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Inference from Streaks in Random Outcomes: Experimental Evidence on Beliefs in Regime Shifting and the Law of Small Numbers


  • Elena Asparouhova

    () (David Eccles School of Business, University of Utah, Salt Lake City, Utah 84112)

  • Michael Hertzel

    () (W. P. Carey School of Business, Arizona State University, Tempe, Arizona 85287)

  • Michael Lemmon

    () (David Eccles School of Business, University of Utah, Salt Lake City, Utah 84112)


Using data generated from laboratory experiments, we test and compare the empirical accuracy of two models that focus on judgment errors associated with processing information from random sequences. We test for regime-shifting beliefs of the type theorized in Barberis et al. (Barberis, N., A. Shleifer, R. Vishny. 1998. A model of investor sentiment. J. Financial Econom. 49(3) 307-343) and for beliefs in the "law of small numbers" as modeled in Rabin (Rabin, M. 2002. Inference by believers in the law of small numbers. Quart. J. Econom. 117(3) 775-816). In our experiments, we show subjects randomly generated sequences of binary outcomes and ask them to provide probability assessments of the direction of the next outcome. Inconsistent with regime-shifting beliefs, we find that subjects are not more likely to predict that the current streak will continue the longer the streak. Instead, consistent with Rabin (2002), subjects are more likely to expect a reversal following short streaks and continuation after long streaks. Results of a "test-of-fit" analysis based on structural estimation of each model also favor the model in Rabin. To provide more insight on Rabin, we use an additional experimental treatment to show that as the perception of the randomness of the outcome-generating process increases, subjects are more likely to predict reversals of current streaks.

Suggested Citation

  • Elena Asparouhova & Michael Hertzel & Michael Lemmon, 2009. "Inference from Streaks in Random Outcomes: Experimental Evidence on Beliefs in Regime Shifting and the Law of Small Numbers," Management Science, INFORMS, vol. 55(11), pages 1766-1782, November.
  • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:11:p:1766-1782
    DOI: 10.1287/mnsc.1090.1059

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    References listed on IDEAS

    1. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    2. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-317, May.
    3. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 775-816.
    4. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    5. Cade Massey & George Wu, 2005. "Detecting Regime Shifts: The Causes of Under- and Overreaction," Management Science, INFORMS, vol. 51(6), pages 932-947, June.
    6. repec:hrv:faseco:30747159 is not listed on IDEAS
    7. Alon Brav & J.B. Heaton, 2002. "Competing Theories of Financial Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 575-606, March.
    8. Gregory R. Durham & Michael G. Hertzel & J. Spencer Martin, 2005. "The Market Impact of Trends and Sequences in Performance: New Evidence," Journal of Finance, American Finance Association, vol. 60(5), pages 2551-2569, October.
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