Put a bird on it
LeBron links to Stephen Williamson's post about the statistical problems inherent in calculating the vague and unobservable path of "potential output", especially when using the HP filter. I recently criticized the CBO's approach.
This is a sad but general problem in modern macro. Theories are built around unobservable variables. To calculate the output gap, we need potential output, but it's not observable. In growth & development, many issues hinge on the behavior of total factor productivity (TFP), but it is also unobservable.
Modern business cycle theory has made an art form of this. In seeking to better replicate real world data, more and more driving shocks are needed. So we discover that "shocks to the mark-up" for example (or shocks to "preferences") are now an important force in business cycles. These shocks too, are unobservable and receive even less scrutiny than do potential output or TFP (they are typically not ever displayed or forced to pass an "eyeball" test of reasonableness).
Modern business cycle theory also frequently uses the HP filter to produce the business cycle data that it calibrates to or uses for estimation. This use of the HP filter is no less problematic that the use criticized by Williamson in the original linked post.
People, when you read or hear people talking about unobservables like they were data, it's good to remember that the series in question were created by someone using a model with assumptions and limitations. Ask them to show you their series, to defend its derivation and its time series properties.
The bottom line is that no one knows what potential output is or what TFP is. I certainly don't agree with Williamson and Lacker that we are currently at or near maximum output/employment, but I do agree that we have no idea exactly how far away from that point we are currently operating.