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Econometric applications of maxmin expected utility

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Author Info
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.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 15 (2000)
Issue (Month): 6 ()
Pages: 625-644
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Handle: RePEc:jae:japmet:v:15:y:2000:i:6:p:625-644

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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  2. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April. [Downloadable!] (restricted)
  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, 02. [Downloadable!] (restricted)
  4. Claire Chambolle & Keisuke Hirano, 1999. "Predictive Distributions based on Longitudinal Earnings Data," Annales d'Economie et de Statistique, ADRES, issue 55-56, pages 09, Juillet-D. [Downloadable!]
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  1. Alexei Onatski & Noah Williams, 2002. "Modeling model uncertainty," Working Paper Series 169, European Central Bank. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!] (restricted)
  3. David Backus & Bryan Routledge & Stanley Zin, 2004. "Exotic Preferences for Macroeconomists," NBER Working Papers 10597, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!] (restricted)
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