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Econometric applications of maxmin expected utility

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  • Gary Chamberlain

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

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    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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    File URL: http://qed.econ.queensu.ca:80/jae/2000-v15.6/
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    Bibliographic Info

    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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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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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.
    2. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, 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, 02.
    4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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    Cited by:
    1. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," NBER Working Papers 9566, National Bureau of Economic Research, Inc.
    2. Klaus Adam, 2001. "On the Relation between Robust and Bayesian Decision Making," CSEF Working Papers 68, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. David Backus & Bryan Routledge & Stanley Zin, 2004. "Exotic Preferences for Macroeconomists," NBER Working Papers 10597, National Bureau of Economic Research, Inc.
    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.
    5. Levine, Paul & McAdam, Peter & Pearlman, Joseph, 2012. "Probability models and robust policy rules," European Economic Review, Elsevier, vol. 56(2), pages 246-262.
    6. 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.
    7. 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.

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