Capital regulation and monetary policy with fragile banks

Optimizing banks subject to runs are introduced in a macro model to study the transmission of monetary policy and its interplay with bank capital regulation when banks are risky. A monetary expansion and a positive productivity shock increase bank leverage and risk. Risk-based capital requirements amplify the cycle and are welfare detrimental. Within a class of simple policy rules, the best combination includes mildly anticyclical capital ratios (as in Basel III) and a response of monetary policy to asset prices or bank leverage.