Validity of Subsampling and “plug-in Asymptotic” Inference for Parameters Defined by Moment Inequalities

This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and “plug-in asymptotic” tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the pointwise asymptotic distributions of the test statistics of interest have discontinuities as functions of the true distribution that generates the observations. The size results are quite general because they hold without specifying the particular form of the moment conditions—only 2+ δ moments finite are required. The results allow for independent and identically distributed (i.i.d.) and dependent observations and for preliminary consistent estimation of identified parameters.