Random Sets in Econometrics Econometric Society Monographs Series

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.

1. Basic concepts; 2. Selections; 3. Expectation of random sets; 4. Limit theorems for Minkowski sums; 5. Estimation and interference.

Ilya Molchanov is Professor of Probability at the Universität Bern, Switzerland, having previously worked in Germany, the Netherlands and Scotland. His research and publications focus on probability theory, spatial statistics, and mathematical finance, with the main emphasis on stochastic geometry and the theory of random sets.
Francesca Molinari is the H. T. Warshow and Robert Irving Warshow Professor of Economics at Cornell University, New York. She is a specialist in econometric theory, with emphasis on partial identification. She authored numerous papers in this area, including empirical ones on estimation of risk preferences using property insurance data.