RESEARCH ARTICLE Correlated Observations, the Law of Small Numbers and Bank Runs Gergely Horváth1☯¤a*, Hubert János Kiss2☯¤b 1 Department of Economic Theory, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, Bavaria, Germany, 2 Department of Economics, Eötvös Loránd University and Momentum(LD-004/2010) Game Theory Research Group at MTA KRTK, Budapest, Hungary ☯ These authors contributed equally to this work. ¤a Current address: Department of Economic Theory, Friedrich-Alexander-Universität Erlangen-Nürnberg, Lange Gasse 20, D-90403 Nuremberg, Germany ¤b Current address: Department of Economics, Eötvös Loránd University and Momentum(LD-004/2010) Game Theory Research Group at MTA KRTK, Budapest, Hungary *
[email protected] Abstract OPEN ACCESS Empirical descriptions and studies suggest that generally depositors observe a sample of Citation: Horváth G, Kiss HJ (2016) Correlated previous decisions before deciding if to keep their funds deposited or to withdraw them. Observations, the Law of Small Numbers and Bank These observed decisions may exhibit different degrees of correlation across depositors. In Runs. PLoS ONE 11(4): e0147268. doi:10.1371/ journal.pone.0147268 our model depositors decide sequentially and are assumed to follow the law of small num- bers in the sense that they believe that a bank run is underway if the number of observed Editor: Giovanni Ponti, Universidad de Alicante, ITALY withdrawals in their sample is large. Theoretically, with highly correlated samples and infi- nite depositors runs occur with certainty, while with random samples it needs not be the Received: September 23, 2014 case, as for many parameter settings the likelihood of bank runs is zero. We investigate the Accepted: January 1, 2016 intermediate cases and find that i) decreasing the correlation and ii) increasing the sample Published: April 1, 2016 size reduces the likelihood of bank runs, ceteris paribus.