Real GDP per capita in developed countries

Abstract Growth rate of real GDP per capita is represented as a sum of two components – a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of real GDP per capita with a numerator potentially constant for the largest developed economies. Statistical analysis of 19 selected OECD countries for the period between 1950 and 2004 shows a very weak linear trend in the annual GDP per capita increment for the largest economies: the USA, Japan, France, Italy, and Spain. The UK, Australia, and Canada show a larger positive linear trend. The fluctuations around the trend values are characterized by a quasi-normal distribution with potentially Levy distribution for far tails. Developing countries demonstrate the increment values far below the mean increment for the most developed economies. This indicates an underperformance in spite of large relative growth rates.

Key words: economic development, economic trend, business cycle, GDP per capita

JEL classification: E32, O11, O57

Introduction Real economic growth has been studied numerically since Kuznets’ works on accounting of national income and aggregate factor inputs. Hodrick and Prescott [1980] introduced a concept of two-component economic growth – an economic trend and a deviation or business cycle component. The trend component is responsible for the long-term growth and defines economic efficiency. In the long run, the deviation component of economic growth has to have a zero mean value. In 2004, Prescott and Kydland received a Nobel Prize for the study of “the driving forces behind business cycle” [Bank of Sweden, 2004], what demonstrates the importance of the best understanding of the growth processes and the explanation of the two-component behavior.

Prescott and Kydland, along with many other researchers, have proposed and studied exogenous shocks as the force driving fluctuations of real GDP growth rate. Their research during the last 25 years has revealed numerous features of principal variables involved in the description of the economic growth. There are many problems left in the theory of economic growth.

Kitov [2005a] proposed a model with GDP growth dependent only on the change in a specific age cohort in the population and the attained level of real GDP per capita. According to this model, real GDP per capita has a constant growth increment and the observed fluctuations can be explained by the population component change. In developed countries, real GDP per capita has to grow with time along a straight line, if no large change in the specific age population is observed. Relative growth rate of real GDP per capita has to be an inverse function of the attained

1 level of real GDP per capita with a potentially constant numerator for developed economies. The paper is devoted to validation of the model using GDP per capita and population data for some selected developed countries. Our principal purpose is to demonstrate the possibility to decompose GDP per capita growth into the two components.

1. The model and data Kitov [2005a] has developed a model explaining the observed real GDP growth rate variations in the USA. He has distinguished two principal sources of the per capita GDP growth in the USA – the change in 9-year old population and the economic trend related to the measured GDP per capita level. The trend has the simplest form – no change in absolute growth (annual increment) values and is expressed by the following relationship:

dG/dt=A (1)

where G is the absolute value of real GDP per capita, A is a constant. The solution of this equation is as follows:

G(t)=At+B (2)

where B=G(t0), t0 is the starting time of the studied period. Hence, evolution of real GDP per capita is represented by a straight line if the second factor of growth has no cumulative effect. As discussed below, only some developed countries are characterized by a significant influence of the second factor.
Then, relative growth rate can be expressed by the following relationship:

dG/Gdt=A/G(t) (3)

Relationship (3) indicates that the relative growth rate of per capita GDP is inversely proportional to the attained level of real GDP per capita, i.e. the observed growth rate should asymptotically decay to zero with increasing GDP per capita. On the other hand, the lower the level, the higher the growth rate. This inference might be a potential explanation for the concept of economic

2 convergence. Relative growth rate must be higher in less developed countries, but the observed absolute gap in GDP per capita can not b

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