This paper studies a New Keynesian model with a banking system. The central bank targets the interest rate on short safe bonds that are held by banks to back inside money and hence earn convenience yield for their safety or liquidity. Central bank operating procedures matter. In a floor system, the reserve rate and the quantity of reserves are independent policy tools that affect banks’ cost of safety. In a corridor system, increasing the interbank rate by making reserves scarce increases banks’ cost of liquidity and generates strong pass-through to other rates of return, output and inflation. In either system, policy rules that do not respond aggressively to inflation – such as an interest rate peg – need not lead to self-fulfilling fluctuations. The stabilizing effect from an endogenous convenience yield is stronger when there are more nominal rigidities in bank balance sheets.