Intersection Bounds: Estimation and Inference

doi:10.3982/ECTA8718

Intersection Bounds: Estimation and Inference

2013-01-01

237

OA

AI

V

Victor Chernozhukov *

DOI：10.3982/ECTA8718

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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.

Keyword:

Bound analysis

conditional moments

partial identification

strong approximation

infinite-dimensional constraints

linear programming

concentration inequalities

anti-concentration inequalities

non-Donsker empirical process methods

moderate deviations

adaptive moment selection

Intersection Bounds: Estimation and Inference

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