The Empirical Saddlepoint Estimator

TL;DR

The paper introduces the Empirical Saddlepoint (ESP) estimator, a new moment-based method that improves stability and accuracy in estimating parameters from empirical moment conditions, with proven theoretical properties.

Contribution

It defines the ESP estimator, proves its statistical properties, and shows it reduces instability compared to existing moment-based estimators.

Findings

Proves existence, consistency, and asymptotic normality of ESP estimator.

Demonstrates ESP estimator's reduced instability over traditional methods.

Provides novel test statistics for empirical moment conditions.

Abstract

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.