Econometric applications of maxmin expected utility
Article first published online: 5 FEB 2001
Copyright © 2000 John Wiley & Sons, Ltd.
Journal of Applied Econometrics
Special Issue: Inference and Decision Making
Volume 15, Issue 6, pages 625–644, November/December 2000
How to Cite
Chamberlain, G. (2000), Econometric applications of maxmin expected utility. J. Appl. Econ., 15: 625–644. doi: 10.1002/jae.583
- Issue published online: 5 FEB 2001
- Article first published online: 5 FEB 2001
- Manuscript Revised: 31 AUG 2000
- Manuscript Received: 30 SEP 1999
Gilboa and Schmeidler (1989) develop a set of axioms for decision making under uncertainty. The axioms imply a utility function and a set of distributions such that the preference ordering is obtained by calculating expected utility with respect to each distribution in the set, and then taking the minimum of expected utility over the set. In a portfolio choice problem, the distributions are joint distributions for the data that will be available when the choice is made and for the future returns that will determine the value of the portfolio. The set of distributions could be generated by combining a parametric model with a set of prior distributions. We apply this framework to obtain a preference ordering over decision rules, which map the data into a choice. We seek a decision rule that maximizes the minimum expected utility (or, equivalently, minimizes maximum risk) over the set of distributions. An algorithm is provided for the case of a finite set of distributions. It is based on solving a concave programme to find the least-favourable mixture of these distributions. The minimax rule is a Bayes rule with respect to this least-favourable distribution. The minimax value is a lower bound for minimax risk relative to a larger set of distributions. An upper bound can be found by fixing a decision rule and calculating its maximum risk. We apply the algorithm to an estimation problem in an autoregressive, random-effects model for panel data. Copyright © 2000 John Wiley & Sons, Ltd.