In most banking models, money is merely modeled as a medium of transactions, but in reality, money is also the most liquid asset for banks. Central banks do not only passively supply money to meet demand for transactions, as often assumed in these models, instead they also actively inject liquidity into market, taking banks' illiquid assets as collateral. We examine both roles of money in an integrated framework, in which banks are subject to aggregate illiquidity risk. With fixed nominal deposit contracts, the monetary economy with an active central bank can replicate constrained efficient allocation. This allocation, however, cannot be implemented in market equilibrium without additional regulation: Due to moral hazard problems, banks invest excessively in illiquid assets, forcing the central bank to provide liquidity at low interest rates. We show that interest rate policy to reduce systemic liquidity risk on its own is dynamically inconsistent. Instead, the constrained efficient solution can be achieved by imposing an ex ante liquidity coverage requirement.