Roger Farmer and Olivier Blanchard have been in a mini-debate about the Phillips curve on Twitter, and David Andolfatto has a nice overview. My thoughts on the Phillips curve are in a post from a couple weeks ago. But generally without a big upswing in labor force participation, price level (e.g. CPI) inflation and unemployment won't have a relationship. The only relationship will be between unemployment and wage growth — with unemployment shocks in recessions