Estimation and Confidence Regions for Parameter Sets in Econometric Models

This paper develops a framework for performing estimation and inference in econo- metric models with partial identification, focusing particularly on models character- ized by moment inequalities and equalities. Applications of this framework include the analysis of game-theoretic models, revealed p...

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Bibliographic Details
Published in:Econometrica 2007-09, Vol.75 (5), p.1243-1284
Main Authors: Chernozhukov, Victor, Hong, Han, Tamer, Elie
Format: Article
Language:English
Subjects:
Applications
bootstrap
Bootstrap mechanism
Consistent estimators
contour sets
Distribution theory
Econometric models
Econometrics
Economic models
Estimation
Estimation methods
Estimators
Exact sciences and technology
Inference
Insurance, economics, finance
Mathematical functions
Mathematical independent variables
Mathematics
Model testing
Modeling
moment equalities
moment inequalities
Nonparametric inference
Parametric inference
Parametric models
Probability and statistics
resampling
Sciences and techniques of general use
Set estimator
Significance tests
Statistics
Working papers
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Summary:This paper develops a framework for performing estimation and inference in econo- metric models with partial identification, focusing particularly on models character- ized 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 $\Theta_I$ of an econometric criterion function $Q(\Theta)$. In applications, the criterion function embodies testable restrictions on economic models. A parameter value Θ that describes an economic model satisfies these restrictions if $Q(\Theta)$ 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, $Q_n(\Theta)$, of the population criterion, $Q(\Theta)$, 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.
ISSN:0012-9682
1468-0262
DOI:10.1111/j.1468-0262.2007.00794.x