Simultaneous Equations Model

Economists formulate models for consumption, production, investment, money demand and money supply, and labor demand and labor supply to attempt to explain the workings of the economy. These behavioral equations are estimated equation by equation or jointly as a system of equations. These are known as simultaneous equations models. Much of today’s econometrics has been influenced and shaped by a group of economists and econometricians known as the Cowles Commission who worked together at the University of Chicago in the late 1940s, see Chap. 1. Simultaneous equations models had their genesis in economics during that period. Haavelmo (Supplement to Econometrica 12:1944) work emphasized the use of the probability approach to formulating econometric models. Koopmans and Marschak (Statistical Inference in Dynamic Economic Models (John Wiley and Sons: New York), 1950) and Koopmans and Hood ( Studies in Econometric Method (John Wiley and Sons: New York), 1953) in two influential Cowles Commission monographs provided the appropriate statistical procedures for handling simultaneous equations models. In this chapter, we first give simple examples of simultaneous equations models and show why the least squares estimator is no longer appropriate. Next, we discuss the important problem of identification and give a simple necessary but not sufficient condition that helps check whether a specific equation is identified. Sections 11.2 and 11.3 give the estimation of a single and a system of equations using instrumental variable procedures. Section 11.4 gives a test of over-identification restrictions, whereas Sect. 11.5 gives a Hausman specification test. Section 11.6 concludes with an empirical example. The Appendix revisits the identification problem and gives a necessary and sufficient condition for identification.