Banks, money, and the zero lower bound on deposit rates

We develop a New Keynesian model where all payments between agents require bank deposits through deposits-in-advance constraints, bank deposits are created through disbursement of bank loans, and banks face a convex lending cost. At the zero lower bound on deposit rates (ZLBD), changes in policy rates affect activity through both real interest rates and banks' net interest margins (NIM). At estimated credit supply elasticities, the Phillips curve is very flat at the ZLBD, because inflationary pressures increase NIM. This strongly increases credit and thereby output, but it dampens inflation by relaxing price setters' credit rationing constraint. At the ZLBD, monetary policy has far larger effects on output relative to inflation, and Taylor rules stabilize output less effectively than rules that also respond to credit. For post-COVID-19 policy, this suggests urgency in returning inflation to targets, avoidance of negative policy rates, and a strong influence of credit conditions on rate setting.