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Scoring rules for subjective probability distributions

Listed author(s):
  • Harrison, Glenn W.
  • Martínez-Correa, Jimmy
  • Swarthout, J. Todd
  • Ulm, Eric R.

Subjective beliefs are elicited routinely in economics experiments. However, such elicitation often suffers from two possible disadvantages. First, beliefs are recovered in the form of a summary statistic, usually the mean, of the underlying latent distribution. Second, recovered beliefs are biased significantly due to risk aversion. We characterize an approach for eliciting the entire subjective belief distribution that is minimally biased due to risk aversion. We offer simulated examples to demonstrate the intuition of our approach. We also provide theory to formally characterize our framework. And we provide experimental evidence which corroborates our theoretical results. We conclude that for empirically plausible levels of risk aversion, one can reliably elicit most important features of the latent subjective belief distribution without undertaking calibration for risk attitudes providing one is willing to assume Subjective Expected Utility.

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File URL: http://www.sciencedirect.com/science/article/pii/S0167268116302839
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Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 134 (2017)
Issue (Month): C ()
Pages: 430-448

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Handle: RePEc:eee:jeborg:v:134:y:2017:i:c:p:430-448
DOI: 10.1016/j.jebo.2016.12.001
Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

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  1. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
  2. Steffen Andersen & John Fountain & Glenn Harrison & E. Rutström, 2014. "Estimating subjective probabilities," Journal of Risk and Uncertainty, Springer, vol. 48(3), pages 207-229, June.
  3. Constantinos Antoniou & Glenn Harrison & Morten Lau & Daniel Read, 2015. "Subjective Bayesian beliefs," Journal of Risk and Uncertainty, Springer, vol. 50(1), pages 35-54, February.
  4. Grether, David M., 1992. "Testing bayes rule and the representativeness heuristic: Some experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 17(1), pages 31-57, January.
  5. Kenneth C. Lichtendahl, Jr. & Robert L. Winkler, 2007. "Probability Elicitation, Scoring Rules, and Competition Among Forecasters," Management Science, INFORMS, vol. 53(11), pages 1745-1755, November.
  6. Jeff Dominitz & Charles F. Manski, 2011. "Measuring and interpreting expectations of equity returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(3), pages 352-370, 04.
  7. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
  8. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2015. "Reduction of compound lotteries with objective probabilities: Theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 32-55.
  9. Holt, Charles A. & Smith, Angela M., 2009. "An update on Bayesian updating," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 125-134, February.
  10. Theo Offerman & Joep Sonnemans & Gijs Van De Kuilen & Peter P. Wakker, 2009. "A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes ," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1461-1489.
  11. Glenn W. Harrison & Jia Min Ng, 2016. "Evaluating The Expected Welfare Gain From Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 91-120, 01.
  12. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2014. "Eliciting subjective probabilities with binary lotteries," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 128-140.
  13. Costa-Gomes, Miguel A. & Huck, Steffen & Weizsäcker, Georg, 2014. "Beliefs and actions in the trust game: Creating instrumental variables to estimate the causal effect," Games and Economic Behavior, Elsevier, vol. 88(C), pages 298-309.
  14. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, 03.
  15. Antoniou, Constantinos & Harrison, Glenn W. & Lau, Morten I. & Read, Daniel, 2017. "Information Characteristics and Errors in Expectations: Experimental Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(02), pages 737-750, April.
  16. Charles A. Holt & Susan K. Laury, 2005. "Risk Aversion and Incentive Effects: New Data without Order Effects," American Economic Review, American Economic Association, vol. 95(3), pages 902-912, June.
  17. Delavande, Adeline & Giné, Xavier & McKenzie, David, 2011. "Measuring subjective expectations in developing countries: A critical review and new evidence," Journal of Development Economics, Elsevier, vol. 94(2), pages 151-163, March.
  18. Offerman, Theo & Sonnemans, Joep & Schram, Arthur, 1996. "Value Orientations, Expectations and Voluntary Contributions in Public Goods," Economic Journal, Royal Economic Society, vol. 106(437), pages 817-845, July.
  19. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
  20. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
  21. Glenn W. Harrison & J. Todd Swarthout, 2012. "The Independence Axiom and the Bipolar Behaviorist," Experimental Economics Center Working Paper Series 2012-01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
  22. Fiore, Stephen M. & Harrison, Glenn W. & Hughes, Charles E. & Rutstrm, E. Elisabet, 2009. "Virtual experiments and environmental policy," Journal of Environmental Economics and Management, Elsevier, vol. 57(1), pages 65-86, January.
  23. Merkle, Christoph & Weber, Martin, 2011. "True overconfidence: The inability of rational information processing to account for apparent overconfidence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 116(2), pages 262-271.
  24. Glenn Harrison & J. Swarthout, 2014. "Experimental payment protocols and the Bipolar Behaviorist," Theory and Decision, Springer, vol. 77(3), pages 423-438, October.
  25. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
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