COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1815R

Similar-on-the-Boundary Tests for Moment Inequalities Exist,
But Have Poor Power

Donald W. K. Andrews

August 2011
Revised March 2012

This paper shows that moment inequality tests that are asymptotically similar on the boundary of the null hypothesis exist, but have very poor power. Hence, existing tests in the literature, which are asymptotically non-similar on the boundary, are not deficient. The results are obtained by first establishing results for the finite-sample multivariate normal one-sided testing problem. Then, these results are shown to have implications for more general moment inequality tests that are used in the literature on partial identification.

Keywords: Moment inequality, One-sided test, Power, similar, Test

JEL Classification: C12, C15