## 2/11/12

### Real GDP per capita in Japan: 1871-2008

We continue presenting historical estimates of real GDP per capita in developed countries. The USA and Austria have demonstrated that the period between 1871 and 1940 supports our model of constant annual increment of real GDP per capita. We have also found that there was a transition period between 1940 and 1950 when the mean annual increment rose by a factor of 5. It might be the result of a new measurement procedure introduced during this period after the concept of GDP had been developed by Simon Kuznets. The next country we would like to present is Japan. For the period from 1871 to 1940, Japan also has a constant annual inctement.
All measurements in developed countries do support the concept of constant annual increment in real GDP per capita, G(t), which can be described by a simple model: in the long run, the GDP growth as a linear function of time:

G(t-t0)=G0+A(t-t0) (1)
where G0 is the initial level of GDP per capita at time t0 in a given country, A is the country dependent annual increment measured in PPP dollars. Unlike in the Solow model and its successors, the rate of growth of real GDP per capita, dG/Gdt, has a decelerating nonlinear trend. Differentiating with respect to time and dividing both sides of (1) by G(t), one obtains

dG/Gdt = A/G (2)

This model has given excellent statistical results and explained the evolution of real GDP per capita in developed countries [1,2] since 1950. Figure 1 presents the case of Japan: annual increment in real GDP per capita is plotted against the level of real GDP per capita. (Equation (2) uses time implicitly.) It demonstrates the accuracy of our concepts. 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. The linear regression line for Japan is very close to the constant level. Actually, it slightly oscillates around the mean value over time, as the cases for 2007 (upper panel) and 2009 (lower panel) demonstrate. The hypothesis of the constant increment looks sound.

Figure 1. Annual increment of real GDP per capita (2007 and 2009 US\$) vs. real GDP per capita in Japan for the period between 1950 and 2007 (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 \$605 (2007 US\$) and \$596 (2009 US\$) for the population corrected sets. Two solid lines show linear regressions lines. Corresponding linear relationships are displayed, the lower relationship being associated with the original data set.
Figure 2 presents the whole period between 1871 and 2008. There is a spurious time trend which can be split into to segments and one transition period. Before 1945, the mean annual increment was \$32 (1990 International Geary-Khamis dollars) as Figure 3 shows and practically no increase in the annual increment with time (no linear time trend). After 1950, the mean increment jumped to \$341 also without linear trend (see Figure 1).
All in all the case of Japan validates our model of inertial economic growth by its 130-year history of measurements. One should not expect the rate of growth observed in the second part of the 20th century to extent into the 21st century.

Figure 2. Annual increment of real GDP per capita (historical data) between 1871 and 2008. There is no linear trend.
Figure 3. Annual increment of real GDP per capita (historical data) between 1875 and 1944. There is no linear trend.