Bias correction through filtering omitted variables and instruments

This paper proposes a combination of the particle-filter-based method and the expectation-maximization algorithm (PFEM), in order to filter unobservable variables and hence, to reduce the omitted variables bias. Furthermore, I consider as an unobservable variable, an exogenous one that can be used as an instrument in the instrumental variable (IV) methodology. The aim is to show that the PFEM is able to eliminate or reduce both the omitted variable bias and the simultaneous equation bias by filtering the omitted variable and the unobserved instrument, respectively. In other words, the procedure provides (at least approximately) consistent estimates, without using additional information embedded in the omitted variable or in the instruments, since they are filtered by the observable variables. The validity of the procedure is shown both through simulations and through a comparison to an IV analysis which appeared in an important previous publication. As regards the latter point, I demonstrate that the procedure developed in this article yields similar results to those of the original IV analysis.