Nick Rowe says that succesful inflation targetting may make the Phillips curve flatter or may cause the empirical Phillips curve to be flatter even though the structural relationship behind the Phillips curve is unchanged. He illustrates his argument with an example of a Phillips straight line. I give him a hard time in comments.
I have to note an even simpler expanation. The Phillips curve is a curve. In Phillips's data for anchored inflation (pre 70s indeed pre 60s) equation one is rejected. The Phillips curve was convex so the slope was low for low inflation rates.
I think this is an absolutely fair critique of the IMF research paper which asserts that the Phillips curve has changed. It is only valid analysis if by "curve" means "straight line"
Long before any systematic thought about expectatiions, Phillips, Samuelson and Solow could have predicted that the slope of inflation with respect to Y would be low at low inflation rates.
In the available data, successfully targeted inflation and low inflation occur mostly at the same times and places.
Your story is interesting, but it can only be distinguished from the curves curve hypothesis is there is an episode of inflation targeting with a high target or an episode of unsuccessfully targeted but low inflation . There has not yet been a high inflation target, so the (post Phillips) example would have to be Japan where inflation has been very low and under target often over the past two decades. The Japanese Phillips curve is flat. The result is more nearly low inflation implies low slope not successful targeting implies a low slope.
Note the original Phillips curve as graphed by Phillips generally showed a low slope at low inflation rates http://en.wikipedia.org/wiki/Phillips_curve
There were two years of sharp deflation, one of -3% and 11 (of 36 in the scatter graph I am eyeballing) with inflation from -2% to +2% and unemployment from 10 % to 22%.
A flat Phillips curve at low inflation rates is not a new phenomenon which occured after monetary authorities learned how to successfully target inflation. Phillips's data set also includes a year with nominal wage inflation of 32%.