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

ABSTRACT: This paper introduces a class of ordered probit models with endogenous regime switching. The models also allow explanatory variables to be endogenous. The paper contributes to three strands of literature. First, it implements the regime-switching approach in the models of ordered choice, and estimates the discrete-choice monetary policy rules with short-lived oscillating switches in the three latent policy regimes evolving endogenously in response to the state of the economy. Recurring regime changes are detected during a relatively stable policy period such as the Greenspan era. Second, it estimates the discrete-choice policy rules with endogenous explanatory variables. 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 applications, they not only have better fit in the Greenspan era but also produces better out-of-sample forecast than the existing models for the entire Bernanke era, correctly predicting 91 percent of target rate changes. Third, from microeconomic perspective, the paper develops a cross-nested ordered probit model that generalizes the zero-inflated ordered probit models to make them suitable for ordinal data that take on negative, zero and positive values and are characterized by abundant and heterogeneous observations in the zero (status quo) category.

KEYWORDS: ordered discrete choice · endogenous regime switching · federal funds rate target · monetary policy rules · endogeneity · zero-inflated model