Based upon the working paper by Jan Eeckhout (UPF Barcelona), here’s the PCE inflation rate up to December:
Figure 1: Year-on-year PCE inflation (blue), quarter-on-quarter (sky blue), month-on-month (black circle), and instantaneous inflation (T=12, a=4) (bold red), all annualized. NBER peak-to-trough defined recession dates shaded gray. Red dashed line at 2%. Source: BEA and author’s calculations.
Note that the instantaneous rate (a=4, tau=12) tracks the Q/Q inflation rate pretty well.
The instantaneous inflation rate upweights the most recent observation. How does this compare with alternative measures that attempt to track trends.
Figure 2: Instantaneous PCE inflation (a=4, T=12) (bold red), Q/Q inflation (tan), 16% trimmed mean M/M inflation (sky blue), and core M/M (purple), all annualized. NBER peak-to-trough defined recession dates shaded gray. Source: BEA and author’s calculations.
Interestingly, neither core m/m nor trimmed mean m/m tracks particularly well instantaneous inflation (a=4, T=12); different values of a might lead to different outcomes (a=infinity is full weight on most recent observation, a=0 is equal weights on all tau observation, a=1 is linearly declining weights).
What’s clear is PCE inflation measured with high weight on the most recent observation is declining, as I noted on Marketplace on Friday.