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 Log Real GDP (blue) and fitted trendline (orange). Trend annualized growth rate = 3.25%. Data from FRED

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