Reduced form estimation in partially specified simultaneous equations models

Abstract

Using Monte Carlo methods, this dissertation investigates the relative efficiency of alternative reduced form estimators for partially specified simultaneous equations models, including both non-censored and censored endogenous variables. The research has been undertaken with two major objectives in mind. First, our research is designed to more fully investigate the conditions determining the relative efficiency of the currently available reduced form estimators for these models. As is well known, the relative efficiency of these estimators will depend crucially on several parameters corresponding to the models. The values of these parameters are generally allowed to vary over a specified range and across experiments. However, past studies have limited this variation to very narrow ranges and, thus, have failed to fully catalogue the affects of alternative parameter specifications on the relative efficiency of these estimators. Our research is designed to explore a more complete range of values for these crucial parameters and investigate their affects on the relative performance of the reduced form estimators. Second, past studies have implicitly treated models with censored dependent variables separately from those containing non-censored dependent variables. Our research, however, demonstrates that the reduced form estimators for these two cases are, at least in spirit, quite similar. These similarities are exploited in such a way as to allow for a more thorough investigation of the relative performance of the alternative estimators for the censored case. In addition, we propose several new estimators that differ from previous estimators in the way the overidentifying restrictions are employed to estimate the reduced form models. Our experiments also compare and contrast the performance of these new estimators to those currently available. In some cases these new estimators perform quite well. Overall, our research has been successful and we are able to offer several rules thumb to guide the researcher in a choice among alternative estimators of the reduced form model, where the structural model is only partially specified. There are many extensions to this research, some of which are being investigated by the author.