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Inference by Believers in the Law of Small Numbers

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  • Rabin, Matthew

Abstract

Many people believe in the "Law of Small Numbers," exaggerating the degree to which a small sample resembles the population from which it is drawn. To model this, I assume that a person exaggerates the likelihood that a short sequence of i.i.d. signals resembles the long-run rate at which those signals are generated. Such a person believes in the "gambler's fallacy", thinking early draws of one signal increase the odds of next drawing other signals. When uncertain about the rate, the person over-infers from short sequences of signals, and is prone to think the rate is more extreme than it is. When the person makes inferences about the frequency at which rates are generated by different sources -- such as the distribution of talent among financial analysts -- based on few observations from each source, he tends to exaggerate how much variance there is in the rates. Hence, the model predicts that people may pay for financial advice from "experts" whose expertise is entirely illusory. Other economic applications are discussed.

Suggested Citation

  • Rabin, Matthew, 2000. "Inference by Believers in the Law of Small Numbers," Department of Economics, Working Paper Series qt4sw8n41t, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  • Handle: RePEc:cdl:econwp:qt4sw8n41t
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    References listed on IDEAS

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    1. Harrison Hong & Terence Lim & Jeremy C. Stein, 2000. "Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies," Journal of Finance, American Finance Association, vol. 55(1), pages 265-295, February.
    2. De Bondt, Werner F M & Thaler, Richard H, 1990. "Do Security Analysts Overreact?," American Economic Review, American Economic Association, vol. 80(2), pages 52-57, May.
    3. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    4. repec:bla:jfinan:v:53:y:1998:i:6:p:1839-1885 is not listed on IDEAS
    5. 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.
    6. Matthew Rabin, 1998. "Psychology and Economics," Journal of Economic Literature, American Economic Association, vol. 36(1), pages 11-46, March.
    7. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    8. Camerer, Colin F, 1989. "Does the Basketball Market Believe in the 'Hot Hand'?," American Economic Review, American Economic Association, vol. 79(5), pages 1257-1261, December.
    9. Nicholas Barberis & Ming Huang & Tano Santos, "undated". "Prospect Theory and Asset Prices," CRSP working papers 494, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    10. Brown, William O & Sauer, Raymond D, 1993. "Does the Basketball Market Believe in the Hot Hand? Comment," American Economic Review, American Economic Association, vol. 83(5), pages 1377-1386, December.
    11. Keren, Gideon & Lewis, Charles, 1994. "The Two Fallacies of Gamblers: Type I and Type II," Organizational Behavior and Human Decision Processes, Elsevier, vol. 60(1), pages 75-89, October.
    12. De Bondt, Werner F M & Thaler, Richard H, 1987. "Further Evidence on Investor Overreaction and Stock Market Seasonalit y," Journal of Finance, American Finance Association, vol. 42(3), pages 557-581, July.
    13. Harrison Hong & Jeremy C. Stein, 1999. "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets," Journal of Finance, American Finance Association, vol. 54(6), pages 2143-2184, December.
    14. W. Edwards, 2010. "Probability Learning in 1000 Trials," Levine's Working Paper Archive 553, David K. Levine.
    15. Matthew Rabin & Joel L. Schrag, 1999. "First Impressions Matter: A Model of Confirmatory Bias," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 37-82.
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    Cited by:

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    6. Temple, Jonathan, 2001. "Growing into Trouble: Indonesia After 1966," CEPR Discussion Papers 2932, C.E.P.R. Discussion Papers.

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