On the consistency of the two-step estimates of the MS-DFM: a Monte Carlo study

The Markov-Switching Dynamic Factor Model (MS-DFM) has been used in different applications, notably in the business cycle analysis. When the cross-sectional dimension of data is high, the Maximum Likelihood estimation becomes unfeasible due to the excessive number of parameters.In this case, the MS-DFM can be estimated in two steps, which means that in the first step the common factor is extracted from a database of indicators, and in the second step the Markov-Switching autoregressive model is fit to this extracted factor. The validity of the two-step method is conventionally accepted, although the asymptotic properties of the two-step estimates have not been studied yet. In this paper we examine their consistency as well as the small-sample behavior with the help of Monte Carlo simulations. Our results indicate that the two-step estimates are consistent when the number of cross-section series and time observations is large, however, as expected, the estimates and their standard errors tend to be biased in small samples