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Title:Intersection bounds: Estimation and inference PDF Logo
Authors:Chernozhukov, Victor
Lee, Sokbae
Rosen, Adam M.
Issue Date:2009
Series/Report no.:cemmap working paper CWP19/09
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 in 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 finite samples, routinely underestimating the length of the identified set, we also offer a (downward/upward) median unbiased estimator of these (upper/lower) bounds as a natural by-product of our inferential procedure. Furthermore, our method appears to be the first and currently only method for inference in nonparametric models with a continuum of inequalities. We develop asymptotic theory for our method based on the strong approximation of a sequence of studentized empirical processes by a sequence of Gaussian or other pivotal processes. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for general series estimators, which may be of independent interest. We illustrate the usefulness of our method with Monte Carlo experiments and an empirical example.
Subjects:bound analysis
conditional moments
partial identification
strong approximation
infinite dimensional constraints
linear programming
concentration inequalities
anti-concentration inequalities
JEL:C12
C13
C14
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2009.1909
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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