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Correlated observations, the law of small numbers and bank runs

Author

Listed:
  • Gergely Horváth

    () (Department of Economic Theory, Universität Erlangen-Nürnberg)

  • Hubert János Kiss

    () (‘Momentum’ Game Theory Research Group, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Eötvös Loránd University - Department of Economics)

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 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 high. 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 less than one. To investigate the intermediate cases, we use simulations and find that decreasing the correlation reduces the likelihood of bank runs, often in a non-linear way. We also study the effect of the sample size and show that increasing it makes bank runs less likely. Our results have relevant policy implications.

Suggested Citation

  • Gergely Horváth & Hubert János Kiss, 2014. "Correlated observations, the law of small numbers and bank runs," IEHAS Discussion Papers 1429, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  • Handle: RePEc:has:discpr:1429
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    File URL: http://econ.core.hu/file/download/mtdp/MTDP1429.pdf
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    References listed on IDEAS

    as
    1. Kinateder, Markus & Kiss, Hubert János, 2014. "Sequential decisions in the Diamond–Dybvig banking model," Journal of Financial Stability, Elsevier, vol. 15(C), pages 149-160.
    2. Kiss, Hubert Janos & Rodriguez-Lara, Ismael & Rosa-García, Alfonso, 2014. "Do social networks prevent or promote bank runs?," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 87-99.
    3. Ennis, Huberto M. & Keister, Todd, 2009. "Run equilibria in the Green-Lin model of financial intermediation," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1996-2020, September.
    4. Roger Hartley & Gauthier Lanot & Ian Walker, 2014. "Who Really Wants To Be A Millionaire? Estimates Of Risk Aversion From Gameshow Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 861-879, September.
    5. Arifovic, Jasmina & Hua Jiang, Janet & Xu, Yiping, 2013. "Experimental evidence of bank runs as pure coordination failures," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2446-2465.
    6. Cormac O Grada & Morgan Kelly, 2000. "Market Contagion: Evidence from the Panics of 1854 and 1857," American Economic Review, American Economic Association, vol. 90(5), pages 1110-1124, December.
    7. Costain James S, 2007. "A Herding Perspective on Global Games and Multiplicity," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-55, June.
    8. Davison, Lee K. & Ramirez, Carlos D., 2014. "Local banking panics of the 1920s: Identification and determinants," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 164-177.
    9. Sultanum, Bruno, 2014. "Optimal Diamond–Dybvig mechanism in large economies with aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 95-102.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    bank runs; law of small numbers; samples; threshold decision rule;

    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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