Condence Sets for Partially Identied Parameters that Satisfy a Finite Number of Moment Inequalities

In this paper, I devise a new way to construct con…dence sets for a parameter of interest in models comprised of a …nite number of moment inequalities. Many models of this form have appeared in the literature to date, particularly in the recent literature on partial identi…cation, but performing statistical inference in these settings is an area of ongoing research. Toward this end, I establish a link between the class of moment-inequality models I study and the previous literature on multivariate one-sided hypothesis tests. I build on results from that literature to test the hypothesis that any particular element of the parameter space is logically consistent with the restrictions of the model. The associated test statistic is shown to have an asymptotic distribution that is a mixture of chi-square random variables. The test statistic can then be inverted to construct an asymptotically valid con…dence set for the parameter of interest, even if that parameter is not point identi…ed. The con…dence sets are easy to compute with standard statistical software that can compute CDF values for the chi-square distribution. The procedure for building con…dence sets is then demonstrated with two speci…c examples, and the con…dence sets are shown to perform well in these examples by means of Monte Carlo simulations.