Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach

Vector autoregressions with Markov-switching parameters (MS-VARs) offer dramatically better data fit than their constant-parameter predecessors. However, computational complications, as well as negative results about the importance of switching in parameters other than shock variances, have caused MS-VARs to see only sparse usage. For our first contribution, we document the effectiveness of Sequential Monte Carlo (SMC) algorithms at estimating MSVAR posteriors. Relative to multistep, model-specific MCMC routines, SMC has the advantages of being simpler to implement, readily parallelizable, and unconstrained by reliance on convenient relationships between prior and likelihood. For our second contribution, we exploit SMC's flexibility to demonstrate that the use of priors with superior data fit alters inference about the presence of time variation in macroeconomic dynamics. Using the same data as Sims, Waggoner, and Zha (2008), we provide evidence of recurrent episodes characterized by a flat Phillips curve.