K-state switching models with time-varying transition distributions—Does loan growth signal stronger effects of variables on inflation?

Two Bayesian sampling schemes are outlined to estimate a time-varying Markov switching transition distribution. Using data augmentation transforms the non-linear, non-normal logit transition model into a linear-normal one. A partial representation of the difference in random utility model in combination with random permutation sampling provides highest sampling efficiency. The level of the covariate in the transition distribution which balances the persistence across states is defined to be the threshold level. For illustration, we estimate a two-pillar Phillips curve for the euro area, in which loan growth affects the transition distribution.