Chapter 7 Specification and estimation of simultaneous equation models

The simultaneous equation models are the most remarkable development in econometrics. Econometric research has led to further developments and applications of these statistical models. This chapter discusses the specification for the estimation of simultaneous equation models. The most important set of identification conditionsnamely coefficient restrictions, involves determining whether a sufficient number of instruments are available. It has recently been proved that the other type of identification restrictions used in linear simultaneous equation modelsnamely covariance restrictions, are most easily understood in terms of instrumental variables. In terms of estimation almost all consistent estimators are either instrumental variables estimators or asymptotic approximations to them. The original maximum likelihood estimator (FIML) proposed for the simultaneous equation model is an instrumental variable estimator; other estimators rely on asymptotic approximations to the basic likelihood equations. The chapter discusses exogeneity tests and specification tests in reference to the simultaneous equation model. The nonlinear simultaneous equation model is also discussed in the chapter.