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Intersection Bounds: Estimation and Inference

Author

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  • Victor Chernozhukov
  • Sokbae Lee
  • Adam M. Rosen

Abstract

We develop a practical and novel method for inference on intersection bounds, namely bounds de?ned by either the in?mum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially in?nite constraint set. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in ?nite samples, routinely underestimating the size of the identi?ed set, we also o?er a median-bias-corrected estimator of such bounds as a natural by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.
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Suggested Citation

  • Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
  • Handle: RePEc:ecm:emetrp:v:81:y:2013:i:2:p:667-737
    DOI: ECTA8718
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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