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Set identification, moment restrictions, and inference

Author

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  • Christian Bontemps

    (ENAC - Ecole Nationale de l'Aviation Civile, TSE - Toulouse School of Economics - EHESS - École des hautes études en sciences sociales - INRA - Institut National de la Recherche Agronomique - CNRS - Centre National de la Recherche Scientifique - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées)

  • Thierry Magnac

    (TSE - Toulouse School of Economics - EHESS - École des hautes études en sciences sociales - INRA - Institut National de la Recherche Agronomique - CNRS - Centre National de la Recherche Scientifique - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées)

Abstract

For the past 10 years, the topic of set identification has been much studied in the econometric literature. Classical inference methods have been generalized to the case in which moment inequalities and equalities define a set instead of a point. We review several instances of partial identification by focusing on examples in which the underlying economic restrictions are expressed as linear moments. This setting illustrates the fact that convex analysis helps not only for characterizing the identified set but also for inference. From this perspective, we review inference methods using convex analysis or inversion of tests and detail how geometric characterizations can be useful.

Suggested Citation

  • Christian Bontemps & Thierry Magnac, 2017. "Set identification, moment restrictions, and inference," Post-Print hal-01575813, HAL.
  • Handle: RePEc:hal:journl:hal-01575813
    DOI: 10.1146/annurev-economics-063016-103658
    Note: View the original document on HAL open archive server: https://hal-enac.archives-ouvertes.fr/hal-01575813v2
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    Cited by:

    1. Walter Beckert & Daniel Kaliski, 2019. "Honest inference for discrete outcomes," CeMMAP working papers CWP67/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    3. Bontemps, Christian & Kumar, Rohit, 2020. "A geometric approach to inference in set-identified entry games," Journal of Econometrics, Elsevier, vol. 218(2), pages 373-389.
    4. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    5. Ryo Okui, 2021. "A moment inequality approach to statistical inference for rankings," The Japanese Economic Review, Springer, vol. 72(2), pages 169-184, April.

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    More about this item

    Keywords

    Moment inequality; Set identification; Convex set; Support function;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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