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Chapter 12 Multivariate Models 12.1 Introduction Up to this point, almost all the models we have discussed have involved just one equation. In most cases, there has been only one equation because there has been only one dependent variable. | Chapter 12 Multivariate Models 12.1 Introduction Up to this point almost all the models we have discussed have involved just one equation. In most cases there has been only one equation because there has been only one dependent variable. Even in the few cases in which there were several dependent variables interest centered on just one of them. For example in the case of the simultaneous equations model that was discussed in Chapter 8 we chose to estimate just one structural equation at a time. In this chapter we discuss models which jointly determine the values of two or more dependent variables using two or more equations. Such models are called multivariate because they attempt to explain multiple dependent variables. As we will see the class of multivariate models is considerably larger than the class of simultaneous equations models. Every simultaneous equations model is a multivariate model but many interesting multivariate models are not simultaneous equations models. In the next section which is quite long we provide a detailed discussion of GLS feasible GLS and ML estimation of systems of linear regressions. Then in Section 12.3 we discuss the estimation of systems of nonlinear equations which may involve cross-equation restrictions but do not involve simultaneity. Next in Section 12.4 we provide a much more detailed treatment of the linear simultaneous equations model than we did in Chapter 8. We approach it from the point of view of GMM estimation which leads to the well-known 3SLS estimator. In Section 12.5 we discuss the application of maximum likelihood to this model. Finally in Section 12.6 we briefly discuss some of the methods for estimating nonlinear simultaneous equations models. 12.2 Seemingly Unrelated Linear Regressions The multivariate linear regression model was investigated by Zellner 1962 who called it the seemingly unrelated regressions model. An SUR system as such a model is often called involves n observations on each of g dependent .
