“New tools to monitor inflation in real time” by Simon C. Smith and Alexander L. Wolman is a FEDS Note released a few days ago by two Fed economist (Smith currently works on the inflation desk at the Board). The note introduces a new metric using the entire distribution of price changes to monitor aggregate inflation. The conclusion is that PCE price inflation has come close to its pre-pandemic level but remains higher than target and sticky.
We repeated a similar exercise in CPI space. The conclusion is more worrying, as there is evidence that we remain well above pre-pandemic levels with some possible acceleration.
What the note does and main results
The main result of Smith and Wolman (2024) is shown in Figure 1. The authors show that over the period 1995 to 2020 (the grey dots in Figure 1), there is a positive correlation between price changes (the y-axis in Figure 1) and a measure of skewness (the x-axis in Figure 1). The intuition is simple: when the mean is higher than the median, PCE inflation is driven by the right tail. The authors claim that an inflation rate driven by a higher median is more concerning than one that is driven by increased right skewness (mean – median > 0).
Figure 1. Correlation between MoM PCE inflation and a measure of skewness
The authors also show a time series of inflation deviations, defined as the difference between actual inflation and the pre-pandemic fitted inflation rate based on Figure 1. In other words, they show how much the current distribution deviates from what it is implied by the correlation in the low and stable period. The conclusion is that “inflation is much closer to its pre-pandemic level than it was, but still has a little further to go”.
Why the note is important and our critique
The FEDS note is important because, in our experience, it generally reflects the point of view of the Fed staff. Therefore, we can infer two important things. First, the Fed staff pays a lot of attention to the distributions (we told you..). Indeed, we repeat what we generally write in each CPI report: pay attention to the distribution and dismiss any ad-hoc story of the sell-side. Second, it seems that the Fed staff is on board with the idea that inflation has moderated but we are not at target yet.
A similar exercise in CPI space is sending worrying signals. Figure 2 shows the result of a similar (but simpler) exercise we carried out. The red line shows the difference between the mean and the median of the unweighted monthly distributions (MoM ar) in core CPI space. In order to smooth the lines, we plotted the MA(12) of the difference. The blue line in Figure 2 shows the MA(12) of the median (minus 1 percent to compare it to the red line). The point of the FEDS note is that the median of the distribution has normalized, and therefore we should be less worried about the right tail which remains thick. We agree with the Fed staff that a high MoM of core CPI is more worrying if associated with an entire movement of the distribution (that is, with a higher median and not a higher difference mean-median). However, taking zero signal from the mean-median is precisely the mistake the staff (and the FOMC) made back in 2021. When inflation accelerates, it generally does so in a few sectors/items in the first place; then, if demand conditions remain accommodative, it extends to the entire distribution (it becomes “broad-based”). Indeed, as shown in Figure 2, back in 2021 we first saw a sharp increase in the mean-median difference that the Fed staff and the FOMC labeled as “transitory” (precisely because the median did not move, it wasn’t “broad-based” – or more appropriately because pi* did not move). However, when the median started to increase with a large lag… it was already too late.
Figure 2. Mean-Median MA(12) and Median rescaled MA(12) in core CPI space
In the last 12 months, we saw a re-acceleration of the mean-median difference; the median has remained low. As shown by the red arrow in Figure 2, the mean-median difference has raised again (this evidence applies also to core PCE space, although to a less extent). Put it simply: something is still wrong with the right tail. So far, the median has not moved, but given what happened in 2021-2022, the question is: should the Fed staff and the FOMC be relaxed? (As a reminder: Figure 2 is very much consistent with the evidence of the distributions we circulate after each CPI report. The issue is that the tails are very thick; overall, the distribution in core CPI space remains very different than pre-Covid).
To sum up: we are not at target, and some metrics (especially in CPI space) are concerning. With a large fiscal deficit and a non-aggressive central bank, in case, where is the stop-loss?