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Title:Intersection bounds: Estimation and inference PDF Logo
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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