Paul Krugman writes:
OK, several correspondents have weighed in on the story I’d heard about the economics department that abandoned econometrics because it was rejecting its models. It wasn’t quite as alleged, but close enough.
The department in question was the University of Minnesota. For those readers new to this discussion, “freshwater-saltwater” was a distinction originally due to Bob Hall, who noted that the economics departments that had rejected Keynes and anything reminiscent of Keynes were inland schools like Minnesota, Chicago, and Rochester, whereas the places that retained a belief in the usefulness of monetary and fiscal policy were places like MIT, Princeton, and Berkeley.
So the story as I now have it was that there was harsh conflict between the macroeconomic theorists at UMinn, especially Prescott, and the econometricians who had the nasty habit of showing that those models didn’t work. And for at least some period econometrics was dropped as a required course for the Ph.D. — I don’t know whether it has been restored.
The Hodrick-Prescott (HP) filter is the optimal estimator of the trend component in a smooth trend model with signal-to-noise ratio parameter fixed at 1/1600. It gives the detrended observations, , for large samples and t not near the beginning or end of the series
Bear in mind that if the smooth trend model was believed to be the true model there would be no reason to apply the HP filter. The filtered data of a smooth trend model contain nothing more than white noise. The belief here is clearly different.
We can easily show that the gain from the detrending filter is given by:
Note that the smaller the the more the filter concentrates on removing low frequencies.