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*Duke Economics Working Paper #95-20*

# Which Moments to Match

##
A. Ronald Gallant

and

George E. Tauchen

### Abstract

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.

JEL: C14

Published in *Econometric Theory*, Vol. 12, No. 4, October 1996, pp.
657-681.