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Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments

JoonHwan Cho and Thomas M. Russell

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Abstract: This paper considers uniformly valid inference for linear functionals and scalar subvectors of partially identified parameters defined by linear moment inequalities. Our proposed procedure amounts to bootstrapping the value functions of four carefully constructed "perturbed" linear programming problems, and does not require the researcher to grid over the parameter space. Our low-level conditions for uniform validity rely on a novel application of Sard's Theorem from differential topology, and may be of substantial separate interest. Our procedure is asymptotically conservative for the true partially identified parameter, but draws its appeal from the fact that it is valid under weak assumptions, it performs well in finite samples, and is computationally simple to implement.

Date: 2018-10, Revised 2020-12
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