Duration-Dependent Markov-Switching VAR Models with Applications to the Business Cycle Analysis

Hamilton (1989) introduced the Markov-switching models (from now on MS) to the business cycle researchers. He applied the MS model to the real U.S. GDP and showed how good the probability of being in recession or expansion generated by his model matched the NBER dating. Since then, the studies on business cycles that exploited the MS model have grown exponentially. Nevertheless, the basic MS model, when used to model the business cycle, has at least two theoretical weaknesses: (i) it is univariate, (ii) it does not allow duration dependence. Since business cycles are fluctuations of aggregate economic activity, which express themselves through the comovements of many macro variables, point (i) is not a negligible limitation. The multivariate generalization of the MS model was carried out by Krolzig (1997), in his excellent work on the MS-VAR model. As far as point (ii) is concerned, some authors, such as Diebold, Rudebusch and Sichel (1993), Watson (1994), have found evidence of duration dependence in the U.S. business cycles, and therefore, as Diebold et al. (1993) point out, the MS model results miss-specified. In the present paper a duration dependent MS-VAR model is presented and applied to the four macroeconomic time series that the NBER uses to date the U.S. business cycle. Bayesian inference on the unknown quantities of the model is carried out using Markov chain Monte Carlo methods, which outrun some limitation of the maximum-likelihood approach to such models.