Partial identification using random set theory

By Arie Beresteanu, Ilya S. Molchanov, Francesca Molinari. Journal of Econometrics, 2010

71 citations recorded by the source corpus.

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 , Manski, 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 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.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/7f9d72f189e3a580249ca88db930f3f437a1a632

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In Artificial Intelligence

1. Elie Tamer
2. Brendan Kline

Citations in the corpus

• Bayesian inference in a class of partially identified models (2016, background): “See also Beresteanu, Molchanov, and Molinari (2012).”