We propose a framework for estimation and inference about the parameters of an economic model and predictions based on it, 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 derive formulas to construct estimators whose mean squared error is minimax in a neighborhood of the reference model, based on simple one-step adjustments. We construct confidence intervals that contain the true parameter under both correct specification and local misspecification. We calibrate the degree of misspecification using a model detection error approach. Our approach allows us to perform systematic sensitivity analysis when the parameter of interest may be partially or irregularly identified. To illustrate our approach we study panel data models where the distribution of individual effects may be misspecified and the number of time periods is small, and we revisit the structural evaluation of a conditional cash transfer program in Mexico.