Estimation and Confidence Regions for Parameter Sets in Econometric Models

TLDR

The framework applies to models with moment inequalities and equalities, such as game‑theoretic, revealed preference, missing‑data regressions, auctions, structural quantile regressions, and asset‑pricing models, where the criterion function embodies testable restrictions and the identified set consists of parameter values minimizing it. The paper develops a framework for estimation and inference in partially identified econometric models, providing estimators and confidence regions for the identified set of minimizers of a criterion function. The authors construct estimators and confidence regions by inverting the sample criterion function, and develop methods to analyze its asymptotic properties under set identification, establishing consistency, convergence rates, and inference results. The proposed estimators and confidence regions are shown to be consistent, converge at established rates, and provide valid inference for the identified set.

Abstract

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 Θ I of an econometric criterion function Q(θ). In applications, the criterion function embodies testable restrictions on economic models. A parameter value θ that 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, Q n (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.