The new Keynesian Phillips curve (NKPC) has become central to monetary theory and policy. A seemingly benign NKPC prediction is that trend shocks dominate price level fluctuations at all forecast horizons. Since the NKPC cycle of the U.S. GDP deflator peaks at each of the last seven NBER dated recessions, support for the NKPC is limited. The authors develop monetary business cycle models that contain different combinations of nominal (sticky-price) and real (labor market search) rigidities to understand this puzzle. Simulations indicate that a model combining labor market search and flexible prices is better able to match actual price level movements than sticky-price models do. This model represents a challenge to claims that sticky prices are a key part of the monetary transmission mechanism.