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Nonmanipulable Bayesian testing

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  • Colin, Stewart

Abstract

This paper considers the problem of testing an expert who makes probabilistic forecasts about the outcomes of a stochastic process. I show that, as long as uninformed experts do not learn the correct forecasts too quickly, a likelihood test can distinguish informed from uninformed experts with high prior probability. The test rejects informed experts on some data-generating processes; however, the set of such processes is topologically small. These results contrast sharply with many negative results in the literature.

Suggested Citation

  • Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:2029-2041
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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, May.
    2. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
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    9. Al-Najjar, Nabil I. & Sandroni, Alvaro & Smorodinsky, Rann & Weinstein, Jonathan, 2010. "Testing theories with learnable and predictive representations," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2203-2217, November.
    10. Wojciech Olszewski & Alvaro Sandroni, 2009. "Strategic Manipulation of Empirical Tests," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 57-70, February.
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    12. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Wojciech Olszewski & Marcin Pęski, 2011. "The Principal-Agent Approach to Testing Experts," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 89-113, May.
    14. Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 199-210.
    15. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
    16. Alvaro Sandroni & Rann Smorodinsky & Rakesh V. Vohra, 2003. "Calibration with Many Checking Rules," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 141-153, February.
    17. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
    18. ,, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    19. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
    20. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
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    Cited by:

    1. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
    2. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.

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    More about this item

    Keywords

    Probability forecasts Testing Experts;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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