Consistent and Asymptotically Unbiased MinP Tests of Multiple Inequality Moment Restrictions

Abstract

This paper considers the general problem of testing multiple inequality moment restrictions against an unrestricted alternative. We first introduce a test based on a maximum statistic and show how, via a partially recentered bootstrap scheme, we may obtain a testing procedure that delivers, at least asymptotically, an exact alpha-level test for any configuration of the parameters on the boundary of the null hypothesis. We prove that this bootstrap test is asymptotically unbiased and that it weakly dominates analogous testing procedures based on the canonical (fully centered) bootstrap. Building on these results we introduce a computationally inexpensive minimum p-value test. The minimum p-value test enjoys the asymptotic unbiasedness property of the underlying partially recentered bootstrap test. Additionally, the minimum $p$-value test delivers balance of power among the individual moment inequalities under test without studentization, and also allows users to gauge the strength of the evidence against the individual moment inequalities. To illustrate the use of our proposed testing procedure we examine the distributional effects of Vietnam veteran status on earnings. In particular, the results from our procedure when applied to testing for stochastic dominance and normalized stochastic dominance demonstrate that there is unambiguously greater poverty and greater relative inequality in earnings for veterans.