Applications of Random Set Theory in Econometrics

Ilya Molchanov and Francesca Molinari
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Ilya Molchanov: Department of Mathematical Statistics and Actuarial Science, University of Bern, 3012 Bern, Switzerland

Annual Review of Economics, 2014, vol. 6, issue 1, 229-251

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.

Keywords: capacity functional; Aumann expectation; support function; partial identification (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C57 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (11)

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