An endogenous regime-switching model of ordered choice with an application to federal funds rate target

This paper introduces a class of ordered probit models with endogenous switching among N latent regimes and possibly endogenous explanatory variables. The paper contributes to and bridges two strands of microeconometric literature. First, it extends endogenous switching regressions to models of ordered choice with N unknown regimes. Second, it generalizes the existing zero-inflated ordered probit models to make them suitable for ordinal data that take on negative, zero and positive values and characterized by abundant and heterogeneous zero observations. From a macroeconomic perspective, it is the first attempt to implement regime switching and accommodate endogenous regressors in discrete-choice monetary policy rules. Recurring oscillating regime switches in the three regimes evolving endogenously in response to the state of economy are detected during a relatively stable policy period such as the Greenspan era. The Monte Carlo experiments and an application to the federal funds rate target demonstrate that ignoring endogeneity and regime-switching environment can lead to seriously distorted statistical inference. In the simulations, the new models perform well in small samples. In the application, they not only have better in-sample fit for the Greenspan era than the existing models but also forecast better out of sample for the entire Bernanke era, correctly predicting 91 percent of policy decisions.