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Constraint Qualifications in Partial Identification

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  • Hiroaki Kaido
  • Francesca Molinari
  • Jorg Stoye

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

  • Hiroaki Kaido & Francesca Molinari & Jorg Stoye, 2019. "Constraint Qualifications in Partial Identification," Papers 1908.09103, arXiv.org, revised Apr 2021.
    • Handle: RePEc:arx:papers:1908.09103
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    1. 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.
    2. Yildiz, Neşe, 2012. "Consistency Of Plug-In Estimators Of Upper Contour And Level Sets," Econometric Theory, Cambridge University Press, vol. 28(2), pages 309-327, April.
    3. Hiroaki Kaido & Andres Santos, 2014. "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities," Econometrica, Econometric Society, vol. 82(1), pages 387-413, January.
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    7. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Alon Eizenberg, 2014. "Upstream Innovation and Product Variety in the U.S. Home PC Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1003-1045.
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    10. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    11. Bulat Gafarov, 2019. "Simple subvector inference on sharp identified set in affine models," Papers 1904.00111, arXiv.org, revised Jul 2024.
    12. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
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    Cited by:

    1. 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.
    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. 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.
    5. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    6. Bei, Xinyue, 2024. "Local linearization based subvector inference in moment inequality models," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.

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