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arXiv · 2510.27633

Testing Inequalities Linear in Nuisance Parameters

Gregory Fletcher Cox·Xiaoxia Shi·Yuya Shimizu
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Abstract

This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment (in)equality models, specification testing of such models, and inference for parameters bounded by linear programs. The new test uses a two-step test statistic and a chi-squared critical value with data-dependent degrees of freedom that can be calculated by an elementary formula. Its simple structure and tuning-parameter-free implementation make it attractive for practical use. We establish uniform asymptotic validity of the test, demonstrate its finite-sample size and power in simulations, and illustrate its use in an empirical application that analyzes women's labor supply in response to a welfare policy reform.

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Gregory Fletcher Cox, Xiaoxia Shi, Yuya Shimizu. 2025-10-31. Testing Inequalities Linear in Nuisance Parameters. https://arxiv.org/abs/2510.27633

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