This continues these two posts (here and here) trying to understand the issue raised by Brad DeLong, why GDP (gross domestic product) and GDI (gross domestic income), quantities which ought to be the same on average, differ systematically through time. This is slightly technical and involves a data issue, so you may want to skip this post and the next one.
Initially, I chose NI and GNP to look at this question as those were in Fred (the St. Louis Fed data), the first place I looked. GDI would have been a much better choice, but when the pattern was nearly identical to Brad DeLong’s, I didn’t bother to get the GDI data. Now that there appears to be a correlation to look at, I decided to rectify that and went to the BEA website and got GDI data along with the statistical discrepancy (the difference between GDP and GDI). In doing so, I’ve arrived where I should have started.
Here’s what I did. I used three data series, GDI (gross domestic income), the statistical discrepancy ( the difference between GDP and GDI, call it DISC), and G (government spending). Here’s a graph of DISC/GDI and G/GDI:
Why are these two series so closely related? I would have thought, before seeing this picture, that the discrepancy was mostly random and unpredictable, but it isn’t. It appears largely predictable from movements in G, though this may be spurious, e.g. a third variable may be causing both.
With the question is better formulated, the next step is
understanding the correlation. William Polley suggests in an email it
may be that business cycle conditions are driving both variables, i.e.
G acts as an automatic stabilizer and varies negatively with output
over the business cycle, and the discrepancy also varies systematically
over the cycle so that the correlation in the graph is spurious. This
is worth checking because, as he notes, it would mean we are
systematically mismeasuring output over the business cycle.
In the first post, there was also a suggestion that I/GDI moves with the discrepancy. It does, but not as closely as G/GDI, particularly between approximately 1991 and 1996:
Some progress, but, once again, more to follow...
Update: Here is a graph of the Disc/G ratio:
Because G trends upward, this is essentially a graph of the Disc with a heteroskedasticity correction. The scale is shifted a bit relative to the graph above it because it's not a two-scale graph, but the pattern is the same. You can see the correction here (note this starts at 1959):
Dividing by G normalizes the larger movements at the end. Dividing G by GDI and Disc by GDI in the graphs above does the same thing, dividing by GDI normalizes G and Disc.
The surprise to me was that dividing G by GDI produced the pattern evident in the raw Disc series, and even more evident in the normalized series.