PCE data coming out tomorrow ...
Forecasts, vintage forecasts, bold speculation ... and LaTex support!
The FOMC put up their “projections” (I tend to get pushback in the past for calling them “forecasts”) for inflation from their December meeting [pdf] and the graphic above shows. I’ve put the Dynamic Information Equilibrium Model (DIEM) forecast alongside it; the FOMC projection is substantially higher in the near term. The next data point comes out tomorrow so you can check back here to see how it goes.
Sidenote: I got a DM from someone at substack to check out their new beta LaTeX support. I’ll take the opportunity to show the DIEM for core PCE inflation with P being the PCE price level less food and energy (PCEPILFE) tells us that:
(Seems to work pretty well — straightforward interface. I’ll be in the archives repairing the LaTeX imported from blogspot/mathjax over time.)
Here, α is the dynamic equilibrium rate (measured to be ~ 1.7%/y), c is a constant, and the σᵢ are the non-equilibrium shocks. There are two shocks here: the COVID negative shock and the re-opening (and/or vaccination, and/or stimulus) positive shock.
This falls out of an information equilibrium relationship directly related to Okun’s law where
where α + 1 ≡ k is the information transfer index.
Another thing I wanted to show is the forecast from around the time of the first Fed rate hike of the current cycle on March 17th, 2022. Here’s core PCE inflation using the data released March 31st, 2022 (20220331 in yyyymmdd format, downloaded from ALFRED) in blue alongside the latest data (including revisions) in black.
This data would be from the prior month (i.e. February 2022), so this is the DIEM forecast before the first Fed rate hike. It undershoots the data, but the big difference between this and the forecast using the latest data is how long the non-equilibrium shock is. It is approximately the same height, but the duration (shock width) is about two quarters longer. In the year-over-year version (same data, same model, same forecast, just a different representation) we can see those big peaks in the month-to-month data in mid-to-late 2022 led to a broadening of the peak — again by about two quarters.
Here’s the headline CPI data from similar vintages — 20220310 with data for Feb 2022 released before the Fed rate hike, and 20220412 released after but includes data from Mar 2022. Overall, similar undershooting that improves with the additional data point including March of 2022.
The big takeaway is that all the forecasts were returning to the dynamic equilibrium rate (1.7%/y for core PCE, 2.5%/y for headline CPI) around the same time as the Fed rate hike. If anything, the model was underestimating the rate of return to equilibrium, which, in this picture, means that it’s hard to ascribe a causal link between the Fed rate hikes and the lower inflation of the second half of 2022.
I wrote some time ago that you could forecast inflation fairly well in New Zealand and Canada from before the adoption of their inflation targets:
New Zealand
Canada
If a forecast that ignores the treatment can accurately predict the result, whether a 2% inflation target or an interest rate hike, can we really say that treatment is doing anything?
So excited about the LaTeX I forgot to add the “bold speculation” — the inflation “gravity wave”. In the data during the post war period as well as along the broad demographic shock in the 70s and 80s due to women entering the workforce there is a small 2nd order oscillation relative to the overall non-equilibrium shock. I wrote about it a few years ago. You could call it the Phillips curve — it’s a modulation of the price level while labor force expansion is happening at a rate greater than the dynamic equilibrium rate where inflation rises and then is cut off by rising unemployment.
I’ve since speculated that the recent inflation might be due to labor force re-entry post-COVID, which raises the possibility that we could see deflation in the next several quarters:
To get at the mechanism, let’s say labor force growth has a dynamic equilibrium rate β₀. This drives (nominal) economic growth at a rate k β₀, which then (due to the information equilibrium relationship at the top of the page) drives inflation at a rate π = (k − 1) β₀. When we get an exogenous shock to β₀ bring us to β₀ + σ(t), this increases both inflation and growth. This exogenous shock is something like men returning from war or a demographic shift where more women enter the workforce. Increasing inflation brings some amount of economic headwinds1 that make it more difficult for that exogenous shock to add to the labor force — σ(t) falls or even goes negative if unemployment starts to rise. Regardless, inflation π = (k − 1) (β₀ + σ(t)) falls until economic recovery gets underway sufficient to support that exogenous shock again. Due to noise in the time series, this will only be visible if β₀ + σ(t) is fairly high compared to the equilibrium level, i.e. if π = (k − 1) β₀ + η(t) with η(t) being the noise term we only see the gravity wave if
A quick back of the envelope calculation. With RMS error on CPI inflation ~ 3.5 pp, we’d have to have conditions where inflation was above the dynamic equilibrium (k − 1) β₀ ~ 2.5%/y plus the error. That’s about 6%/y — which is what we’ve seen!
The most recent CPI data points have been ever-so-slightly more consistent with the linear decrease mid-oscillation than they have been with the fading of a logistic shock, but it’s way too soon to tell. However, 2023 will be interesting — if we see some actual deflation in the 2nd half of next year it could be evidence for this bold speculation.
Note that we could couple this with the “limits to wage growth” hypothesis where nominal wage growth exceeding nominal GDP growth eats into firms profits and causes a recession. (You could also say e.g. the Fed starts increasing interest rates to fight inflation. We are being agnostic as to the cause of the recessionary pressure.)