Simultaneous Equation Models and Dynamic Systems

We discussed at the end of Chapter 7 one type of multiple equation model (SUR). Here we’ll present a second type of such models known as simultaneous equation models. A preliminary type of such a model was adopted at the beginning of Chapter 1, where the structural model described by Equations (1.1)–(1.3) was presented; finally the obtained reduced form was shown in (1.13). This was an attempt for a first familiarization with simultaneous equation models, where explanatory variables from one equation can be dependent variables in other equations. Note that each endogenous explanatory variable is explicitly specified in the relevant structural equation. It is recalled that in each structural equation endogenous explanatory variables are correlated with the corresponding disturbance term, which implies that OLS estimates are inconsistent. Thus other estimation methods should be employed when estimating the parameters of the structural form of such a model. The most popular one is a single-equation method, namely two stage least squares (2SLS). However, more efficient methods can be employed using the entire model, which has the form presented in Equations (7.11)–(7.11a) of Chapter 7.