  We define a moment-based estimator that maximizes the empirical saddlepoint
(ESP) approximation of the distribution of solutions to empirical moment
conditions. We call it the ESP estimator. We prove its existence, consistency
and asymptotic normality, and we propose novel test statistics. We also show
that the ESP estimator corresponds to the MM (method of moments) estimator
shrunk toward parameter values with lower estimated variance, so it reduces the
documented instability of existing moment-based estimators. In the case of
just-identified moment conditions, which is the case we focus on, the ESP
estimator is different from the MM estimator, unlike the recently proposed
alternatives, such as the empirical-likelihood-type estimators.
