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Nonmanipulable Bayesian Testing

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Author Info
Colin Stewart

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Abstract

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, under general conditions on the tester's prior, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on data-generating processes where the tester quickly learns the true probabilities by updating her prior. However, the set of processes on which informed experts are rejected is topologically small. These results contrast sharply with many negative results in the literature.

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Publisher Info
Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-360.

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Length: 23 pages
Date of creation: 24 Jun 2009
Date of revision:
Handle: RePEc:tor:tecipa:tecipa-360

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Related research
Keywords: Probability forecasts; testing; experts;

Find related papers by JEL classification:
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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References listed on IDEAS
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  1. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, 05. [Downloadable!] (restricted)
  2. Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763. [Downloadable!] (restricted)
  3. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Review of Economic Studies, Blackwell Publishing, vol. 73(4), pages 893-906, October. [Downloadable!] (restricted)
    Other versions:
  4. Alvaro Sandroni & Wojciech Olszewski, 2008. "Manipulability of Future-Independent Tests," PIER Working Paper Archive 08-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
    Other versions:
  5. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May. [Downloadable!] (restricted)
  6. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October. [Downloadable!] (restricted)
  7. 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)
  8. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September. [Downloadable!] (restricted)
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  9. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer, vol. 32(1), pages 151-159, December. [Downloadable!] (restricted)
  10. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January. [Downloadable!] (restricted)
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  11. Alvaro Sandroni & Wojciech Olszewski, 2008. "Strategic Manipulation of Empirical Tests," PIER Working Paper Archive 08-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
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  12. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Society for Economic Theory, vol. 3(3), pages 367-382, September. [Downloadable!]
  13. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-47, September.
  14. Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer, vol. 28(2), pages 199-210. [Downloadable!] (restricted)
  15. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, 05. [Downloadable!] (restricted)
    Other versions:
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