## 12/31/10

### Real GDP per capita in Japan

Couple months ago we presented the concept of constant annual increment in real GDP per capita, G(t), as observed in developed countries. The concept 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. This is an empirical model and is based only on observations of real GDP in developed countries. This is in striking contrast to the mainstream macroeconomic models based on axioms; not empirically proved axioms.

Unlike in the Solow model and its successors, the rate of growth of real GDP per capita, dG/G, has a decelerating nonlinear trend. Differentiating with respect to time and dividing both sides of (1) by G(t), one obtains

dG/G = A/G (2)

This model gives excellent statistical results and explains the evolution of real GDP per capita in developed countries [1,2] since 1950. This year is considered as the year of relatively accurate measurements of GDP. We are using the data base provided by the Conference Board.

In the post related to labor productivity in Turkey, we introduced a model explaining the evolution of productivity as based on the deviation from constant annual increment of real GDP per capita. Therefore, model (1) provides an empirical framework for the productivity model and we need to illustrate the predictive power of (1).

Figure1 presents a very important case of Japan: annual increment in real GDP per capita is plotted against the level of real GDP per capita. (Equation (1) 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.

Both original linear regression line is practically parallel to the x-axis. The corrected line is characterized by a slightly negative trend. There were two periods of very quick growth between \$12000 and \$20000 and between \$28000 and \$33000. Both ended in periods of low (sometimes - negative) growth rates. This effect might be expected in any country which demonstrates very fast growth during an extended period of time. A good example is Ireland. A candidate is China, but its growth is supported by the army of unemployed with very low salaries. Therefore, China may grow mainly due to extensive factors and real GDP per capita do not grow so fast as the overall GDP.

Following the general rule of the constant increment, one may expect a slow recovery of the Japanese economy over decades. However, this recovery is unlikely because the Japanese population is on long-term decline [3].

References
1. Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html

2. Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.

3. Kitov, I., 2006. "The Japanese economy," MPRA Paper 2737, University Library of Munich, Germany