COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1676

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

Donald W.K. Andrews and Panle Jia

September 2008

This paper is concerned with tests and confidence intervals for partially-identified parameters that are defined by moment inequalities and equalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare a wide variety of these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. In addition, we provide a data-dependent procedure for choosing the key moment selection tuning parameter and a data-dependent size-correction factor.

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

JEL Classifications: C12, C15