Correlated Observations, the Law of Small Numbers and Bank Runs

27 Pages Posted: 14 Nov 2014

See all articles by Gergely Horvath

Gergely Horvath

Friedrich-Alexander University

Hubert Janos Kiss

Eötvös Loránd University; Hungarian Academy of Sciences (HAS) - Institute of Economics CERS-HAS (IEHAS)

Date Written: October 31, 2014

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.

Keywords: bank runs, law of small numbers, samples, threshold decision rule

JEL Classification: D03, G01, G02

Suggested Citation

Horvath, Gergely and Kiss, Hubert Janos, Correlated Observations, the Law of Small Numbers and Bank Runs (October 31, 2014). Available at SSRN: https://ssrn.com/abstract=2523611 or http://dx.doi.org/10.2139/ssrn.2523611

Gergely Horvath

Friedrich-Alexander University ( email )

Lange Gasse 20
Nuremberg, 90020
Germany

HOME PAGE: http://sites.google.com/site/horvathgergely/

Hubert Janos Kiss (Contact Author)

Eötvös Loránd University ( email )

Pazmany Peter setany 1A
Budapest, -- H1117
Hungary

Hungarian Academy of Sciences (HAS) - Institute of Economics CERS-HAS (IEHAS) ( email )

Budaorsi ut 45
Budapest, 1112
Hungary

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