Before revision:  Our refinement has multiple appealing features, including an intuitive characterization, lower computational cost, and stable predictions. Focusing on moment inequality models, we propose bootstrap inference on the refinement and provide generic conditions under which the inference is uniformly asymptotically valid. We present and discuss results from our Monte Carlo study and an empirical application based on a model with top-coded data.
After revision:  We provide a representation of this subset which can be used to simplify the implementation. We illustrate our message using moment inequality models, and provide an empirical application based on a model with top-coded data.