Traditional convergence tests with Penn World Table 9.01
Disparity in growth rates among countries
1. Disparity
in Growth
Rates
Among
Countries
(-Convergence and
- Convergence)
Abstract
In this paper we develop a coherent framework that integrates
both traditional measures of β-convergence and σ-convergence
within a study of cross-country income dynamics. We provide a
broad empirical picture of convergence. Our framework offers a
simple algebraic decomposition of σ-convergence, β-convergence
and leapfrogging among countries. We illustrate our approach
using data for the period 1995-2014.
3. 3
Introduction
Why are we so rich and they so poor? This is the fundamental question in macroeconomics.
Economists agree that the main way to enrich a country and its people is to create the conditions
which allow it to grow its way out of poverty. We use GDP for the process of estimation of growth.
The idea of convergence in economics (also sometimes known as the catch-up effect) is the
hypothesis that poorer economies' per capita incomes will tend to grow at faster rates than richer
economies. As a result, all economies should eventually converge in terms of per capita income. The
theory is based on the idea that the growth rate will slow as an economy approaches the steady
state level of capital per worker. Developing countries have the potential to grow at a faster rate
than developed countries because diminishing returns (in particular, to capital) are not as strong as
in capital-rich countries. Furthermore, poorer countries can replicate the production methods,
technologies, and institutions of developed countries.
In the 1980s, the field of growth economics has split into endogenous and exogenous models,
differentiated by the assumption regarding the returns to scale of the accumulating factor. The
model classes differ sharply in their implications. The neoclassical growth model with decreasing
returns predicts that productivity growth rates across countries will converge over time. In sharp
contrast, endogenous growth models with constant, or increasing returns typically generate
persistent or even widening growth rate differences. Government policy is largely ineffective in
affecting long- run growth in the exogenous models but potentially highly effective in the newer
endogenous growth models.
There are mainly three forms of long run per capita income convergence: absolute convergence,
whereby convergence occurs independently of the initial conditions facing each economy;
conditional convergence, whereby convergence occurs among economies which have identical
structural characteristics, independently of their initial conditions; and club convergence, whereby
convergence occurs only if the structural characteristics are identical and initial conditions are also
similar.
Convergence is again divided into beta and sigma convergence. ß-convergence implies that over
time, for a given group of economies, growth rates will converge and that initially poor countries
grow faster than rich countries, in other words, there is an inverse relationship between the growth
rate and the initial level of per capita income (or productivity).Sigma convergence refers to the
reduction in the dispersion of income levels over time, i.e. the variance of income across the
economies will decline and is generally measured by the coefficient of variation. ß-convergence
does not necessarily imply sigma convergence primarily because shocks which have a localised or
differential impact may increase income dispersion and thus offset the effects of ß-convergence.
Moreover, income differentials between two economies can increase in absolute terms even if they
decrease in percentage terms.
4. 4
Objective
The two major objectives of this paper are to
Estimate and analyse the sigma convergence for 3 groups ofcountries.
Estimate and analyse the beta convergence for the entire sample ofcountries.
Beta convergence and sigma convergence are the two major aspects that we evaluate while
studying growth and convergence. Being an important and widely analysed topic, there are
different methods available to examine convergence. With the data that we have obtained, from
1995-2010, of three different groups (underdeveloped, developing and developed) with 10
countries each, we feel these two methods would be appropriate for our analysis. As explained in
the introduction, they are two unique methods and are found effective in evaluating convergence.
GDP and growth are very essential for any economy’s smooth functioning and studying them is of
utter importance. Convergence is seen to be a major means by which we can study growth. ”Why do
some countries grow faster than the others?” is a question very often faced by economists. Growth
and convergence studies try to address this query and find solutions to it. By taking a substantial
number of countries in each of three development groups we examine the pattern of growth in each
of these groups. Thereby we intend to test whether the convergence theories hold.
5. 5
Literature Review
Allaoui Zohra (2006) in his study of heterogeneous sample of 12 counties (8 OECD Countries and 4
Mediterranean countries) over the period 1980-2000 concludes that there are marked tendencies
that developing countries did not converge with developed countries in terms of GDP. He reached
at this conclusion by using following tests that are beta absolute convergence tests, beta
conditional tests and sigma convergence tests. Also, Danny T. Quah (1995) reached the
approximately same conclusion. According to him the 2% rate of convergence could arise that has
nothing to do with the dynamics of economic growth. Sometimes time series modeling , panel data
analysis could be misleading for understanding convergence. The data reveals that immobility
across countries is the reason behind divergence as a result the poor getting poorer, and the rich
richer, with the middle class vanishing. Thus the absence of imperfect factor mobility is a necessary
condition for the convergence theory to hold.
Also the result for convergence varies between the groups and within the groups may be within the
group we get the convergence while in between the groups we get divergence or vice versa. We
have a supporting paper also for the same given by David Mayer-Foulkes (2002). According to him
there is divergence globally in the growth rate across group of countries but some successive
groups converge while mostly diverge. Income inequality between these groups of countries has
increased while income inequality within the groups has remained almost unchanged. He came to
this conclusion after exercising on the data of non-mainly-petroleum-exporting countries during
the period 1960-1997 which was divided into five clusters of countries. The five clusters
correspond to advanced countries, especially fast growing countries, and three tiers of less
developed countries. These countries exhibit convergence within the groups but beta and sigma
income divergence between groups. The convergence found within groups is consistent with the
relative convergence found in the literature. Andrea Bassanini, Stefano Scarpetta, Philip Hemmings
(2001) too claim that convergence speeds to vary across countries. Also there can convergence in
some areas and not in general. Yvonne Sperlich, Stefan Sperlich( 2012) claimed that there may be
sigma convergence in some areas, but the income dispersion is not decreasing in general. So it can
be the case that there is convergence in some particular area but not as a whole. He checked this
between member countries of South-South agreements. In general notion also, we expect beta
convergence because the developing countries are growing at faster rates than richer countries.
The biggest reason behind faster growth of developing countries is that they can replicate the
technology of the developed ones. They do not need to spend much in research and development.
The Public welfare policies in developing countries have a Rawlsian perspective; they seek to uplift
the poor, the poorest of the poor inparticular.
For the support of convergence we found out the empirical evidence by Bernhard Herz (2003). He
took a sample of 31 Central and Eastern European regions over the period 1990-2002 for the
analysis of regional growth and convergence and he found no evidence for sigma-convergence but
found evidence for conditional beta convergence at country level. Robert J. Barro too claimed the
same results that there is lack of sigma convergence with the presence of beta convergence. He took
data from 34 countries with GDP data starting between1870 and 1896. He analyzed that for 34
countries-including China and India-observed since 1896, the dispersion of per capita GDP declines
since the late 1970s, especially when the country data are weighted by population.
The interesting question raised by Dani Rodrik (2011) is whether this gap in performance between
the developed and developing worlds can continue and whether developing nationscan sustain the
rapid growth they have experienced of late. The key to growth is getting the economy’s resources to
6. 6
flow into those “convergence industries”. Sustained convergence is likely to remain restricted to a
relatively small number of countries. The rate at which lagging (Developing) economies catch up is
determined by their abilities to absorb ideas and knowledge from the technology frontier.
According to his study there is unconditional convergence in manufacturing industries.
In his paper Holger C. Wolf(1994) try to show that a dependence between the development level,
labor force participation rates and labor quality generates a coefficient bias towards rejection of the
convergence hypothesis. They re-estimate the standard convergence equation using labor
productivity both for total output and for sectoral output. While the results suggest convergence for
aggregate output, agriculture and services, no significant convergence trend is found for
manufactures, suggesting that endogenous growth models might play some role in that sector.
First, studies examining economies on different levels of economic development tend to reject
convergence more frequently if no allowance for different steady states is made. Studies examining
economies on similar development levels tend to find in favor of convergence regardless of whether
steady state controls are included.Second, overall studies using per capita income tend to reject
convergence relative to studies using labor productivity. However, in studies examining economies
at similar development levels the choice of dependent variable appears to be of little importance.
They showed in this paper that at least some of the ambiguities can be resolved by taking into
account the measurement bias introduced by the frequent but far from innocuous substitution of
income per capita for the theoretically correct variable, labor productivity. Re-estimation of the
convergence equations using economy-wide labor productivity yielded results generally supportive
of convergence. Estimation of sectoral convergence equations, however, suggested that the global
convergence may predominantly reflect strong convergence in the primary and tertiary sector. In
contrast, manufacturing, arguably the source of most of the externalities underlying the
endogenous growth literature, showed little tendency towardsconvergence.
20th century saw a sudden surge in globalization and it was a great breakthrough in the field of
economics but the world has not converged likewise. In their paper Michael D. Bordoand Alan M.
Taylor(2003) ,seeks to implore into this issue. They have analysed the economic growth of counries
with respect to their membership to the convergence club. . Lucas (2000) showed that such a
framework with the assumption of a once-and-for-all switch for an economy’s joining the
convergence club could account in a stylized fashion for much of the global experience of the past
two centuries. The paper basically analyses these insights.
First, the OECD economies—as they were defined in the 1980s—have effectively
completed the process of convergence. Second, there is the East Asian miracle, which has seen the
fastest-growing economies anywhere, any time. Third, successful post-1980 development in China
and India has put countries that together amount for two-fifths of the world’s population “solidly on
the escalator to modernity,” in Lawrence Summers’s (1994) phrase. However, these episodes of
successful economic growth and convergence have been counterbalanced by many economies’ loss
of their membership in the world’s convergence club.
A summary of their empirical findings runs as follows:
7. 7
• The failure of the world’s poorest countries to catch up to the income levels of the richest
countries over the past four decades is attributable to the poverty-trap conditions of subsistence
income, low saving and investment, low levels of education, and high fertility.
• Openness to the world economy does appear to provide a significant boost to growth, but it does
not necessarily promote convergence. A large number of the poorer countries have opened their
economies since 1980. But it is precisely during this period that the benefits of openness appear to
have diminished.
In another important paper, Philip Epstein, Peter Howlett and Max-Stephan Schulze(1999) have
examined 12 western European economies for the period 1870 to 1992 and an expanded group of
24 European economies for the period 1955 to 1992. In each case, the period is divided into sub-
periods.
The purpose of this exploratory paper is to measure the extent to which a new approach based on
income distribution dynamics might be of use to economic historians interested in long-run income
and productivity convergence. In this first application of Quah’s technique (Quah is known for his
research on estimation techniques for disentangling the effects of different disturbances on
economies) in historical research, his method has been used to examine the evidence on
convergence on the empirical basis of Maddison’s widely used per capita income data.
These are some findings:
They found that there was significant sigma convergence in the 12 countries during the post war
period. The only other economy to experience an upward move of three income states in any of the
three sub-periods was Austria between 1955 and 1992.The period of greatest convergence, 1955-
1992, was also the period of greatest mobility. The findings on distribution shape dynamics, point
to complex patterns of stratification, persistence and polarization that traditional growth
regressions do not uncover. In short, this approach to the systematic analysis of income distribution
across economies has a lot to offer to thehistorian.
8. 8
Methodology
The term ‘convergence’ can be interpreted in different ways. Therefore, multiple methods have to
be applied to measure processes of convergence or divergence in a comprehensive way. In this
paper we will limit our test of convergence till and convergence.
In line with our objective, we test for convergence and divergence among nations. We initiate by
taking a sample of 30 countries. We then clubbed the countries in 3 groups on the basis of their
income levels (as per World Bank). Our segregation is as follows i.e. high income countries
(developed countries), upper middle income countries (developing countries) and lower income
countries (least developed countries) We conducted our analysis from the year 1995 to 2014 using
GDP data at market prices (constant US$).
Section-1 of the paper focuses on finding the growth rate of each and every country over the period
of analysis. The secular GDP growth rate was computed by fitting a linear semi-log trend to the data
for each country in all the 3 groups. Model is as follows:
ln yt = a+bt
Here the beta coefficient gives us the compound growth rate of countries. We then analyze the
trend in growth rates over the years and noting their behavioralpatterns.
Section 2: Deals with calculating the - Convergence. Convergence is captured by coefficient of
variation and then regressing it on time period used in the study.
The coefficient of variation is a measure of spread that describes the amount of variability relative
to the mean. Because the coefficient of variation is unit less, you can use it instead of the standard
deviation to compare the spread of data sets that have different units or different means.
The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean μ
CV = (Standard Deviation (σ) / Mean (μ))*100
It focuses attention on the dispersion of outputs over a cross-section of economies at each point of
time for each group. Fitting a linear trend model as follows:
CVz = a+ bt
where z represents each subgroup.
Section 3: Deals with the -Convergence. Denoting the GDP at t by Yt involves first estimating the
relationship ln Yt = a+bt for each country and then regressing the estimated value of b on GDP of
initial year (Y95 ) .The phenomenon of -convergence occurs if the latter regression line yields a
negative coefficient. In other words, this involves regressing income growth rates on initial income
to test whether poor countries grow faster than rich countries. The regression equation is given as
b = a+b1Y95
where b represents the growth rate of the countries. We will be checking for -Convergence for the
for the entire sample.
9. 9
Results
The sole goal of our study is to find out whether the transition economies involved have converged
or diverged over time. We do not discuss the determinants of this process- e.g. We do not attempt
to explain why some countries have developed typically compared with the majority of the group
concerned. We do not address the issue of conditional convergence either as this would call for a
tentative determination of the most important factors of economicgrowth
Section 1: Behavioral pattern of growth rates
Growth rate is an important parameter to capture convergence. Examining the growth performance
of the countries over different time periods The estimated growth rates of the 3 groups are as
follows-
Developing
countries
Growth
Rates
Least Developed
Countries
Growth
Rates
Developed
Countries
Growth
Rates
India 10.19% Mozambique 8.79% United Kingdom 4.60%
China 14.74% Nigeria 17.29% Germany 3.44%
Bangladesh 7.31% Congo, Dem. Rep. 9.69% France 4.42%
Brazil 7.93% Sierra Leone 10.40% Greece 4.78%
Bhutan 10.96% Ghana 12.63% Italy 4.16%
Sri lanka 10.35% Tanzania 11.28% Spain 6.08%
Thailand 6.73% Burundi 6.93% Argentina 4.96%
Mauritius 6.74% Nepal 9.05% Belgium 4.79%
Mexico 6.31% Uganda 9.14% Sweden 5.05%
Fiji 5.04% Equatorial Guinea 26.45% New Zealand 7.15%
All the regression gives significant results for growth rate i.e. over the years GDP has increased for
all the countries. The average growth rate of developed nations is around 5% .For developing
countries the average growth rate is around 8.5% and the drivers for the same are China, India and
Bhutan growing at the rate of more than 10%. The highest average growth rate of 12.5% comes
from the least developed countries which is not at all surprising because poor nations have more
scope for development and advancement. The trend can be seen that least developed countries are
growing by the highest rate followed by the developing countries and developed countries
respectively. Developing countries have the potential to grow at a faster rate than developed
countries because diminishing returns (in particular, to capital) are not as strong as in capital-rich
countries. Furthermore, poorer countries can replicate the production methods, technologies,
and institutions of developedcountries.
10. 10
Though the differences in the average growth rate of 3 groups shows some sort of convergence
because least developed nations are growing at higher rate and developed countries at a lower rate
so they will converge after some time. It is possible to observe poor countries growing faster than
rich countries and yet for incomes to diverge. In the growth context this captures the notion of
leapfrogging. Analyzing convergence only on the basis of growth rate does not give us a clear
picture so we further need to study the deviations of the countries across the time period for
checking -Convergence
Section 2: σ -convergence
The term σ-convergence is defined as follows: “a group of economies are converging, in the sense of
σ, if the dispersion of their GDP levels tends to decrease over time” .The concept of Sigma-
convergence is more revealing of the reality as it directly describes the distribution of income
across economies without relying on the estimation of a particularmodel.
The most frequently used summary measures of Sigma convergence are the standard deviation or
the coefficient of variation of GDP. The economies are said to satisfy the condition of σ-convergence
if this dispersion decreases over time i.e. the coefficient of time is negative.
Estimating the sigma convergence, we report the following results-
Years CV Developed CV Developing CV Least Developed
1995 99.53375916 123.9752297 135.7911435
1996 95.67793497 124.287624 144.105883
1997 92.66967263 125.9337838 139.2481587
1998 92.56811153 128.6862501 125.4574352
1999 92.05269413 127.2924907 135.7763545
2000 90.56680217 128.9842415 139.2876173
2001 90.58882327 134.5117307 146.5969965
2002 93.76340187 138.4221798 163.7470199
2003 91.80485421 140.0790737 167.4376014
2004 90.37718666 141.7509142 174.2904422
2005 89.09800278 141.2847914 176.6913728
2006 88.2012681 143.5336753 181.1321439
2007 87.3961068 147.6789288 179.292507
2008 86.17452091 158.2666097 180.7619846
2009 86.14651058 166.8645235 167.0816417
2010 84.7469153 164.001368 216.6922736
2011 84.78269552 170.5943643 213.61185
2012 84.49095766 179.9144885 214.850052
2013 85.25207211 186.115686 216.5079357
2014 87.30159827 190.0191695 223.5467954
11. 11
VARIABLES CV
Developed
countries
CV
Developing
countries
CV
Least developed
countries
Time -0.623*** 3.479*** 5.022***
(0.0673) (0.232) (0.423)
Constant 96.20*** 111.6*** 119.4***
(0.806) (2.779) (5.068)
Observations 20 20 20
R-squared 0.826 0.926 0.887
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
The estimated trend is observed to be negative for developed countries and positive for developing,
least developed countries. Thus, there is convergence in developed countries and no convergence is
seen in developing countries as well as least developed countries. Further, the values of R2 were
high in all cases. Interestingly enough, the time coefficient turns out to be the greatest for the least
developed countries because the range of growth rate of least developed countries is the highest.
Intuitively, this is either because economies can converge towards one another but random shocks
push them apart.
The theory also assumes that technology is freely traded and available to developing countries that
are attempting to catch-up. Capital that is expensive or unavailable to these economies can also
prevent catch-up growth from occurring, especially given that capital is scarce in these countries.
This often traps countries in a low-efficiency cycle whereby the most efficient technology is too
expensive to be acquired.
Sigma-convergence simply refers to a reduction of disparities among regions in time whereas, Beta-
convergence focuses on detecting possible catching-up processes. The two concepts are of course
closely related. Further, heading towards -Convergence.
Section 3:-Convergence
β- Convergence is used to capture situations where “poor economies tend to grow faster than rich
ones.”
The traditional test for conditional β-convergence involves regressing growth on initial income,
holding constant a number of additional variables that determine steady state income.
12. 12
However, the β coefficient does not measure the actual pace of income level equalization; rather, it
shows the speed of convergence towards the hypothetical steady state.
The results show that the world is converging because the coefficient of the base year’s (Y95) output
is negative (-3.02e-14, refer annexure part B). The coefficient though is very small so the countries
although converge but they are converging at a very slow rate. The countries with low level of GDP
at base year are growing more rapidly than the rest of the countries. This can be represented
diagrammatically in the following way-
-Convergence, Leapfrogging
-Convergence, no Leapfrogging
Here we are just concerned about convergence. Beta convergence is in line with neo-classical Solow
model .The traditional Solow growth model (Solow (1956)) predicts that countries that are furthest
away from their steady states will grow more quickly than countries closer to their steady state. For
countries with the same steady state this implies that incomes will converge along the transition path.
Overtime Countries with low level of
GDP growth in initial year tends to
leapfrog countries starting with
higher level of GDP
Overtime Countries with low level of
GDP growth in initial year tends to
converge but does not leapfrog
countries starting at higher level of
GDP.
13. 13
Conclusion
The ultimate purpose of our work lies in explanation, it was found that establishing the divergence
or convergence among the countries is in itself an interesting and challenging exercise as well as
one worth reporting.
We establish sigma divergence for 2 groups i.e. developing countries, least developed countries and
sigma convergence among developed countries while beta- convergence is seen across all countries.
Convergence is not occurring everywhere because of the closed economic policy of some
developing countries, which could be solved through free trade and openness. The fact that a
country is poor does not guarantee that catch-up growth will be achieved there is a need for 'Social
Capabilities' to benefit from catch-up growth. These include an ability to absorb new technology,
attract capital and participate in global markets. These prerequisites must be in place in an
economy before catch-up growth can occur, and explain why there is still divergence in the world
today.
This process of catch-up continues as long as the following nations have something to learn from
the leading nations, and will only cease when the knowledge discrepancy between the leading and
following nations becomes very small and eventuallyexhausted.
The present study is, needless to say, limited in scope because a lot more can be done.
20. 20
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