensitivity of consumption growth to the predictable component of income growth. Empirical results suggest that during the 1970's and 1980's, when uncertainty in future income growth was highest, the measure of sensitivity was high and statistically significant, while it was not significant in the rest of the sample.