  We consider inference in models defined by approximate moment conditions. We
show that near-optimal confidence intervals (CIs) can be formed by taking a
generalized method of moments (GMM) estimator, and adding and subtracting the
standard error times a critical value that takes into account the potential
bias from misspecification of the moment conditions. In order to optimize
performance under potential misspecification, the weighting matrix for this GMM
estimator takes into account this potential bias, and therefore differs from
the one that is optimal under correct specification. To formally show the
near-optimality of these CIs, we develop asymptotic efficiency bounds for
inference in the locally misspecified GMM setting. These bounds may be of
independent interest, due to their implications for the possibility of using
moment selection procedures when conducting inference in moment condition
models. We apply our methods in an empirical application to automobile demand,
and show that adjusting the weighting matrix can shrink the CIs by a factor of
3 or more.
