Resolving new keynesian puzzles

New Keynesian models generate puzzles when confronted with the zero lower bound (ZLB) on nominal interest rates (e.g. the forward guidance puzzle or the paradox of flexibility). We show that these puzzles are absent in simple and medium-scale models when monetary policy approximates optimal policy, even loosely. The standard approach to modeling monetary policy at the ZLB does not approximate the policy a rational inflation targeting central bank would choose at the ZLB. It is this disconnect that is responsible for the puzzles. The puzzles, therefore, are best thought of as the plausible predictions of implausible monetary policy rather than implausible predictions to plausible monetary policy. We show how to write monetary policy rules that capture the same policy objective with and without the ZLB.