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http://hdl.handle.net/10419/64663
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| Title: | | Intersection bounds: Estimation and inference  |
| Authors: | | Chernozhukov, Victor Lee, Sokbae Rosen, Adam M. |
| Issue Date: | | 2011 |
| Series/Report no.: | | cemmap working paper CWP34/11 |
| Abstract: | | 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. 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 infinite samples, routinely underestimating the size of the identified set, we also offer 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. |
| Subjects: | | 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 |
| JEL: | | C12 C13 C14 |
| Persistent Identifier of the first edition: | | doi:10.1920/wp.cem.2011.3411 |
| Document Type: | | Working Paper |
| Appears in Collections: | | cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)
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