Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79516
Authors: 
Chernozhukov, Victor
Lee, Sokbae
Rosen, Adam
Year of Publication: 
2012
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP33/12
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. 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 non-separable 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 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: 
Document Type: 
Working Paper

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