Honest confidence sets in nonparametric IV regression and other ill-posed models

Abstract

This paper provides novel methods for inference in a very general class of ill-posed models in econometrics, encompassing the nonparametric instrumental regression, different functional regressions, and the deconvolution. I focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). I first show that it is not possible to develop inferential methods directly based on the uniform central limit theorem. To circumvent this difficulty I develop two approaches that lead to valid confidence sets. I characterize expected diameters and coverage properties uniformly over a large class of models (i.e. constructed confidence sets are honest). Finally, I illustrate that introduced confidence sets have reasonable width and coverage properties in samples commonly used in applications with Monte Carlo simulations and considering application to Engel curves.

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Reference

Andrii Babii, “Honest confidence sets in nonparametric IV regression and other ill-posed models”, TSE Working Paper, n. 17-803, May 2017.