Overconfidence is a well-established behavioral phenomenon that involves an overestimation of own capabilities. We introduce a model, in which managers and agents exert effort in a joint production, after the manager decides on the allocation of the tasks. A rational manager tends to delegate the critical task to the agent more often than given by the efficient task allocation. In contrast, an overconfident manager is more likely to hoard responsibility, i.e. to delegate the critical task less often than a rational manager. In fact, a manager with a sufficiently high ability and a moderate degree of overconfidence increases the total welfare by hoarding responsibility and exerting more effort than a rational manager. Finally, we derive the conditions under which responsibility hoarding can persist in an organization, showing that the bias survives as long as the overconfident manager can rationalize the observed output by underestimating the ability of the agent.