Which Moments to Match?

Abstract

We describe an intuitive, simple, and systematic approach to generating moment conditions for generalized method of moments (GMM) estimation of the parameters of a structural model. The idea is to use the score of a density that has an analytic expression to define the GMM criterion. The auxiliary model that generates the score should closely approximate the distribution of the observed data but is not required to nest it. If the auxiliary model nests the structural model then the estimator is as efficient as maximum likelihood. The estimator is advantageous when expectations under a structural model can be computed by simulation, by quadrature, or by analytic expressions but the likelihood cannot be computed easily.