We develop a medium-size semi-structural time series model of inflation dynamics that is consistent with the view - often expressed by central banks - that three components are important: a trend anchored by long-run expectations, a Phillips curve and temporary fluctuations in energy prices. We find that a stable long-term inflation trend and a well identified steep Phillips curve are consistent with the data, but they imply potential output declining since the new millennium and energy prices affecting headline inflation not only via the Phillips curve but also via an independent expectational channel. A high-frequency energy price cycle can be related to global factors affecting the commodity market, and often overpowers the Phillips curve thereby explaining the inflation puzzles of the last ten years.