["Journal of Money, Credit and Banking, EarlyView. ", "\nAbstract\nWe show that banks do not decentralize the first best in a nominal Diamond–Dybvig economy with inside money. Furthermore, state‐contingent deposit contracts do not expand the consumption possibility set to include the first best either. Central banks can improve welfare but only for savers and only with unconventional monetary policy. Finally, central banks could prevent runs using their lender‐of‐last‐resort facility. These results suggest that, without an explicit incorporation of inside money, it is not trivial to provide a theoretical argument about the ability of the banking sector to efficiently supply liquidity in our economies."]