Conditional Versus Absolute Convergence 141m28

Conditional versus Absolute convergence The discussion of convergence cannot take place without an outline of the basic theory. In the economic literature there are two distinctly defined types of convergence: β-convergence (conditional) and σ-convergence (absolute). Conditional convergence is a necessary but not a sufficient condition for absolute convergence. The hypothesis of absolute convergence states that in the long run, GDP per worker (or per capita) converges to the same growth path in all countries. This implies that all countries converge to the same level of income per worker. Furthermore, this would mean that all countries converge to the same level of capital-labor ratio, output per capita and consumption (k*, y*, c*) with an equal growth rate g. Figure 1 presents absolute convergence as described by the Solow model. The diagram depicts a situation where kp and kr represent the initial capital-labor ratios of the poor and the rich country respectively (depreciation is taken to be zero in the diagram, one can take that to be positive too). The model assumes that all other factors are equal. Thus the Solow model predicts that both countries would tend to converge to the same level of k*. The figure also shows that the growth of the poorer country will have to exceed that of the rich country, if the convergence is to take place. This would also mean that the marginal product of capital in the poor country would be higher than that of a rich one. y

Y L

yr

y=f(k)

y* ir=nk yp

i=sf(k)

i*

n 0

k  kp

k*

kr

K L

Figure 1 Absolute convergence, where kp and krare the initial capital-labor ratios of the poor and the rich country respectively;k* is the steady state.

However, there is enough evidence to say that the absolute convergence hypothesis does not find in the data. Countries often differ based on their basic structural characteristics and their levels of saving and investment. This would mean that countries with, for example, higher savings rates have higher level of GDP per worker. Furthermore, the level of GDP per worker cannot converge to the same level for all the countries due to their differences in the structural characteristics and the initial conditions. Nevertheless, it seems that convergence can still take place. The more likely scenario is that convergence will occur, conditional on a number of factors. Thus, the theory of conditional convergence states that a country’s income per worker (or per capita) converges to a country specific long-run growth path, which is given by the basic structural characteristics of the country. Thus, the lower the countries original level of GDP per worker, the higher is the expected subsequent growth. This implies that the countries that start below their long run growth path are likely to grow at a faster pace. y

Y L

yr*

y=f(k)

yp*

ir=nk

cr* *

ir=srf(k)

ir* ip=spf(k)

i p*

n 0

k Kp*

Kr*

K L

Figure 2 Conditional convergence,where kp* and kr*are the steady states of the poor and the rich country respectively. Figure 2 is a graphical representation of the conditional convergence hypothesis as described in the Solow model. The hypothesis of conditional convergence is similar to the absolute convergence hypothesis in that it states that countries converge to the same point. However, there is one important difference between the two: the latter requires the countries to be similar.

Therefore, only after controlling for structural differences we will be able to observe the negative relationship between the initial level of GDP per worker and subsequent growth. Economic literature shows evidence of both the presence and the absence of income convergence. This is often attributed to the fact that in the early studies did not have enough data to accurately measure the development process of a country. However, some recent works have identified a clear trend. They claim that all countries, rich and poor, over the period of time seem to converge towards each other at a constant rate of about 2 % per annum (Quah, 1995). Furthermore, the literature also suggests that countries need to have relatively homogenous political situations as well as similar legal systems and technological adoption methods in order to show evidence of convergence. This suggests that it might be desirable to arrange countries into regions and compare them among each other within these regions (Barro, 1994). Doing a simple cross country analysis would be problematic as all countries have very different initial positions.