Transition Variables in the Markov-switching Model: Some Small Sample Properties

This paper researches small-sample properties of the Markov-switching model with time-varying transition probabilities. By means of simulation, it is shown that the likelihood ratio statistic is over-sized for sample sizes relevant in many empirical applications. The number of regime switches occurring in the sample rather than the total number of observations is central to the magnitude of the distortion, with other factors such a persistence in transition equation variables and the precision at which states are inferred being influential on size. In an application to possible predictors of switches to recessions in U.S. data, it is shown that critical values for the likelihood ratio statistic need to be adjusted far upwards to reflect true confidence levels.