The conventional wisdom that inflation and unemployment are unrelated in the long-run implies that these phenomena can be analysed by separate branches of economics. The macro literature tries to explain inflation dynamics and estimates the NAIRU. The labour macro literature tries to explain unemployment dynamics and determine the real economic factors that drive the natural rate of unemployment. We show that the orthodox view that the New Keynesian Phillips curve is vertical in the long-run and that it cannot generate substantial inflation persistence relies on the implausible assumption of a zero interest rate. In the light of these results, we argue that a holistic framework is needed to jointly explain the evolution of inflation and unemployment.