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Constraint Qualifications In Partial Identification

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  • Kaido, Hiroaki
  • Molinari, Francesca
  • Stoye, Jörg

Abstract

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian–Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

Suggested Citation

  • Kaido, Hiroaki & Molinari, Francesca & Stoye, Jörg, 2022. "Constraint Qualifications In Partial Identification," Econometric Theory, Cambridge University Press, vol. 38(3), pages 596-619, June.
    • Handle: RePEc:cup:etheor:v:38:y:2022:i:3:p:596-619_6
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    Cited by:

    1. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    2. Marcoux, Mathieu & Russell, Thomas M. & Wan, Yuanyuan, 2024. "A simple specification test for models with many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 242(1).
    3. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    4. Semenova, Vira, 2025. "Generalized Lee bounds," Journal of Econometrics, Elsevier, vol. 251(C).
    5. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    6. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    7. 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.
    8. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).

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