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Calibrated Forecasting and Merging

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  • Ehud Kalai

Abstract

Consider a general finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links the unobserved reliability of forecasts to their observed empirical performance by demonstrating full equilvalence between notions of merging and of calibration. It also indicates some implications of this equilvalence for the literatures of forecasting and learning.

Suggested Citation

  • Ehud Kalai, 1995. "Calibrated Forecasting and Merging," Discussion Papers 1144R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1144r
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
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    3. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    4. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    6. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
    7. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    8. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
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    10. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    11. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, pages 438-452.
    12. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    13. Ehud Kalai & Ehud Lehrer, 1990. "Merging Economic Forecasts," Discussion Papers 1035, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, pages 104-130.
    2. Yossi Feinberg & Nicolas Lambert, 2015. "Mostly calibrated," International Journal of Game Theory, Springer;Game Theory Society, pages 153-163.
    3. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, pages 541-559.
    6. Feinberg, Yossi & Dekel, Eddie, 2004. "A True Expert Knows which Question Should Be Asked," Research Papers 1856, Stanford University, Graduate School of Business.
    7. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
    8. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy bounds on Bayesian learning," Journal of Mathematical Economics, Elsevier, pages 24-32.
    9. Yuichi Noguchi, 2009. "Note on universal conditional consistency," International Journal of Game Theory, Springer;Game Theory Society, pages 193-207.
    10. Feinberg, Yossi & Lambert, Nicolas S., 2011. "Mostly Calibrated," Research Papers 2090, Stanford University, Graduate School of Business.
    11. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications, Elsevier.
    12. Aukutsionek, Sergei P. & Belianin, Alexis V., 2001. "Quality of forecasts and business performance: A survey study of Russian managers," Journal of Economic Psychology, Elsevier, pages 661-692.
    13. Dean P. Foster & Rakesh V. Vohra, 1999. "Calibration, Expected Utility and Local Optimality," Discussion Papers 1254, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Eddie Dekel & Yossi Feinberg, 2005. "No Manipulation Results for Non-Bayesian Tests," Levine's Working Paper Archive 784828000000000217, David K. Levine.
    15. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 893-906.
    16. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, pages 131-137.
    17. Turdaliev, Nurlan, 2002. "Calibration and Bayesian learning," Games and Economic Behavior, Elsevier, vol. 41(1), pages 103-119, October.
    18. Mannor, Shie & Shimkin, Nahum, 2008. "Regret minimization in repeated matrix games with variable stage duration," Games and Economic Behavior, Elsevier, vol. 63(1), pages 227-258, May.
    19. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
    20. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    21. 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.

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