## 8/13/11

### Revised GDP estimates support the model of inertial growth

On July 29, the BEA revised real GDP estimates for the years after 2007. The most important news is:
` `
`For 2007-2010, real GDP decreased at an average annual rate of 0.3 percent; in the previously `
published estimates, real GDP had increased at an average annual rate of less than 0.1 percent. From the fourth quarter of 2007 to the first quarter of 2011, real GDP decreased at an average annual rate of 0.2 percent; in the previously published estimates, real GDP had increased at an average annual rate of 0.2 percent.

These new BEA data strongly support our model of real economic growth. Previously in this blog, we found that real GDP per capita in developed countries grows as a linear function of time. Similarly to classical mechanics, we interpret this linear growth as “inertial” growth. When the population pyramid does not change over time one can write the following relationship for real GDP per capita, G(t):
G(t) = At + C           (1)
Relationship (1) defines the linear trajectory of the GDP per capita, where C=Gi(t0)=G(t0) and t0 is the starting time. In the regime of inertial growth, the real GDP per capita increases by the constant value A per time unit. Figure 1 depicts the evolution of annual increment of real GDP per capita in the U.S. since 1950. The new GDP revision makes the slope of the linear regression line (trend) almost negligible (+\$1.9 per year) and thus supports our concept. In 2011, the slope may become negative if the increment is below \$432. After the two mediocre quarters in 2011, we would not expect real GDP per capita in 2011 to grow faster than in 2010.
On June 5 we had a post on the current position of the U.S. economy relative to some long term trend. As a rule, economists consider real growth as an exponential process and see the U.S. economy far below its trend. We compared the trends in real GDP and GDP per capita. The latter should be a linear one. Figure 2 depicts the evolution of both variables between 1950 and 2010 with the new readings between 2007 and 2010.
The real GDP curve has an exponential shape as related to the growth in total population. One can easily observe the current deviation from the exponential trend and blame poor economic conditions after 2007. With the decelerating rate of total population growth we would not expect the observed curve to return to the exponential trend (exponential extrapolation of the previous growth.)
The real GDP per capita evolves along a straight line. After the revision, the curve falls below the linear trend. It touched the trend with the previous set of GDP estimates. All in all, during the past four years the observed curve returned to the long-term trend and may stay below the trend for a while.   We also presented an exponential trend which has a small coefficient of 0.02. This coefficient effectively makes the line very close to a straight one between 1 and 60. However, the deviation from the (extrapolated) exponential trend will be growing and observations will contradict the hypothesis of exponential growth.
Figure 1. Annual increment of real GDP per capita in the U.S. between 1950 and 2010.

Figure 2. The evolution of real GDP and real GDP per capita between 1950 and 2010.