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Why has the Phillips curve, displaced by the NAIRU and the output gap, come back into the economic debate after so long in the cold?

If haircuts and dress styles can come back into fashion, then so can economic theories.
That is why policymakers have recently been debating the implications of the shape of that very 1960s concept, the Phillips curve.
New Economist September 29, 2006

In the 1970s, the trade-off between unemployment and inflation seemed to evaporate; both rose at the same time, a phenomenon known as stagflation. ...

So the Phillips curve fell out of favour and was replaced by its corollary, the NAIRU, or non-accelerating inflation rate of unemployment (in effect, the natural rate). Economists spent much of the 1980s and 1990s debating what the rate might be.

Why has the Phillips curve, displaced by the NAIRU and the output gap (which suggests that inflation will rise when economic growth is above trend), come back into the economic debate after so long in the cold?

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