(Warning: Might be considered “wonky” by some) In many economic analyses, one wants to isolate the “business cycle” component of macroeconomic series. Here is one such series, which has had a detrending technique applied to it. Try to guess what it is.
The above series is the Hodrick-Prescott filtered net exports to GDP series for the United States. (I’ve discussed the HP filter in the context of output gaps before .) If one believes that the HP filter properly identifies the cyclical versus trend components, then the plot shows the cyclical component of net exports; hence in this context cyclical net exports were in rough balance in 2007.
Of course, this series is much different than the one we are accustomed to. I plot the filtered and actual series in Figure 2.
Figure 2: Net exports to GDP ratio (red) and HP-filtered NX/GDP series, using lambda = 1600 (blue). NBER defined recessions shaded gray, assumes last recession ended 2009Q2. Source: BEA, advance 2009Q3 GDP release, NBER, and author’s calculations.
While it would appear that the HP filtered series does capture essential features of business cycle fluctuations in net exports (consider how the cycles correlate with NBER-defined recessions), filtering does impart some substantively different properties to the series. For instance, the unfiltered series is highly persistent, with the autoregressive coefficient in an AR(1) specification equal to 0.98, standard error 0.013. On the other hand, the filtered series exhibits much lower persistence, with an AR coefficient of 0.79.
In many studies, the variable of interest is the ratio of real exports to real imports. Here are the unflitered and filtered series:
Figure 3: Ratio of real exports to real imports in Ch.2005$ (red, right scale) and HP-filtered (blue, left scale). NBER defined recessions shaded gray, assumes last recession ended 2009Q2. Source: BEA, advance 2009Q3 GDP release, NBER, and author’s calculations.
The degree of persistence is once again lower with the HP-filtered data, as is the variability, especially during the latter portion of the sample. The HP-filtered series also indicates almost no business cycle related fluctuation in the exports/imports ratio over the entire 1997-2007 period. Perhaps that’s the right interpretation. It certainly does give one pause for thought.
What’s the bottom line? For me, it’s not that HP-filtering is necessarily a bad idea. It’s just that one has to be real careful, and think about what is being extracted, and what remains, when applying any detrending technique.
For more formal discussion of the use of various filters, see Cogley and Nason [link updated 4pm Pacific].