The problems with H-P Filtering
Matthew Martin 7/12/2012 11:56:00 AM
|Figure 1. US Time Series Data|
|Figure 2. Simulated Data from an RBC model.|
Ok, back up. There is actually a very good reason for using something like the HP filter. Here is the growth rate in (unfiltered) real GDP:
|Figure 2. Annual Growth Rate in US Real GDP|
One way to do this would be to simply subtract 3.4% from the annual growth rates in the data, and then assume that the remainder is the amount of the fluctuation that is due to the business cycle. Of course, you could argue that 3.4% is arbitrary, and that the trend growth rate itself fluctuates over time. And this is where the macroeconomic research begins to loose its sanity. I don't object to the basic premise--the trend GDP probably does fluctuate over time. The problem is that HP filtering attempts to figure all this out based only on a single data series--in econometrics, we would say that our model suffers from under-identification. We are attempting to extract more information from the data than it contains. Ultimately, the way we do this is by making certain "identifying assumptions"--in the case of HP filtering, we assume that the trend GDP must satisfy a specific degree of "smoothness," and that any fluctuation that violates this smoothness must be the volatility due to the business cycle.
|Figure 3. US real GDP (red) and HP-filtered "trend" GDP (blue).|
So here are some challenges to the conventional paradigm of HP-filtering: first, if the HP trend is supposed to represent potential GDP, why would we always assume that it fluctuates less than the overall business cycle? Wouldn't it be possible that the actual fluctuation in GDP would be less than the fluctuation in potential GDP? That actually makes a bit of sense to me, since economic agents tend to be too slow to adapt to technologies or other fundamental changes, not too fast. Second, why would we assume that potential GDP is pro-cyclical? Sure, we could argue that prolonged depressions destroy capital, for example, but why would we filter that effect out of the data, rather than include it in our model? And, given that we believe that the fluctuation in the business cycle is in addition to the fluctuation in the potential GDP, there ought to be plenty of instances where actual and "trend" GDP move in opposite directions, which never happens with HP-filtering.
Now, this is not to say that HP-filtering should never be used to look at the business cycle, but I do think it is fair to say that if your argument depends mostly on how the HP filter interprets the data, then you are probably wrong. (James Bullard, this means you)