Xiaoxia Shi, University of Wisconsin - Madison

Multiple Inequality Testing in the Presence of Linear Nuisance Parameters

Joint with Gregory Cox

Abstract:  In this paper, we propose a new and easy test for the null hypothesis defined by multiple inequalities when possibly partially identified nuisance parameters are present. The test extends the subvector conditional chi-squared test proposed in Cox and Shi (2022) for linear conditional moment inequality models to the more general setting where conditional model is no longer required. The extension makes the test applicable to a much greater set of problems, including linear unconditional moment inequality models, nonparametric instrumental variable models with discrete regressor and instruments, inference for optimal values of linear programming problems, as well as semi-parametric panel data multinomial choice models. We also derive a simplified formula for computing the critical value that makes the computation of the proposed

test elementary.