This work, while illuminating in many respects, does not seem to have greatly advanced the empirical forecasting of inflation. And, the microeconomic behaviors we describe to justify the empirical specifications of our macroeconomic models often do not coincide very well with what we find when we directly observe the decisionmaking of workers and firms.
I think we need to push forward along these microeconomic lines. I have a lengthy list of macroeconomic inflation puzzles whose answers would make me a better policymaker, but, for the most part, the solutions to the puzzles rest on a better understanding of how workers and firms set wages and prices.