Which Moments to Match?
A. Ronald Gallant, George Tauchen
Econometric Theory, Vol. 12, No. 4, (Oct., 1996), pp. 657-681.
We describe an intuitive, simple, and systematic approach to
generating moment conditions for 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.