Inference Based on Many Conditional Moment Inequalities

82 Pages Posted: 30 Apr 2016 Last revised: 21 May 2016

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Xiaoxia Shi

University of Wisconsin - Madison; Yale University

Multiple version iconThere are 2 versions of this paper

Date Written: April 28, 2016

Abstract

In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably in finite, or uncountably in finite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature.

The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo experiments for a conditional stochastic dominance example and a random-coefficients binary-outcome example support the theoretical results.

Keywords: Asymptotic size, Conditional moment inequalities, Confidence set, Many moments, Multiple equilibria, Partial identification, Random coefficients, Stochastic dominance, Test

JEL Classification: C1, C2, C3

Suggested Citation

Andrews, Donald W. K. and Shi, Xiaoxia, Inference Based on Many Conditional Moment Inequalities (April 28, 2016). Cowles Foundation Discussion Paper No. 2010R, Available at SSRN: https://ssrn.com/abstract=2772179 or http://dx.doi.org/10.2139/ssrn.2772179

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Xiaoxia Shi

University of Wisconsin - Madison ( email )

1180 Observatory Drive
Madison, WI 53706
United States

Yale University

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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