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This paper considers three measures of the systemic importance of a financial institution within an interconnected financial system. The measures are applied to study the relation between the size of a financial institution and its systemic importance. Both the theoretical model and empirical analysis reveal that, when analyzing the systemic risk posed by one financial institution to the system, size should not be considered as a proxy of systemic importance. In other words, the too big to fail argument is not always valid, and measures of systemic importance should be considered. We provide the estimation methodology of systemic importance measures under the multivariate extreme value theory (EVT) framework.