Methods for inference in large multiple-equation Markov-switching models

Abstract

a b s t r a c tInference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely to appear in smaller models. Our framework allows for many regimes in the transition matrix, without letting the number of free parameters grow as the square as the number of regimes, but also without losing a convenient form for the posterior distribution. Calculation of marginal data densities is difficult in these high-dimensional models. This paper gives methods to overcome these difficulties, and explains why existing methods are unreliable. It makes suggestions for maximizing posterior density and initiating MCMC simulations that provide robustness against the complex likelihood shape.

Realized and Optimal Monetary Policy Rules in an Estimated Markov‐Switching DSGE Model of the United Kingdom

“… Notes: The log marginal likelihood values presented here are approximated using both Geweke (1999) and Sims et al The estimates of q L obtained from Sims et al. are also presented in parentheses along with the marginal likelihood values in the last column.…”

“…Estimates of q L provide an indication of how much of overlap between the weighting matrix and the posterior density. Sims et al (2008, p. 264) stress that q L ≥ 1.0 − 05 to ensure the calculated marginal likelihood is reliable.…”

“…We first implemented the commonly used the modified harmonic‐mean estimator of Geweke (1999) for this task. In addition, we also used the approach of Sims et al (2008) as a robustness check. The latter is designed for models with time‐varying parameters, where the posterior density tends to be non‐Gaussian.…”

“…The latter is designed for models with time‐varying parameters, where the posterior density tends to be non‐Gaussian. In contrast to Geweke, who uses a truncated normal density as the weighting function, Sims et al. use a truncated elliptical density.…”

“…use a truncated elliptical density. The marginal likelihood value calculated using both the Geweke and Sims et al. approaches are presented in Table 7 later in this article, and we note here that there is little difference between the two sets of likelihood values.…”