Sensitivity analysis using approximate moment condition models

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.

Sensitivity Analysis using Approximate Moment Condition Models

“…Section 6 presents an empirical application. Additional results and proofs are collected in the Appendices in the Online Supplementary Material (Armstrong and Kolesár (2021)).…”

An Averaging Estimator for Two-Step M-Estimation in Semiparametric Models

“…The approach here is still useful, since how the nuisance function is modeled affects both variance and bias even when it is known and needs no estimation. Third, among the literature on sensitivity analysis (e.g., Rosenbaum and Rubin, 1983;Leamer, 1985;Imbens, 2003;Altonji, Elder, and Taber, 2005;Andrews, Gentzkow, and Shapiro, 2017;Mukhin, 2018;Oster, 2019), Bonhomme and Weidner (2021) and Armstrong and Kolesár (2021) are the closest to this paper. They take a restricted model as benchmark and study the sensitivity of the results with respect to possible local misspecification that deviates from it.…”

Salvaging Falsified Instrumental Variable Models

“…Several recent papers use local asymptotics to study sensitivity to misspecification. For example, see Andrews, Gentzkow, and Shapiro (2017), Bonhomme and Weidner (2018), and Armstrong and Kolesár (2021). This approach assumes the baseline model is approximately correct, in the sense that the magnitude of model misspecification is similar to the magnitude of sampling uncertainty.…”