Indirect estimation of Markov switching models with endogenous switching

Markov Switching models have been successfully applied to many economic problems. The most popular version of these models implies that the change in the state is driven by a Markov Chain and that the state is an exogenous discrete unobserved variable. This hypothesis seems to be too restrictive. Earlier literature has often been concerned with endogenous switching, hypothesizing a correlation structure between the observed variable and the unobserved state variable. However, in this case the classical likelihood-based methods provide biased estimators. In this paper we propose a simple “estimation by simulation” procedure, based on indirect inference. Its great advantage is in the treatment of the endogenous switching, which is about the same as for the exogenous switching case, without involving any additional difficulty. A set of Monte Carlo experiments is presented to show the interesting performances of the procedure.