TAILIEUCHUNG - Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 14

Generalized Method of Moments and Minimum Distance Estimation In Chapter 8 we saw how the generalized method of moments (GMM) approach to estimation can be applied to multiple-equation linear models, including systems of equations, with exogenous or endogenous explanatory variables, and to panel data models. | Generalized Method of Moments and Minimum Distance Estimation In Chapter 8 we saw how the generalized method of moments GMM approach to estimation can be applied to multiple-equation linear models including systems of equations with exogenous or endogenous explanatory variables and to panel data models. In this chapter we extend GMM to nonlinear estimation problems. This setup allows us to treat various efficiency issues that we have glossed over until now. We also cover the related method of minimum distance estimation. Because the asymptotic analysis has many features in common with Chapters 8 and 12 the analysis is not quite as detailed here as in previous chapters. A good reference for this material which fills in most of the gaps left here is Newey and McFadden 1994 . Asymptotic Properties of GMM Let w e Rm i 1 2 . denote a set of independent identically distributed random vectors where some feature of the distribution of w is indexed by the P x 1 parameter vector 0. The assumption of identical distribution is mostly for notational convenience the following methods apply to independently pooled cross sections without modification. We assume that for some function g w 0 e RL the parameter 0o e 0 c RP satisfies the moment assumptions E g wf 0O 0 As we saw in the linear case where g w - 0 was of the form Z y X 0 a minimal requirement for these moment conditions to identify 0o is L P. If L P then the analogy principle suggests estimating 0o by setting the sample counterpart N 1 Pi 1 g w 0 to zero. In the linear case this step leads to the instrumental variables estimator see equation . When L P we can choose 0 to make the sample average close to zero in an appropriate metric. A generalized method of moments GMM estimator 0 minimizes a quadratic form in Pi 1 g w - 0 N min g w y y e Y äj z 1 N J2g wi y i 1 where 13 is an L x L symmetric positive semidefinite weighting matrix. Consistency of the GMM estimator follows along the lines of consistency

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