This paper develops a framework for performing estimation and inference in econometric models with partial identification, focusing particularly on models characterized by moment inequalities and equalities. Applications of this framework include the analysis of game-theoretic models, revealed preference restrictions, regressions with missing and corrupted data, auction models, structural quantile regressions, and asset pricing models.
Specifically, we provide estimators and confidence regions for the set of minimizers ΘI of an econometric criterion function Q(θ). In applications, the criterion function embodies testable restrictions on economic models. A parameter value θthat describes an economic model satisfies these restrictions if Q(θ) attains its minimum at this value. Interest therefore focuses on the set of minimizers, called the identified set. We use the inversion of the sample analog, Qn(θ), of the population criterion, Q(θ), to construct estimators and confidence regions for the identified set, and develop consistency, rates of convergence, and inference results for these estimators and regions. To derive these results, we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification.