Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables

We consider multivariate Markov switching first-order autoregression models with endogenous explanatory variables, propose a joint estimation algorithm of type EM, written at vector-matrix level, to account for endogeneity, and derive matrix formulas for the ML estimators of model parameters. Then we prove the consistency of such estimators, provide matrix expressions for their asymptotic covariances, and present some tests for endogeneity. Further, a simulation study is proposed to illustrate the theoretical results and provide evidence on the usefulness of the considered model.