Estimation of Regression Relationships Containing Unobservable Independent Variables

Abstract

as an independent variable. Last in Zellner [10], it is shown that equations of simultaneous equation models can be brought into a regression form involving some observable and some unobservable independent variables. Given that regression relationstcontaining unobservable independent occur quite frequently, and -in' fact are a special case of errors in the variables models, it is important to have good methods for analyzing them. Previous analyses have almost always involved the use of an instrumental variable approach, an approach which leads to estimators with the desirable large sample property of consistency. However, it is not clear that the instrumental variable approach leads to asymptotically efficient estimators for all parameters of a model and the small sample properties of instrumental variable estimators are for the most part unknown. In the present paper, we first consider the specification and interpretation of the models under consideration in Section 2. Then in Section 3 we apply a least squares approach to generate an estimator which, with a normality assumption, is a maximum likelihood estimator. The relationship of this estimator to certain instrumental variable estimators is set forth. Then in Section 4, a Bayesian analysis of the model is presented. Finally, in Section 5 some concluding remarks are presented.