Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many b...

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Bibliographic Details
Main Authors: Chernozhukov, Victor V. (Contributor), Lee, Sokbae (Author), Rosen, Adam M. (Author)
Other Authors: Massachusetts Institute of Technology. Department of Economics (Contributor)
Format: Article
Language:English
Published: John Wiley & Sons, Inc, 2013-12-05T21:43:29Z.
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Online Access:Get fulltext
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100 1 0 |a Chernozhukov, Victor V.  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Economics  |e contributor 
100 1 0 |a Chernozhukov, Victor V.  |e contributor 
700 1 0 |a Lee, Sokbae  |e author 
700 1 0 |a Rosen, Adam M.  |e author 
245 0 0 |a Intersection Bounds: Estimation and Inference 
260 |b John Wiley & Sons, Inc,   |c 2013-12-05T21:43:29Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/82644 
520 |a We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. 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 nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a 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 are 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. 
520 |a Economic and Social Research Council (Great Britain) (RES-589-28-0001) 
520 |a Economic and Social Research Council (Great Britain) (RES-000-22-2761) 
520 |a European Research Council (ERC-2009-StG-240910-ROMETA) 
520 |a National Science Foundation (U.S.) 
546 |a en_US 
655 7 |a Article 
773 |t Econometrica