COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1631 Inference for Parameters Defined by Moment Inequalities Donald W.K. Andrews and Gustavo Soares October 2007 The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and "plug-in asymptotic" (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests. Keywords: Asymptotic size, Asymptotic power, Confidence set, Exact size, Generalized moment selection, m out of n bootstrap, Subsampling, Moment inequalities, Moment selection, Test JEL Classification Numbers: C12, C15 |
