Module or unconditional (absolute convergence). However, in this paper

 

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Introduction

The
issue of convergence has been one topic of interest to many economists over the
years. Many have come up with theoretical and empirical analysis both in favour
and against this controversial issue. Convergence is when the per capita income
of poorer economies tends to grow faster than richer economies. It is sometimes
known as the catch-up effect. Convergence in growth theory can be either
conditional or unconditional (absolute convergence). However, in this paper our
focus is on absolute convergence. The main objective of this paper is to
discuss the evidence in favour and against the hypothesis of absolute
convergence based on the literatures of various economists. That is whether the
hypothesis of absolute convergence holds or not.

Absolute
convergence allows us to compare economic growth across countries to determine
if various countries are catching up in terms of their growth rates and level
of income per capita. Thus, absolute convergence implies that countries
converge to a common steady state irrespective of their initial capital stock
or GDP. It again implies that countries with a lower level of initial capital
stock tends to grow faster than those with a higher level.

Many
empirical studies on cross-country regressions have strongly led to the
rejection of the absolute convergence hypothesis. This is because countries
across the world differ in terms of their basic structural characteristics and
initial conditions and hence will usually not have the same level of capital-labour ratio, output per
capita and consumption (k*, y*, c*)
with an equal growth rate of technology (g) in the long run. Even in cases where
countries begin at the same initial level, it is still possible for them to
diverge with time. For instance, Botswana and Nigeria initially had the same
level of GDP per capita in the early 1960s but later, Botswana grew relatively
faster than Nigeria, leading to a huge difference in their level of income per
capita today. From the data bank of the World Bank, the GDP per capita of
Botswana in 2016 is greater than that of Nigeria by an amount of about
4,700(current US $).

Other
studies by economists such as Kaitila (2004) tends to provide evidence that
supports the hypothesis of absolute convergence. Most of such evidence of
convergence holds for countries within the same region or countries with
similar structural characteristics. Thus, I tend to agree with Barro (1993) on
his statement that, “If different economies-say, countries or regions of
countries have the same underlying technology, preferences, and government
policies, then the standard growth model predicts an absolute form of
convergence”.

 

Absolute
Convergence

Absolute convergence as
mentioned earlier, is when different economies obtain the same level of income
per capita in their steady states with the same rate of technological progress,
despite their initial conditions.

The
graph below can be used to explain the hypothesis of absolute convergence. The graph below can be used to explain the hypothesis of
absolute convergence.

Figure 1: Absolute convergence

Source: The
Convergence Hypotheses, (http://cruel.org/econthought/essays/growth/neoclass/solowconv.html)

 

Let’s assume that k1 represents the capital per labour of
poor countries and k2 represents the capital per labour of
rich countries. From the graph, both groups of countries converge to a common
steady state irrespective of where they start from. Based on the explanation of
convergence from the Solow growth model, when a country (in this case poor)
starts at the point where capital per worker is equal to k1, it will gradually converge to k*. This is because at k1, actual investment is greater than
breakeven investment and hence, k increases gradually till it reaches
a level of
k*, where actual investment is equal to
breakeven investment. Similarly, if a country (in this case rich) is initially
at the point where its capital per labour is at k2, then break even investment is
greater than actual investment. This means that there are not enough resources
to sustain capital per labour at its high level. As a result, capital per
labour will gradually fall to k* where actual investment is equal to
breakeven investment. Thus, k* is the steady state level of capital
per worker for both rich and poor countries. This could be possible given that
poor countries grow faster than rich countries and eventually catch up with
them.

The implication of poor countries
growing faster than the rich one can be explained by the law of diminishing
marginal return of capital. At a lower level of capital, the marginal product
of capital is high and when the level of capital is high, its marginal product
is low. Since the capital stock of poor countries is quite low, the marginal
product of capital is high, causing poor countries to grow relatively faster
than the rich countries whose level of capital is high and marginal product of
capital is low.

Evidence
in Favour and Against the Absolute Convergence Hypothesis

According to the Solow model,
population growth and accumulation of human and physical capital are
determinants of the steady state of a country and as such different countries
reach different steady states. However, empirical study by Mankiw, Romer, and
Weil (1992) showed that countries converge to a common income per capita once
the population growth and accumulation of human and physical capital are
controlled.

One
of the studies in support of the absolute convergence hypothesis which I will
like to consider is a study done by Mathur (2005). In this paper, he tested for
the absolute convergence hypothesis using sixteen European Union countries(
Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy,
Luxembourg, Netherlands, Portugal, Spain, Sweden, Norway and the United
Kingdom), five South Asian countries(Bangladesh, India, Nepal, Pakistan and Sri
Lanka), eight East Asian countries(China, Hong Kong, Japan, Malaysia,
Singapore, Thailand, Philippines, Indonesia) and fifteen countries(Azerbaijan,
Belarus, Estonia, Latvia, Lithuania, Moldova, Russia, Tajikistan, Turkmenistan,
Ukraine, Uzbekistan, Kazakistan, Krygistan, Armenia and Georgia) from the
Commonwealth of Independent States(CIS) for the periods 1961-2001, 1970-2001,
1980-2001 and 1990-2001. The test was to determine whether there is evidence of
absolute convergence among countries within each region and among all the 44
countries together. Using the per capita average annual growth rate and initial level of per
capita GDP of these countries, he estimated the equation;

Yit,t+T  = a +
blogyit + eit, where

Yit,t+T = country i’s average of yearly annual growth rates of GDP time t and t+T

log yit  =
the natural log of country i’s GDP per capita at time t

After running a regression, a
negative value was obtained for b, the coefficient of log yit, for
countries in the European Union for each period tested. This value was
statistically significant as well. Therefore, there is generally evidence of
absolute convergence for countries in the European Union. The evidence of
absolute convergence among these countries could be accounted for by the fact
that all these countries are industrialized economies. As such, they have
similar structural characteristics in terms of technological level, population
growth rate and investment rates. For instance, from the graph of annual
population growth rate of the sixteen European Union countries below, these
annual rates are relatively equal for most of the countries with the curves
following a similar trend. Given that population growth is one of the
demographic trends that influence economic growth (Kelly, Schmidt, 2000), it is possible that these countries’ convergence
was partly due to the similarity in their population growth rates. Also, the
population growth rates for these countries are generally low which has a
positive effect on economic growth.

Figure 2: A graph of the annual population growth
rates of the sixteen European Union countries between 1961 to 2001.

Source: Self, using data from World
Development Indicators, World Bank

The regression result for the
European Union and East Asian countries together yielded a negative value of
-0.44 for b which is statistically significant. Therefore, the absolute
convergence hypothesis was not rejected. The evidence of absolute convergence
means that these East Asian countries who were poor some decades ago are
gradually catching up with the industrialized countries. East Asia happens to
be the only region among developing economies catching up with industrialized
countries with countries such as China, Malaysia, Singapore, Thailand,
Philippines and Indonesia recording a high average of 4 percent growth of per
capita GDP between 1960 and 1994(Collins and Bosworth, 1996). During this same
period, the industrialized economies recorded an average GDP per capita of
about 2.6 percent. With the East Asian countries growing at a higher rate than
the industrialized countries, there has been a catching up of the East Asian
countries with the European Union countries. Hong Kong and Singapore are now
part of the 39 countries classified as advanced economies by the International
Monetary Fund. This could explain why the absolute convergence hypothesis holds
for the European Union region and the East Asia region in the above test. The
cause of the tremendous rise in the growth of these East Asian countries is one
question most economies have tried to answer. According to Collins and Bosworth
(1996), increases in physical capital per worker, education per worker and
total factor productivity were the major contributions to this tremendous
growth. Despite the evidence of East Asian countries catching up with the
industrialized economies, the same cannot be said of other developing
countries. Most developing countries seem to be getting poorer if not growing
slower and hence diverging from the rich countries rather than converging. This
is due to factors such as low level of technology, low stock of capital, high
population growth rate with high dependency ratio, low level of foreign direct
investment and others in the developing and undeveloped countries. The rapid
growth in countries such as Hong Kong and Singapore after 1960 should serve as
a source of hope to poor countries today, that it is possible for them to
become rich one day.

The regression result for countries
in all the regions together rejects the absolute convergence hypothesis. This
is because these countries together have different structural characteristics
which determine their steady states. Factors such as demographic trends,
foreign direct investments, political situations, natural resources, trade and
others which affects economic growth, are virtually different for countries in
the world. All countries converging to a common income per capita with the same
growth rate is therefore very difficult to attain, if not impossible.

Timakova
(2011) is another economist who undertook a research on both absolute and
conditional convergence using the Solow model. He extended the study done by
Mankiw, Romer and Weil (1992) by using 87 of the countries they studied, for
the periods 1960 to 2005. He used the following equation in an empirical
analysis, to test for the presence of absolute convergence among different
classifications of countries; Non-oil, Intermediate, Organisation for Economic Co-operation and Development(OECD), Low income and High income

 

Where, ln (

         ? = the rate or speed
of convergence

         SH = the fraction invested
into human capital, H

         n = population growth rate

         g = technological progress

        

With the
data on the 87 countries, he obtained the following results from his regression
of the growth rate of GDP per worker on the initial level of GDP.

Unconditional (absolute) convergence

Regression

Full sample

Non-oil

Intermediate

OECD

Low income

High income

Number of observations

86

78

62

22

43

43

Constant

-0.012
(0.008)

-0.376
(0.376)

-0.404
(0.484)

0.366
(0.805)

-0.674
(0.417)

-0.328
(0.630)

Ln(GDP1960)

0.003***
(0.001)

0.136***
(0.045)

0.133**
(0.057)

0.043
(0.096)

0.189***
(0.049)

0.114
(0.075)

Adj. R-squared

0.083

0.062

0.041

-0.041

0.157

0.021

S.E.E.

0.015

0.644

0.740

0.731

0.571

0.724

Ln(GDP1960) is the log of
the initial level of income per worker. Furthermore, *=10% significance; **=5%
significance; ***=1% significance. Standard errors are in parenthesis below the
estimated coefficients.

Figure 3: A table
of the result obtained from regressing the growth rate of GDP per worker against
the initial level of GDP  

Source: Timakova, (2011), “Conditional Convergence and
the Solow Model: an Empirical Study”, Pg. 39

 

From the table, it can be observed
that the coefficient of the log of GDP for 1960 are positive but close to zero for
all the country classifications. These values are all statistically
significant, except those for OECD and high-income countries.  Also, the adjusted R2 values are
very small for most of the regressions. Thus, the hypothesis of absolute
convergence is rejected for this study, which implies that there is not enough
evidence to show that poor countries grow faster than the rich countries.

However, considering the graphs of
GDP per capita growth rates of low income and high-income countries from his
paper, the following observations can be made. The growth rate of GDP per
worker for low income countries is increasing overtime between 1960 and 2010,
showing an upward sloping trend line. The slope of the trend line is steep,
indicating that the increase in the growth rate overtime is quite slow. On the
other hand, the growth rate of GDP per worker for high income countries is
decreasing overtime between these years. 
The trend line is steep and downward sloping. Similarly, this gradual
decrease in the growth rate of GDP per worker is slow.

Figure
4: Growth
rate dynamics in time, low income countries

Data source: World Bank, 2010

Source: Timakova, (2011), “Conditional Convergence and
the Solow Model: an Empirical Study”, Pg. 36, Fig. 6.1

Figure 5: Dynamics of economic growth in time for high income economies

Data source: World Bank, 2010

Source: Timakova,
(2011), “Conditional Convergence and the Solow Model: an Empirical Study”, Pg.
37, Fig. 6.2

The gradual movement of the growth
rates of GDP per capita for low income and high-income countries in opposite
direction implies that low-income countries are growing faster than the high-income
countries. This shows some evidence of absolute convergence. Based on the
explanation of convergence by Solow in the neoclassical growth model, could it
be that the gradual decrease in the growth rate of GDP per capita for high
income countries could be due to the possibility that these countries are above
their steady states?

Conclusion

As
discussed in the paper, there have been studies both in favour and against the
hypothesis of absolute convergence across countries. Rejecting or failing to
reject this hypothesis was usually dependent on the factors that influence
economic growth and convergence for the countries under study. Different
economists have come out with many different factors that influence economic
growth and convergence. For instance, the
diffusion of technology, the migration of persons, capital mobility and the
savings rate as mentioned by Barro (1993). The difference in these factors
across countries in the world makes it seem quite impossible to achieve
absolute convergence for the whole world. However, countries within the same
region or income level have shown evidence of absolute convergence due to the
similarities in their structural characteristics and initial conditions. This
is often true for the high-income countries with little evidence on convergence
among low-income countries (Noorbakhsk, 2006). There has also been evidence in
favour of absolute convergence among countries within different regions, such
as the convergence between the European Union countries and East Asian
countries discussed in this paper. If the hypothesis of absolute convergence
holds, then poverty among poor countries should be eradicated with time. Thus,
there will be no need for policies such as foreign aid to low income countries
(Timakova, 2011).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Bibliography

1.       Barro,
R. J., 1993. “Economic Growth and Convergence”, An International Centre for Economic Growth Publication. ICS
Press, San Francisco California 1993.

2.      Kaitila,
V., 2004. “Convergence of Real GDP per capita in the EU15: How do the accession
countries fit in?”, European Network of Economic Policy Research Institutes,
25.

3.       Kelley,
A., Schmidt, R., 1995. “Aggregate Population and Economic Growth Correlations:
The Role of Components of Demographic Change”, Demography, Vol. 32, pg. 543-555.

4.       Mankiw,
N.G., Romer, D., Weil, D.N., 1992. “A Contribution to the Empirics of Economic
Growth”, The Quarterly Journal of
Economics, May 1992, pg. 421-429.

5.      Mathur,
S. K., 2005. “Absolute Convergence, Its Speed and Economic Growth for Selected
Countries for 1961-2001”, Journal of the Korean Economy Vol. 6, No. 2 (Fall
2005): pg. 245-273.

6.      Collins,
M. S., Bosworth, B. P., 1996. “Economic Growth in East Asia: Accumulation
versus Assimilation”, pg. 135.

7.      Noorbakhsh,
F., 2006. “International Convergence and Inequality of Human Development:
1975–2001″, Working Papers 2006, pg. 7, Glasgow, Department of
Economics/University of Glasgow.

8.  Romer, D. ed., (2012). The Solow Growth Model. In: Advanced Macroeconomics, 4th edition. New York: McGraw-Hill, pg. 7-37.

 

9.       Timakova,
M. V., 2011. ” Conditional Convergence and the Solow Model : An Empirical
study ” , Rotterdam School of Economics, Department of Economics, Erasmus University.

10.  World
Bank 2018. “World Development Indicators”, World Bank DataBank, 2018.