Estimation of state‐space models with endogenous Markov regime‐switching parameters

This study proposes and estimates state‐space models with endogenous Markov regime‐switching parameters. It complements regime‐switching dynamic linear models by allowing the discrete regime to be jointly determined with observed or unobserved continuous state variables. The estimation framework involves a Bayesian Markov chain Monte Carlo scheme to simulate the latent state variable that controls the regime shifts. A simulation exercise shows that neglecting endogeneity leads to biased inference. This method is then applied to the dynamic Nelson–Siegel yield curve model where the unobserved time‐varying level, slope and curvature factors are contemporaneously correlated with the Markov‐switching volatility regimes. The estimation results indicate that the high volatility tends to be associated with positive innovations in the level and slope factors. More importantly, we find that the endogenous regime‐switching dynamic Nelson–Siegel model outperforms the model with and without exogenous regime‐switching in terms of out‐of‐sample prediction accuracy.