Sensitivity Analysis using Approximate Moment Condition Models

TL;DR

This paper develops a method for constructing near-optimal confidence intervals in models with approximate moment conditions, accounting for potential misspecification and bias, and demonstrates significant improvements in empirical applications.

Contribution

It introduces a GMM-based inference approach that optimally adjusts for misspecification bias, along with asymptotic bounds demonstrating near-optimality under local misspecification.

Findings

Adjusted CIs can be shrunk by a factor of 3 or more.

The proposed weighting matrix accounts for potential bias from misspecification.

Asymptotic efficiency bounds are derived for inference under local misspecification.

Abstract

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.