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Testing theories with learnable and predictive representations

Author

Listed:
  • Al-Najjar, Nabil I.
  • Sandroni, Alvaro
  • Smorodinsky, Rann
  • Weinstein, Jonathan

Abstract

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable prediction about future frequencies. We show that this test passes an expert who knows the data-generating process and cannot be manipulated by a uninformed one. Such a test is not possible if the theory is unrestricted.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2203-2217
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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. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    3. Kalai, Ehud & Lehrer, Ehud & Smorodinsky, Rann, 1999. "Calibrated Forecasting and Merging," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 151-169, October.
    4. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    5. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 253-268.
    6. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    7. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 151-159, December.
    8. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Lance Fortnow & Rakesh V. Vohra, 2009. "The Complexity of Forecast Testing," Econometrica, Econometric Society, vol. 77(1), pages 93-105, January.
    10. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    11. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
    12. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
    13. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    14. Lehrer, Ehud, 2001. "Any Inspection Is Manipulable," Econometrica, Econometric Society, vol. 69(5), pages 1333-1347, September.
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    Cited by:

    1. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.
    2. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications, Elsevier.
    3. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 153-163, February.
    4. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
    5. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Colin, Stewart, 2011. "Nonmanipulable Bayesian testing," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2029-2041, September.
    7. Wojciech Olszewski & Alvaro Sandroni, 2011. "Falsifiability," American Economic Review, American Economic Association, vol. 101(2), pages 788-818, April.
    8. Al-Najjar, Nabil & Sandroni, Alvaro, 2013. "A difficulty in the testing of strategic experts," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 5-9.
    9. Marinovic, Iván & Ottaviani, Marco & Sorensen, Peter, 2013. "Forecasters’ Objectives and Strategies," Handbook of Economic Forecasting, Elsevier.

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    Keywords

    Learning Expert testing;

    Statistics

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