The fragility of the Phillips curve

"We provide a robustness check of the US Phillips curve in the frequency domain. We design frequency-specific coeffcients of correlation (FSCC) and regression (FSCR), based on our frequency-specific data extraction procedure. Being real-valued, signed and normalised, the FSCC is superior to traditional indicators such as coherence and cospectrum. Our FSCC and FSCR estimates suggest that the Phillips tradeoffs vary greatly across frequencies, with frequent sign reversals. They seem to be stable in higher frequencies, but unstable in low and medium frequencies, and they are sensitive to the level and boundaries of frequency aggregation, to the way data are processed prior to analysis (eg detrending) and to the type of variables used. In this sense, the Phillips curves are fragile. The impact of potential cross-frequency model inconsistency on model estimation using conventional time domain methods needs careful scrutiny."