# Econometric applications of maxmin expected utility

## Author

Listed:
• Gary Chamberlain

(Department of Economics, Harvard University, Cambridge, MA 02138, USA)

## Abstract

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.

## Suggested Citation

• Gary Chamberlain, 2000. "Econometric applications of maxmin expected utility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 625-644.
• Handle: RePEc:jae:japmet:v:15:y:2000:i:6:p:625-644
as

File URL: http://qed.econ.queensu.ca:80/jae/2000-v15.6/
File Function: Supporting data files and programs

## References listed on IDEAS

as
1. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April.
2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
3. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2012. "Probability models and robust policy rules," European Economic Review, Elsevier, vol. 56(2), pages 246-262.
2. Szabolcs Deák & Paul Levine & Afrasiab Mirza & Joseph Pearlman, 2019. "Designing Robust Monetary Policy Using Prediction Pools," School of Economics Discussion Papers 1219, School of Economics, University of Surrey.
3. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
4. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
5. Christopher A. Sims, 2001. "Pitfalls of a Minimax Approach to Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 51-54, May.
6. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
7. Levine, P. & Pearlman, J. & Yang, B., 2013. "Imperfection Information, Optimal Monetary Policy and Informational Consistency," Working Papers 13/13, Department of Economics, City University London.
8. Alan S. Blinder & Ricardo Reis, 2005. "Understanding the Greenspan standard," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, issue Aug, pages 11-96.
9. Lars P. Hansen & Thomas J. Sargent, 2016. "Sets of Models and Prices of Uncertainty," NBER Working Papers 22000, National Bureau of Economic Research, Inc.
10. Adam, Klaus, 2004. "On the relation between robust and Bayesian decision making," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2105-2117, September.
11. Lars Peter Hansen & Thomas J. Sargent, 2019. "Macroeconomic Uncertainty Prices when Beliefs are Tenuous," NBER Working Papers 25781, National Bureau of Economic Research, Inc.
12. Gary Chamberlain, 2001. "Minimax Estimation and Forecasting in a Stationary Autoregression Model," American Economic Review, American Economic Association, vol. 91(2), pages 55-59, May.
13. repec:pri:cepsud:114blinderreis is not listed on IDEAS

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