We published a book and a few papers [e.g., 1, 2, 3] on
economic growth. There are numerous plots demonstrating the decelerating rate
of real economic growth in developed countries. The long-term component of real
GDP increase is very simple – annual increment in real GDP per capita, rGDPpc, is
a constant, which does not change with time since the late 1940s. This makes
the rate of growth to be inversely proportional to the current level of rGDPpc:
dln(rGDPpc(t)) = A/rGDPpc(t). The
population component is large in the USA – approximately 1% per year since the 1950s,
but negative in Japan. Therefore, we use rGDPpc instead of rGDP, which is rather
misleading.

In the first paper published in 2005, we used data
between 1950 and 2003 and found that the rGDPpc annual increment has a positive
slope. It was considered as an indication of future problems between 2004 and
2016, which was actually observed as the Great Recession and further sluggish recovery.
Figure 1 displays the original time series between 1947 and 2003 (black
circles) extended by the estimated made since 2004. Instead of time, we use
rGDPpc as argument. For recession periods, when the rGDPpc falls, one observes
loops in the curve. Our prediction was right – the slope of the regression line
has dropped from 0.02 (black linear trend line) to 0.007 (red trend line). The
average increment in rGDPpc was $551 as measured in 2009US$.

Figure 1. Annual increment in real GDP per capita in
the USA since 1947. Black circles show the period between 1947 and 2003, and
red circles show the period extended into 2016. Linear trends are shown in
black and red, respectively. Two regression equations demonstrate the change in
slope since 2003.

There is another problem with the original rGDPpc time
series borrowed from the BEA web site. It is calculated as a ratio of rGDP and
total population, while only economically active population matters. Therefore,
we have to correct the original rGDPpc
for the ratio shown in Figure 2. When the rGDPpc multiplied by the population correction
factor, one obtains a better view on the long-term growth rate, as depicted in
Figure 3. The trend in the rGDPpc annual increment is absent. This observation
means that the rate of real GDP growth in the USA (and other developed countries)
is decaying inversely proportional to rGDPpc. Leading economic countries will
be growing at a rate of about 1.5% per year in the next 20 years. In 2016, the
rate of rGDPpc growth was 0.9% per year. This mediocre growth will be accompanied by decreasing rate of population growth as observed since the earlier 2000s.

Figure 2. The ratio of total population and working
age population (16 and above). The rGDPpc is corrected (multiplied) by this ratio.

Figure 3. Same as in Figure 1, but for the population corrected
rGDPpc.