tailieunhanh - Econometric theory and methods, Russell Davidson - Chapter 9

Chapter 9 The Generalized Method of Moments Introduction The models we have considered in earlier chapters have all been regression models of one sort or another. In this chapter and the next, we introduce more general types of models, along with a general method for performing estimation | Chapter 9 The Generalized Method of Moments Introduction The models we have considered in earlier chapters have all been regression models of one sort or another. In this chapter and the next we introduce more general types of models along with a general method for performing estimation and inference on them. This technique is called the generalized method of moments or GMM and it includes as special cases all the methods we have so far developed for regression models. As we explained in Section a model is represented by a set of DGPs. Each DGP in the model is characterized by a parameter vector which we will normally denote by 3 in the case of regression functions and by 0 in the general case. The starting point for GMM estimation is to specify functions which for any DGP in the model depend both on the data generated by that DGP and on the model parameters. When these functions are evaluated at the parameters that correspond to the DGP that generated the data their expectation must be zero. As a simple example consider the linear regression model yt Xt3 ut. An important part of the model specification is that the error terms have mean zero. These error terms are unobservable because the parameters 3 of the regression function are unknown. But we can define the residuals ut 3 yt Xt3 as functions of the observed data and the unknown model parameters and these functions provide what we need for GMM estimation. If the residuals are evaluated at the parameter vector 30 associated with the true DGP they have mean zero under that DGP but if they are evaluated at some 3 30 they do not have mean zero. In Chapter 1 we used this fact to develop a method of moments MM estimator for the parameter vector 3 of the regression function. As we will see in the next section the various GMM estimators of 3 include as a special case the MM or OLS estimator developed in Chapter 1. In Chapter 6 when we dealt with nonlinear regression models and again in Chapter 8 we used .