Inference in Semiparametric Conditional Moment Modelswith Partial Identification

汇报人：Shengjie Hong(University of Wisconsin-Madison)

时 间：2-3：30pm,Feb.16^th(Thu)

地 点：2号楼217

Abstract

This paper develops inference methods for conditional moment models in which the unknown parameter is partially identified and may contain infinite-dimensional components. I consider testing the hypothesis that a given restriction on the parameter is satisfied by at least one element of the identification set. I propose using the sieve minimum of a Kolmogorov-Smirnov type statistic as the test statistic, derive its asymptotic distribution, and provide consistent bootstrap critical values. In this way a broad family of restrictions can be consistently tested, making the proposed procedure applicable to various types of inference. In particular, I show how to: (1) test the semiparametric model specification; (2) construct confidence sets for unknown parametric components; and (3) construct confidence sets for unknown functions at a given point. The specification test is consistent against fixed alternatives. The confidence sets have correct asymptotic coverage probability, excluding any value outside the identification set with asymptotic probability one. My methods are robust to partial identification, and allow for the moment functions to be nonsmooth. A Monte Carlo study demonstrates finite sample performance.

Keywords: Conditional moment equalities, identification set, model specification test, confidence set, Sieve space, ill-posedness, bootstrap.