Gibbs Sampling for a Duration Dependent Markov Switching Model with an Application to the U.S. Business Cycle

Does the probability of moving from a recession into an expansion depend on how long the economy has been in recession? Similarly, does the probability that the economy may fall into a recession depend on the length of the expansion phase? The present paper tries to answer these two questions, at least as far as the U.S. economy is concerned. Some authors have already dealt with the duration-dependence problem: Diebold et al. [7] and Watson [14] apply nonparametric methods to the NBER’s dating of business cycles, while Durland and McCurdy [8] use an extension of the Hamiton’s [11] Markov switching model. Their conclusions are in favor of the duration dependence hypothesis, at least in the contraction phase. In particular Diebold et al. [7] conclude that, given their results, Hamilton’s Markov switching model is miss-specified because its transition probabilities are constant over time; furthermore they also argue that including duration dependence in a Markov switching problem may raise identification and estimation problems. In this paper we use a model in some way similar to the one used by Durland and McCurdy [8], but with some major differences: (i) we work within a Bayesian framework combined with MCMC (Markov Chain Monte Carlo) methods, (ii) we show that the duration-dependent switching model has a representation as time-invariant Markov switching model, allowing the use of all the standard tools of such models, (iii) we use a probit regression