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Inference for Linear Conditional Moment Inequalities

Author

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  • Isaiah Andrews
  • Jonathan Roth
  • Ariel Pakes

Abstract

We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in settings with nuisance parameters. We first introduce least-favorable critical values which deliver non-conservative tests if all moments are binding. Next, we introduce a novel conditional inference approach which ensures a strong form of insensitivity to slack moments. Our recommended approach is a hybrid technique which combines desirable aspects of the least favorable and conditional methods. The hybrid approach performs well in simulations calibrated to Wollmann (2018, American Economic Review, 108, 1364–1406), with favorable power and computational time comparisons relative to existing alternatives.

Suggested Citation

  • Isaiah Andrews & Jonathan Roth & Ariel Pakes, 2023. "Inference for Linear Conditional Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 2763-2791.
    • Handle: RePEc:oup:restud:v:90:y:2023:i:6:p:2763-2791.
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    File URL: http://hdl.handle.net/10.1093/restud/rdad004
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    Cited by:

    1. Gafarov, Bulat, 2025. "Simple subvector inference on sharp identified set in affine models," Journal of Econometrics, Elsevier, vol. 249(PB).
    2. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    3. Cox, Gregory Fletcher, 2025. "Weak identification with bounds in a class of minimum distance models," Journal of Econometrics, Elsevier, vol. 252(PA).
    4. Alexandre Poirier & Tymon S{l}oczy'nski, 2024. "Quantifying the Internal Validity of Weighted Estimands," Papers 2404.14603, arXiv.org, revised Oct 2025.
    5. Isaiah Andrews & Toru Kitagawa & Adam McCloskey, 2024. "Inference on Winners," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 139(1), pages 305-358.
    6. Hsieh, Yu-Wei & Shi, Xiaoxia & Shum, Matthew, 2022. "Inference on estimators defined by mathematical programming," Journal of Econometrics, Elsevier, vol. 226(2), pages 248-268.
    7. Evan K. Rose & Yotam Shem-Tov, 2021. "On Recoding Ordered Treatments as Binary Indicators," Papers 2111.12258, arXiv.org, revised Mar 2024.
    8. Ricardo E. Miranda, 2026. "On the falsification of instrumental variable models for heterogeneous treatment effects," Papers 2601.14464, arXiv.org.
    9. Myunghyun Song, 2024. "Identification and Inference in General Bunching Designs," Papers 2411.03625, arXiv.org, revised Feb 2025.
    10. Shuowen Chen & Hiroaki Kaido, 2022. "Robust Tests of Model Incompleteness in the Presence of Nuisance Parameters," Papers 2208.11281, arXiv.org, revised Sep 2023.
    11. Lujie Zhou, 2024. "Efficient Computation of Confidence Sets Using Classification on Equidistributed Grids," Papers 2401.01804, arXiv.org, revised Nov 2024.
    12. Ying Jin & Dominik Rothenhäusler, 2024. "Tailored inference for finite populations: conditional validity and transfer across distributions," Biometrika, Biometrika Trust, vol. 111(1), pages 215-233.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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