Interest on reserves, helicopter money and new monetary policy

We build a nonlinear dynamic model with currency, demand deposits and bank reserves. Monetary base is controlled by central bank, while money supply is determined by the interactions between central bank, commercial banks and public. In economic crises when banks cut loans, monetary policy following a Taylor rule is not efficient. Negative interest on reserves or forward guidance is effective, but deflation is still likely to be persistent. If central bank simultaneously targets both interest rate and money supply by a Taylor rule and a Friedman's k-percent rule, inflation and output are stabilized. An interest rate rule policy is just a subset of a more general monetary policy framework in which central bank can move interest rate and money supply in every direction.