Applications of Random Set Theory in Econometrics

The econometrics literature has in recent years shown a growing interest in the study of partially identified models, where the object of economic and statistical interest is a set rather than a point. Characterization of this set and development of its consistent estimators and of inference procedures 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 Annu. Rev. Econ. 2014 6 1941-1383/14/0904-???? of partial identification analysis.