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Flexible Approximation of Subjective Expectations Using Probability Questions: An Application to the Investment Game

  • Bellemare, Charles


    (Université Laval)

  • Bissonnette, Luc


    (Laval University)

  • Kröger, Sabine


    (Université Laval)

We use spline interpolation to approximate the subjective cumulative distribution function of an economic agent over the future realization of a continuous (possibly censored) random variable. The method proposed exploits information collected using a small number of probability questions on expectations and requires a weak prior knowledge of the shape of the underlying distribution. We find that eliciting 4 or 5 points on the cumulative distribution function of an agent is sufficient to accurately approximate a wide variety of underlying distributions. We show that estimated moments of general functions of the random variable can be computed analytically and/or using standard simulation techniques. We illustrate the usefulness of the method by estimating a simple model to asses the impact of expectations on investment decisions in a commonly used trust game.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3121.

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Length: 41 pages
Date of creation: Oct 2007
Date of revision:
Publication status: published as 2 separate articles in: Journal of Business and Economic Statistics, 2012 (Flexible Approximation of Subjective Expectations Using Probability Questions, doi:10.1198/jbes.2011.09053) and in Experimental Economics, 2010 (Bounding Preference Parameters under Different Assumptions about Beliefs: a Partial Identification Approach, doi:10.1007/s10683-010-9244-6)
Handle: RePEc:iza:izadps:dp3121
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  1. Eckel, Catherine C. & Wilson, Rick K., 2004. "Is trust a risky decision?," Journal of Economic Behavior & Organization, Elsevier, vol. 55(4), pages 447-465, December.
  2. Dirk Engelmann & Martin Strobel, 2004. "Inequality Aversion, Efficiency, and Maximin Preferences in Simple Distribution Experiments," American Economic Review, American Economic Association, vol. 94(4), pages 857-869, September.
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  4. Arthur van Soest & Charles Bellemare & Sabine Kroger, 2005. "Actions and beliefs: Estimating distribution-based preferences using a large scale experiment with probability questions on expectations," Artefactual Field Experiments 00007, The Field Experiments Website.
  5. Manski, Charles F., 2002. "Identification of decision rules in experiments on simple games of proposal and response," European Economic Review, Elsevier, vol. 46(4-5), pages 880-891, May.
  6. McKenzie, David & Gibson, John & Stillman, Steven, 2007. "A land of milk and honey with streets paved with gold : do emigrants have over-optimistic expectations about incomes abroad ?," Policy Research Working Paper Series 4141, The World Bank.
  7. Oxoby, Robert J. & McLeish, Kendra N., 2004. "Sequential decision and strategy vector methods in ultimatum bargaining: evidence on the strength of other-regarding behavior," Economics Letters, Elsevier, vol. 84(3), pages 399-405, September.
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  9. repec:tpr:qjecon:v:117:y:2002:i:3:p:817-869 is not listed on IDEAS
  10. Charness, Gary & Rabin, Matthew, 2001. "Understanding Social Preferences with Simple Tests," Department of Economics, Working Paper Series qt4qz9k8vg, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. J. Dominitz & C. F. Manski, . "Using expectations data to study subjective income expectations," Institute for Research on Poverty Discussion Papers 1050-94, University of Wisconsin Institute for Research on Poverty.
  12. Berg Joyce & Dickhaut John & McCabe Kevin, 1995. "Trust, Reciprocity, and Social History," Games and Economic Behavior, Elsevier, vol. 10(1), pages 122-142, July.
  13. Abigail Barr, 2003. "Trust and expected trustworthiness: experimental evidence from zimbabwean villages," Economic Journal, Royal Economic Society, vol. 113(489), pages 614-630, 07.
  14. Engelberg, Joseph & Manski, Charles F. & Williams, Jared, 2009. "Comparing the Point Predictions and Subjective Probability Distributions of Professional Forecasters," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 30-41.
  15. Cox, James C., 2004. "How to identify trust and reciprocity," Games and Economic Behavior, Elsevier, vol. 46(2), pages 260-281, February.
  16. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
  17. Nava Ashraf & Iris Bohnet & Nikita Piankov, 2006. "Decomposing trust and trustworthiness," Experimental Economics, Springer, vol. 9(3), pages 193-208, September.
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