A shadow rate New Keynesian model

We propose a New Keynesian model with the shadow rate, which is the federal funds rate during normal times. At the zero lower bound, we establish empirically the negative shadow rate summarizes unconventional monetary policy with its resemblance to private interest rates, the Fed's balance sheet, and Taylor rule. Theoretically, we formalize our shadow rate New Keynesian model with QE and lending facilities. Our model generates data-consistent results: a negative supply shock is always contractionary. %Relatedly, the government multiplier is under 1. It also salvages the New Keynesian model from the zero lower bound induced structural break.