The output gap is a key concept in macro. Students in my courses have asked about the characteristics of some of the proxies. Here are some representative examples.
Figure 1: Cyclical component from Hodrick-Prescott filter (blue), from Baxter-King band pass filter (red), Hamilton filter (green), and output gap from CBO (gray), all in logs, estimated from 1967-2020 data. NBER defined recession dates shaded gray. Source: BEA 2020Q4 2nd release, CBO (February 2021), NBER, and author’s calculations.
Note that the HP filter (lambda = 1600) and band pass filter (EViews default) tend to imply a relatively small cyclical component. The Hamilton filter (using h=8, p=4) implies substantially larger cycles — with a standard deviation about twice that of the other statistical measures over this sample.
The CBO output gap has a standard deviation of about 2.4% (vs. 3% for the Hamilton filter).
For a discussion of “maximal output” a la Delong and Summers (BPEA, 1988), see this post.
There are also distinctions between potential and natural rates of output, as discussed here.