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Set Identification, Moment Restrictions, and Inference

Author

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  • Christian Bontemps

    (Toulouse School of Economics, Université de Toulouse, 31000 Toulouse, France)

  • Thierry Magnac

    (Toulouse School of Economics, Université de Toulouse, 31000 Toulouse, France)

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," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    • Handle: RePEc:anr:reveco:v:9:y:2017:p:103-129
    DOI: 10.1146/annurev-economics-063016-103658
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    Cited by:

    1. X D’Haultfœuille & C Gaillac & A Maurel, 2025. "Partially Linear Models under Data Combination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(1), pages 238-267.
    2. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    3. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    4. Andreas Tryphonides, 2017. "Set Identified Dynamic Economies and Robustness to Misspecification," Papers 1712.03675, arXiv.org, revised Jan 2018.
    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.
    6. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    7. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.
    8. Ravi Jagadeesan & Scott Duke Kominers & Ross Rheingans-Yoo, 2020. "Lone wolves in competitive equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 215-228, August.
    9. Bontemps, Christian & Menezes Bezerra Sampaio, Raquel, 2020. "Entry games for the airline industry," TSE Working Papers 20-1108, Toulouse School of Economics (TSE).
    10. Thomas Demuynck & Tom Potoms, 2022. "Testing revealed preference models with unobserved randomness: a column generation approach," Working Papers ECARES 2022-42, ULB -- Universite Libre de Bruxelles.
    11. 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.
    12. 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.
    13. Gregory Fletcher Cox, 2020. "Weak Identification with Bounds in a Class of Minimum Distance Models," Papers 2012.11222, arXiv.org, revised Oct 2025.

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    Keywords

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    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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