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Applications of Random Set Theory in Econometrics

Author

Listed:
  • Ilya Molchanov

    (Department of Mathematical Statistics and Actuarial Science, University of Bern, 3012 Bern, Switzerland)

  • Francesca Molinari

    (Department of Economics, Cornell University, Ithaca, New York 14850)

Abstract

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Suggested Citation

  • Ilya Molchanov & Francesca Molinari, 2014. "Applications of Random Set Theory in Econometrics," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 229-251, August.
    • Handle: RePEc:anr:reveco:v:6:y:2014:p:229-251
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    File URL: http://www.annualreviews.org/doi/abs/10.1146/annurev-economics-080213-041205
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    Citations

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    Cited by:

    1. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers CWP05/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    3. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    4. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    5. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    6. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    7. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    8. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. 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.

    More about this item

    Keywords

    capacity functional; Aumann expectation; support function; partial identification;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions

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