How inflationary is an extended period of low interest rates?

Recent monetary policy experience suggests a simple test of models of monetary non-neutrality. Suppose the central bank pegs the nominal interest rate below steady state for a reasonably short period of time. Familiar intuition suggests that this should be inflationary. But a monetary model should be rejected if a reasonably short nominal rate peg results in an unreasonably large inflation response. We pursue this simple test in three variants of the familiar dynamic new Keynesian (DNK) model. All of these models fail this test. Further some variants of the model produce inflation reversals where an interest rate peg leads to sharp deflations.