Instrumental-Variables Estimation in Markov Switching Models with Endogenous Explanatory Variables: An Application to the Term Structure of Interest Rates

This paper considers the problem of estimating Markov regime switching models with endogenous explanatory variables. When the data-generating process for consumption is subject to Markov regime switching, the standard model for the term structure of interest rates based on the Euler equations for a utility-maximizing agent implies the presence of a time-varying risk premium which is also subject to Markov regime shifts. Under such conditions, the regression equations that are typically used to test the expectations hypothesis of the term structure do not only have regime-dependent parameters but also endogenous regressors (that is right-hand-side variables which are correlated with the disturbances within each regime). Using three-month and six-month interest rates for the G7 countries, we show that the (generalized) expectations hypothesis cannot be rejected when we allow for a risk premium with Markov regimes, provided that instrumental variables are used to account for endogeneity.