If I want to find a Phillips curve relationship in the data, then through some process of specification searches, Bayesian estimation with alternative priors, or whatever, I will be able to find it. If I'm looking hard for the Virgin Mary, I can find her in a grilled cheese sandwich.So, Paul Krugman has gone searching for the Virgin Mary and, big surprise, claims success. Of course I can take Krugman's two time series and find something else. Here is the data from October 2009 (peak unemployment) to November 2013: In that figure, the line joins observations for October 2009 on the far right with November 2013 on the far left.
Note two things:
1. Unemployment and wage inflation are positively correlated over that four-year period.
2. Sometimes unemployment is falling when wage inflation is falling; sometimes unemployment is falling when wage inflation is rising.
Krugman seems to forget the key lesson of the 1970s Phillips curve debate, which is that you need theory - structure - to make sense of what we see in the world, in a way that is useful for policy.