Assessment of hybrid Phillips Curve specifications

•The first-difference of inflation negatively depends on its own lag.•The stylized fact rejects the forward-looking NKPC and its hybrid variant with a lag of inflation.•We show that the stylized fact can be reconciled with the hybrid NKPC with lags of inflation.•Firm's forward-looking behavior is relatively more important than backward-looking behavior.

Rudd and Whelan (2006) document evidence that the first-difference of inflation negatively depends on its own lag, and highlight that sticky price models emphasizing the role of firms' forward-looking pricing behavior cannot be reconciled with the stylized fact. We show that the puzzling negative dependence of the first-difference of inflation on its own lag is consistent with the prediction of the hybrid New Keynesian Phillips Curve (NKPC) with lags of inflation, whereas, as it is argued, it is inconsistent with the prediction of both the purely forward-looking NKPC and its hybrid variant with a lag of inflation. Our theoretical results show that the negative dependence appears only when firms' forward-looking pricing behavior is relatively more important than backward-looking behavior in determining inflation dynamics.