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Random Sets in Econometrics


  • Molchanov,Ilya
  • Molinari,Francesca


Random set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.

Suggested Citation

  • Molchanov,Ilya & Molinari,Francesca, 2018. "Random Sets in Econometrics," Cambridge Books, Cambridge University Press, number 9781107121201, December.
  • Handle: RePEc:cup:cbooks:9781107121201

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    Cited by:

    1. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    2. Hiroaki Kaido & Yi Zhang, 2019. "Robust Likelihood Ratio Tests for Incomplete Economic Models," Papers 1910.04610,, revised Dec 2019.
    3. S. Settepanella & A. Terni & M. Franciosi & L. Li, 2022. "The robustness of the generalized Gini index," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 521-539, December.
    4. Levon Barseghyan & Maura Coughlin & Francesca Molinari & Joshua C. Teitelbaum, 2021. "Heterogeneous Choice Sets and Preferences," Econometrica, Econometric Society, vol. 89(5), pages 2015-2048, September.
    5. Martin Dumav & Maxwell B. Stinchcombe, 2021. "The multiple priors of the open-minded decision maker," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 663-692, March.
    6. Diaye, Marc-Arthur & Koshevoy, Gleb A. & Molchanov, Ilya, 2019. "Lift expectations of random sets," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 110-117.
    7. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Ilya Molchanov & Anja Mühlemann, 2021. "Nonlinear expectations of random sets," Finance and Stochastics, Springer, vol. 25(1), pages 5-41, January.
    9. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    10. Ilya Molchanov & Anja Muhlemann, 2019. "Nonlinear expectations of random sets," Papers 1903.04901,
    11. Antonio Avilés López & José Miguel Zapata García, 2020. "Boolean Valued Representation of Random Sets and Markov Kernels with Application to Large Deviations," Mathematics, MDPI, vol. 8(10), pages 1-23, October.
    12. Undral Byambadalai, 2022. "Identification and Inference for Welfare Gains without Unconfoundedness," Papers 2207.04314,

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