As I was putting together some graphs for my post on HP filtering (coming soon), I started playing around with some real GDP data. First, as many have done before, I fit a simple linear trend to the log of real GDP data since 1947

Plotting the data in this way, the Great Recession is clearly visible and seems to have caused a permanent reduction in real GDP as the economy does not seem to be returning to its previous trend. Taking the log of GDP is nice because it allows us to interpret changes as percentage increases. Therefore, the linear trend implies a constant percentage growth rate for the economy. But is there any reason we should expect the economy to grow at a constant rate over time? What if growth is not exponential at all, and instead grows at a slowly decreasing rate over time? Here’s what happens when we take a square root of real GDP instead of a natural log

I have no theoretical justification for taking the square root of RGDP data, but it fits a linear trend remarkably well (slightly better than log data). And here the Great Recession is gone. Instead, we see a ten year period above trend from 1997-2007 followed by a sharp correction. If economic growth is following a quadratic growth pattern rather than an exponential one, it implies that the growth rate is decreasing over time rather than remaining constant. Here’s an illustration of what growth rates would look like in each scenario

Fitting one trend line doesn’t necessarily mean anything, so to better test which growth pattern seemed more plausible, I decided to try to fit each trend through 1986 and then use those trends to predict current RGDP. Actual annualized RGDP in 2016 Q2 was \$16.525 trillion. Assuming exponential growth and fitting the data through 1986 predicts a much higher value of \$23.353 trillion. A quadratic trend understates actual growth, but comes much closer, with a prediction of \$14.670 trillion. I then did the same experiment using data through 1996 and through 2006 and plotted the results

From these graphs, it appears that assuming quadratic growth, which implies a decreasing growth rate over time, would have done much better in predicting future GDP. Notice especially how close a GDP prediction would have been by simply extrapolating the quadratic trend forward by 10 years in 2006. Had the economy stayed on its 2006 trend through the present, RGDP in the last quarter would have been \$16.583 trillion. It was actually \$16.525 trillion for a difference of about \$58 billion (off by 3 tenths of a percent). That is an astonishingly good prediction for a ten year ahead forecast (Just for fun, extending the present trend to 2026 Q2 predicts \$20.200 trillion. Place your bets now).

Of course, this analysis doesn’t prove anything. It could just be a coincidence that the quadratic growth theory happens to fit better than the exponential. But I think it does show that we need to be careful in interpreting the Great Recession.

Using the above pictures, I can come up with two plausible stories. In the first, the Great Recession represents a significant deviation from trend. There was no fundamental reason why we needed to leave the path we were on in 2006 and we should do everything we can to try to get back to that path. Whether that comes through demand side monetary or fiscal stimulus or supply side reforms like cutting regulation and government intervention I will leave aside. But we should do something.

The other story is a bit more pessimistic. In this version, economic growth had been trending downwards for decades. We made a valiant effort to prop up growth on the strength of the internet in the late 1990s and housing in the early 2000s. But these gains were illusory, generated by unsustainable bubbles waiting to be popped rather than true economic progress. The recession, far from an unnecessary catastrophe, was an essential correction required for the economy to reorganize resources and adapt to the low growth reality. Enacting policies that attempt to restore previous growth rates will only fuel new bubbles to replace the old ones, paving the way for future recessions. Doing something will only make things worse.

Which story is more plausible? I wish I knew.

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