title: Correlated Observations, the Law of Small Numbers and Bank Runs.
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.
authors.affiliation: Department of Economic Theory, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, Bavaria, Germany.
authors.forename: Gergely
authors.initials: G
authors.lastname: Horváth
authors.affiliation: Department of Economics, Eötvös Loránd University and Momentum(LD-004/2010) Game Theory Research Group at MTA KRTK, Budapest, Hungary.
authors.forename: Hubert János
authors.initials: HJ
authors.lastname: Kiss
mesh_terms: D000067012:Banking, Personal; D003198:Computer Simulation; D003657:Decision Making; D060909:Economics, Behavioral; D005381:Financing, Organized; D006801:Humans; D008962:Models, Theoretical; D011336:Probability; D018401:Sample Size