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The reproducible properties of correct forecasts


  • Alvaro Sandroni



Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an arbitrary function from sequences of forecasts and outcomes to {0,1}. When the test returns a 0 the test is said to reject the forecasts based on the outcome sequence. When the test resturns a 1 the test is said to not reject the forecasts based on the outcome sequence. Consider any test that does not reject the truth, i.e. it does not reject when the announced forecasts are the conditional probabilities of the data generating process. Based on Fan’s (1953) Minimax theorem, I show that it is possible to produce forecasts that will not be rejected on any sequence of outcomes. Copyright Springer-Verlag 2003

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:32:y:2003:i:1:p:151-159 DOI: 10.1007/s001820300153

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    1. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    2. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
    3. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    4. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 2001. "On the computation of the nucleolus of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 79-98.
    5. Ichiishi,Tatsuro, 1993. "The Cooperative Nature of the Firm," Cambridge Books, Cambridge University Press, number 9780521414449, March.
    6. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    7. Milgrom, Paul & Roberts, John, 1996. "Coalition-Proofness and Correlation with Arbitrary Communication Possibilities," Games and Economic Behavior, Elsevier, vol. 17(1), pages 113-128, November.
    8. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    9. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, March.
    10. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
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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. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.
    4. Schorfheide, Frank & Wolpin, Kenneth I., 2016. "To hold out or not to hold out," Research in Economics, Elsevier, vol. 70(2), pages 332-345.
    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. Feinberg, Yossi & Dekel, Eddie, 2004. "A True Expert Knows which Question Should Be Asked," Research Papers 1856, Stanford University, Graduate School of Business.
    8. 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.
    9. Francisco Barreras & Álvaro J. Riascos, 2016. "Screening multiple potentially false experts," MONOGRAFÍAS 015075, QUANTIL.
    10. David Lagziel & Ehud Lehrer, 2015. "On the Failures of Bonus Plans," Papers 1505.04587,
    11. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
    12. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.
    13. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications, Elsevier.
    14. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
    15. Wojciech Olszewski & Alvaro Sandroni, 2011. "Falsifiability," American Economic Review, American Economic Association, vol. 101(2), pages 788-818, April.
    16. Al-Najjar, Nabil & Sandroni, Alvaro, 2013. "A difficulty in the testing of strategic experts," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 5-9.
    17. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    18. 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.
    19. Glen Weyl, 2009. "A Simple Theory of Scientific Learning," Levine's Working Paper Archive 814577000000000067, David K. Levine.
    20. Marinovic, Iván & Ottaviani, Marco & Sorensen, Peter, 2013. "Forecasters’ Objectives and Strategies," Handbook of Economic Forecasting, Elsevier.

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    Forecasting; Testing; Calibration; Minimax theorem;


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