The Fragility of the Phillips Curve: A Bumpy Ride in the Frequency Domain
Bank for International Settlements, Monetary and Economic Department, 2005 - Inflation (Finance) - 41 pages
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.
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aggregate analysis band spectrum regressions band-pass filter bivariate correlations business cycle business-cycle frequencies causality tests ccohxy coefficient of correlation coherency cohxy confidence intervals correlation and regression cospectra covariance stationary CPlLFESL cross-frequency variations cumulated responses data extraction procedure detrended discrete Fourier transform economic empirical FD filter filtered data frequency bands frequency domain frequency-specific coefficient frequency-wise FSCC GDPDEF GPDlC96 HCNF HP and BP HP-filtered cyclical series HP-filtered trend series inverse Fourier transforms lags linear lndex Long slope DW low-frequency low-pass filter Lucas macroeconomic model selected null hypothesis pair of Phillips PCECC96 PCEPlLFE Phillips correlations Phillips curve Phillips regressions Phillips relations Phillips tradeoff Phillips variables PNFlC96 qCPlAUCSL qPPlACO real activity real coherences real variables regressand Regressions with filtered RHCMA RHCNF s-th Sargent Short slope Long short-run sign reversals signed measure Sims tests slope Long slope Spectral indicators spectral regression squared gain stationary processes supply shocks UNRATE validity versus GDPCTPl WASCUR zero