Eliminating the omitted variable bias by a regime-switching approach

This work shows a procedure that aims to eliminate or reduce the bias caused by omitted variables by means of the so-called regime-switching regressions. There is a bias estimation whenever the statistical (linear) model is under-specified, that is, when there are some omitted variables and they are correlated with the regressors. This work shows how an appropriate specification of a regime-switching model (independent or Markov-switching) can eliminate or reduce this correlation, hence the estimation bias. A demonstration is given, together with some Monte Carlo simulations. An empirical verification, based on Fisher's equation, is also provided.