Simultaneous equations inference in econometrics

Abstract

This paper is a survey of the salient results developed in the literature of econometrics over the past twenty years regarding simultaneous equations systems. Models of economic behavior are generally characterized by simultaneous equations; this characterization is due to the general equilibrium theory of economic phenomena according to which a large number of economic variables are mutually determined so that often causality is held to be bidirectional. A natural formulation of this, for empirical work, is to represent the economic phenomena under consideration by simultaneous (generally linear) equations systems. This presents considerable problems in estimating the parameters of the resulting models since the least squares procedure can be shown to yield inconsistent estimators. To remedy this deficiency a number of estimating procedures have been devised. Such procedures can be classed in two broad categories. Full information procedures take into account, in estimating the parameters, all sample information and a priori restrictions on the coefficients of the entire system. Limited information procedures estimate consistently, but typically inefficiently, the unknown parameters of each equation by taking into account only the immediately relevant part of the sample information and the a priori restrictions that apply specifically to the equation under consideration. The paper examines the several variants proposed in each category and considers models which are dynamic and in which the error vectors are classical, i.e., they constitute a sequence of mutually independent identically distributed random variables, as well as cases where the error vectors are finite order autoregressions. The asymptotic distribution and other relevant properties of all such estimators are either explicitly derived or noted and there is a brief discussion of some small sample results and instances of applications of such techniques to the estimation of economy wide econometric models of various countries such as the U.S., U.K., and Japan.