Minimizing sensitivity to model misspecification

Abstract

We propose a framework for estimation and inference when the model may be misspecified. We rely on a local asymptotic approach where the degree of misspecification is indexed by the sample size. We construct estimators whose mean squared error is minimax in a neighborhood of the reference model, based on one‐step adjustments. In addition, we provide confidence intervals that contain the true parameter under local misspecification. As a tool to interpret the degree of misspecification, we map it to the local power of a specification test of the reference model. Our approach allows for systematic sensitivity analysis when the parameter of interest may be partially or irregularly identified. As illustrations, we study three applications: an empirical analysis of the impact of conditional cash transfers in Mexico where misspecification stems from the presence of stigma effects of the program, a cross‐sectional binary choice model where the error distribution is misspecified, and a dynamic panel data binary choice model where the number of time periods is small and the distribution of individual effects is misspecified.

Counterfactual Sensitivity and Robustness

“…Our approach allows for a wider range of counterfactual (e.g., welfare), shape restrictions, and multinomial choice, in addition to performing sensitivity analyses. 4 Finally, our work is complementary to the recent literature on local sensitivity-see, for example, Kitamura, Otsu, and Evdokimov (2013), Andrews, Gentzkow, andShapiro (2017, 2020), Armstrong and Kolesár (2021), Bonhomme andWeidner (2022), andMukhin (2018). Much of this literature is concerned with local misspecification of moment conditions, which is different from the setting we consider.…”

Optimally-transported generalized method of moments

“…The problem of model misspecification has also been approached from the view point of sensitivity analysis (Andrews, Gentzkow and Shapiro (2017), Bonhomme and Weidner (2022)). However, this treatment is fundamentally limited to local misspecification (whose magnitude decreases with sample size).…”

“…However, this treatment is fundamentally limited to local misspecification (whose magnitude decreases with sample size). It mainly provides diagnostic tools and can only deliver a specific estimator (Bonhomme and Weidner (2022)), if one is willing to specify an a priori bound on the misspecification magnitude.…”

Outlier robust inference in the instrumental variable model with applications to causal effects

“…The desirable estimators and tests should be accurate at F and stable when the data comes from a model in the neighborhood F 𝜖 . Our work is related to the growing literature on local misspecification; see Andrews et al (2017Andrews et al ( , 2020, Bonhomme and Weidner (2022), Ichimura and Newey (2022), Kitamura et al (2013), and references therein. The closest approach is the one by Bonhomme and Weidner (2022), where the minimax robust estimators and confidence intervals under misspecifications of specific aspects of the model are derived.…”