COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1676R

Inference for Parameters Defined by Moment Inequalities:
A Recommended Moment Selection Procedure

Donald W.K. Andrews and Panle Jia

September 2008
Revised August 2011

This paper is concerned with tests and confidence intervals for parameters that are not necessarily identified and are defined by moment inequalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter kappa and a size-correction factor eta.

Keywords: Asymptotic size, Asymptotic power, Bootstrap, Confidence set, Generalized moment selection, Moment inequalities, Partial identification, Refined moment selection, Test, Unidentified parameter

JEL Classification: C12, C15