In our previous post, we have started to present historical GDP data which were estimated by Angus Maddison from Groningen University. We have demonstrated that there was no linear time trend in the annual increment of real GDP per capita in the USA between 1871 and 1940. The year of 1940 was selected to introduce a short transition period between two long intervals of constant annual increment. The Second World War and the development of the GDP concept clearly cut the period from 1871 and 2011 in two pieces. One can consider the transition between 1940 and 1950 as a structural break or change in measurement units.
Here we continue testing our model of the real economic growth by presenting the case of Austria. The model is based on an extensive set of observations in developed countries which show that real GDP per capita, G(t), evolves along a linear time trend with all fluctuations related to the change in age pyramid. In our article, we calculated the inertial term A in
G(t-t0)= G0+A(t-t0) (1)
where G(t) is real GDP per capita as observed in developed countries; G0 is the initial level of GDP per capita at time t0 in a given country; and A is the country dependent annual increment measured in PPP dollars. Since the empirical model and is based only on observations of real GDP in developed countries its predictive power depends on how well it fits observations.
Several years ago we presented a model for Austria. Figure 1 depicts annual increment in real GDP per capita as a function of the level of real GDP per capita instead of time. Since the increment is assumed to be constant, the mean value of the annual GDP increment should coincide (at least should be very close to) with its linear trend. In 2002, the linear regression line for Austria shows a distinct positive trend of +0.0041. According to (1) such deviations must be compensates in the long-run by negative rates of growth. However, the years after 2002 have been demonstrating increasing positive trend. This deviation has been compensated by a severe decline in 2009. Therefore, the inertia of real economic growth has won again. Any deviation creates a returning force likely proportional to the size of the deviation. In 2009, the trend is almost 0 and the hypothesis of the constant increment looks sound.
Figure 1. Annual increment of real GDP per capita (2002 and 2009 US$) vs. real GDP per capita in Austria for the period between 1950 and 2002 (upper panel) and between 1950 and 2009 (lower panel). Two sets are presented - the original (open circles) and that corrected for population (filled diamonds). Subsequent values of the latter set are connected by a solid line for illustration of the evolution in time. Bold lines represent the mean value of $548 (2002 US$) and $700 (2009 US$) for the population corrected sets. Two solid lines show linear regressions lines
In Figure 2, we have plotted all historical GDP data (annual increments) from 1871 to 2008 (138 years). All historical data are estimated in 1990 International Geary-Khamis dollars which are different from 2002 US$ and 2009 US$ in Figure 1. One might suggest that there is a linear trend in the time series, but we have to remove the transition period between 1940 and 1950 and plot only the estimates between 1871 and 1950. Figure 3 evidences that there was not positive trend in this time series. Hence, the overall period has two lengthy periods of constant annual increment and a short transition period, During the transition, the mean increment jumped from $30 (from 1871 to 1940) to $353 (from 1951 to 2008). In other words, there two shelves and a ladder.
The case of Austria validates our model of inertial economic growth with a constant annual increment. This is equivalent to the rate of real GDP per capita grows decays inversely proportionally to the attained level:
dG/dt = A or dG/Gdt=A/G.
Therefore, the rate of real economic growth should asymptotically approach the zero line. It should also be noted that the gap in real GDP per capita between developed countries can hardly be closed and the lag of developing courtiers is forever. In relative terms, convergence is possible when the rate of growth in all countries approaches zero. Empirically speaking, the Solow model is wrong.Figure 2. Annual increment in real GDPper capitafrom 1871 to 2008.
Figure 3. Annual increment in real GDP per capita from 1871 to 1940.