At this point, however, there is wide acceptance of the idea that for a variety of reasons, but especially downward nominal wage rigidity, the Phillips curve is not vertical at low inflation.What Krugman seems to mean is that, in the long run, there is a tradeoff between unemployment and inflation at low rates of inflation. The claim is that this is "widely accepted."
So, first, I have no idea who "accepts" this idea. I haven't heard about it, except in Krugman's blog posts. And why do the accepting people find it so acceptable? Is there a theory? Krugman says its wage rigidity that explains this. Has he written down a theory? Has someone else written down a theory? Has that theory been confronted with the data?
On the empirical front, let me reproduce two charts from my last post. First, let's look at a scatter plot of the pce inflation rate vs. the difference between the unemployment rate and the CBO natural rate of unemployment (quarterly, 1955-2013):
Next, look at what's been happening for the last 9 quarters: