Last friday, 6/28, new PCE (Personal Consumption Expenditures Price Index) data were released. The year-on-year inflation numbers decreased from 2.7% last month to 2.6% [1]:
Let's see how the popular press reports this [2]:
The headline is just very wrong. Inflation was 2.6% but it did not rise by 2.6%. The PCE-based inflation number did actually decrease from 2.7% a month earlier.
I see lots of mistakes in reporting and in posts about inflation and price indices. This is a good (or rather bad) example.
Here is a similar incorrect statement about CPI inflation:
CPI inflation was 3%. It did not rise 3%. It was actually down.
Background
There are a few different quantities here. Here is a summary:
| PCE Index and Inflation | |
|---|---|
| \(x_t\) | PCE index at month \(t\) |
| \(i_t = \displaystyle\frac{x_t-x_{t-12}}{x_{t-12}}\cdot 100\%\) | Inflation at month \(t\) |
| \(i_t - i_{t-1}\) | Change in inflation at month \(t\) |
This hierarchy is often poorly understood by, let's say, amateur economists.
The inflation number is measured year-on-year (i.e. with a 12-month lag). That has the advantage that there are no seasonal effects. The theory behind price indices and their calculation is fascinating, see e.g. [3]. An interesting way to create an "instantaneous inflation" number based on kernel density estimation is shown in [4].
References
- https://www.bea.gov/data/personal-consumption-expenditures-price-index
- https://www.cnbc.com/2024/06/28/may-pce-inflation-report.html
- Walter Erwin Diewert, John Greenlees, Charles R. Hulten, Price Index Concepts and Measurement. (2010). University of Chicago Press.
- Jan Eekhout, Instantaneous Inflation, 2023.