Time-Frequency Relationship between Inflation and Inflation Uncertainty for the U.S.: Evidence from Historical Data

We provide new evidence on the relationship between inflation and its uncertainty in the U.S. on an historical basis, covering the period 1775-2014. First, we use a bounded approach for measuring inflation uncertainty, as proposed by Chan et al. (2013), and we compare the results with the Stock and Watson (2007) method. Second, we employ the wavelet methodology to analyze the co-movements and causal effects between the two series. Our results provide evidence of a relationship between inflation and its uncertainty that varies across time and frequency. First, we show that in the medium- and long-runs, the Freidman–Ball hypothesis holds when the measure of uncertainty is unbounded, while if the opposite applies, the Cukierman–Meltzer reasoning prevails. Second, we discover mixed evidence about the inflation–uncertainty nexus in the short-run, findings which explain the mixed results reported to date in the empirical literature.