{'fraction_non_alphanumeric': 0.01867219917012448, 'fraction_numerical': 0.008298755186721992, 'mean_word_length': 5.840425531914893, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Mis-Specification and Frequency Dependence in a New Keynesian Phillips Curve

A Phillips curve is at the center of New Keynesian macroeconomic modeling. Yet this relationship has proven quite difficult to detect in post-1984 quarterly data. Here we provide compelling evidence that previous models quantifying the dynamic relationship between inflation and unemployment rates have been mis-specified in their assumption that the coefficient on unemployment is a constant. Instead, we find that this coefficient is frequency-dependent: the inflation impact of a fluctuation in the unemployment rate differs for a fluctuation which is part of a smooth pattern of changes versus a fluctuation which is an isolated event, just as the Friedman-Phelps “natural rate” hypothesis suggests. In particular, we analyze the Blanchard/Gali (2005) Phillips Curve regression specification using a newly developed econometric technique capable of consistently estimating the frequency dependence in a feedback relationship. Explicitly allowing for feedback in such a relationship is essential because the two-sided nature of the Fourier transformations used in previous frequency domain studies otherwise confounds the analysis, leading to inconsistent parameter estimates.Using one-sided filtering to allow for observed feedback in the relationship, we find statistically significant frequency dependence. In particular, using quarterly data from 1984:I2003:IV, we find an economically and statistically significant inverse relationship between inflation and unemployment for higher-frequency unemployment rate fluctuations — with periods less than or equal to about one year — but no evidence for an effect of lower-frequency unemployment rate fluctuations. In contrast, an analogous model ignoring frequency dependence finds no statistically significant relationship at all between inflation and unemployment rates during this sample period.