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 simple one-step adjustments. In addition, we provide confidence intervals that contain the true parameter under local misspecification. 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 two binary choice models: a cross-sectional  model where the error distribution is misspecified, and a dynamic panel data  model where the number of time periods is small and the distribution of individual effects is misspecified.
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 simple 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.
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To
As a tool to
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two binary choice models:
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,
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binary choice
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binary choice