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Correlated Observations, the Law of Small Numbers and Bank Runs

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  • Gergely Horváth
  • Hubert János Kiss

Abstract

Empirical descriptions and studies suggest that generally depositors observe a sample of previous decisions before deciding if to keep their funds deposited or to withdraw them. These observed decisions may exhibit different degrees of correlation across depositors. In our model depositors decide sequentially and are assumed to follow the law of small numbers in the sense that they believe that a bank run is underway if the number of observed withdrawals in their sample is large. Theoretically, with highly correlated samples and infinite depositors runs occur with certainty, while with random samples it needs not be the case, as for many parameter settings the likelihood of bank runs is zero. We investigate the intermediate cases and find that i) decreasing the correlation and ii) increasing the sample size reduces the likelihood of bank runs, ceteris paribus. Interestingly, the multiplicity of equilibria, a feature of the canonical Diamond-Dybvig model that we use also, disappears almost completely in our setup. Our results have relevant policy implications.

Suggested Citation

  • Gergely Horváth & Hubert János Kiss, 2016. "Correlated Observations, the Law of Small Numbers and Bank Runs," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-29, April.
  • Handle: RePEc:plo:pone00:0147268
    DOI: 10.1371/journal.pone.0147268
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    Cited by:

    1. Hubert J. Kiss & Ismael Rodriguez-Lara & Alfonso Rosa-Garcia, 2022. "Experimental bank runs," Chapters, in: Sascha Füllbrunn & Ernan Haruvy (ed.), Handbook of Experimental Finance, chapter 25, pages 347-361, Edward Elgar Publishing.
      • Hubert J. Kiss & Ismael Rodriguez-Lara & Alfonso Rosa-Garcia, 2021. "Experimental Bank Runs," ThE Papers 21/03, Department of Economic Theory and Economic History of the University of Granada..
    2. Toni Ricardo Eugenio dos Santos & Marcio Issao Nakane, 2021. "Dynamic bank runs: an agent-based approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(3), pages 675-703, July.
    3. Atmaca, Sümeyra & Schoors, Koen & Verschelde, Marijn, 2020. "Bank loyalty, social networks and crisis," Journal of Banking & Finance, Elsevier, vol. 112(C).
    4. Kiss, Hubert János & Rodriguez-Lara, Ismael & Rosa-Garcia, Alfonso, 2022. "Who withdraws first? Line formation during bank runs," Journal of Banking & Finance, Elsevier, vol. 140(C).

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    More about this item

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • G01 - Financial Economics - - General - - - Financial Crises
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles

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