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Testing Inequalities Linear in Nuisance Parameters

Gregory Fletcher Cox, Xiaoxia Shi, Yuya Shimizu

arXiv 31 Oct 2025 · Statistics — Methodology

arXiv:2510.27633 · PDF · DOI · OpenAlex · Extracted main text

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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44
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88
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bugni, F., Canay, I., and Shi, X (2017) Inference for subvectors and other functions of partially identified parameters in moment inequality models self0.9285580%
2Andrews, I., Roth, J., and Pakes, A (2023) Inference for linear conditional moment inequalities0.92843100%
3Goff, L. and Mbakop, E (2025) Inference on the value of a linear program0.8434375%
4Fang, Z., Santos, A., Shaikh, A., and Torgovitsky (2023) Inference for large-scale linear systems with known coefficients0.84333100%
5Chen, X., Christensen, T. M., and Tamer, E (2018) Monte Carlo confidence sets for identified sets0.81142100%
6Freyberer, J. and Horowitz, J (2015) Identification and shape restrictions in nonparametric instrumental variables estimation0.81142100%
7Voronin, A (2025) Linear programming approach to partially identified econometric models0.7373367%
8Gafarov, B (2025) Simple subvector inference on sharp identified set in affine models0.73732100%
9Cho, J. and Russell, T. M (2024) Simple inference on functionals of set-identified parameters defined by linear moments0.64811427%
10Bei, X (2023) Local linearization based subvector inference in moment inequality models0.64422100%

Showing the top 10 of 50 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Testing the Solvability of Systems of Linear Inequalities1.00093
2Inference for Linear Systems with Unknown Coefficients1.00094
3Synthetic Parallel Trends0.73732
4Identification in Multiple Treatment Models under Discrete Variation0.64452