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Partial identification using random set theory

Author

Listed:
  • Arie Beresteanu

    (Institute for Fiscal Studies and University of Pittsburgh)

  • Ilya Molchanov

    (Institute for Fiscal Studies and University of Bern, Institute of Mathematical Statistics and Actuarial Science)

  • Francesca Molinari

    (Institute for Fiscal Studies and Cornell University)

Abstract

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski's work in partial identification (e.g., Manski (1989, 1990)), focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data, statistical independence and mean independence assumptions, and shape restrictions. We show that the use of the Choquet capacity functional and of the Aumann expectation of a properly defined random set can simplify and extend previous results in the literature. We pay special attention to explaining how the relevant random set needs to be constructed, depending on the econometric framework at hand. We also discuss limitations in the applicability of specific tools of random set theory to partial identification analysis.

Suggested Citation

  • Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2010. "Partial identification using random set theory," CeMMAP working papers CWP40/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:40/10
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