This paper aims to improve the understanding of U.S. inflation dynamics by separating out structural from cyclical effects using frequency domain techniques. Most empirical studies of inflation dynamics do not distinguish between secular and cyclical movements, and we show that such a distinction is critical. In particular, we study traditional Phillips curve (TPC) and new Keynesian Phillips curve (NKPC) models of inflation, and conclude that the long-run secular decline in inflation cannot be explained in terms of changes in external trade and global factor markets. These variables tend to impact inflation primarily over the business cycle. We infer that the secular decline in inflation may well reflect improved monetary policy credibility and, thus, maintaining low inflation in the long run is closely linked to anchored inflation expectations.