Download Global Income Distribution and Convergence 1800-2000

Global Income Distribution and Convergence 1800-2000
Peter Földvari (Warwick University) and Jan Luiten van Zanden (IISH/Utrecht
University)
1. Introduction
Recent research by a.o. Bourguignon and Morrison (2001) has shown that the long run
trend in global inequality in the past 200 years is to a large extent dominated by intercountry differences in GDP per capita. In particular the strong increase in global
inequality during the 19th and the first half of the 20th century is completely driven by
the growing gap between the industrializing rich countries and the non-industrializing
poor nations. In the second half of the 20th century this trend seems to have come to a
halt, and the rise of global inequality appears to have slowed down markedly (and
within country inequality is probably becoming more important). Again, the slowing
down is driven by inter-country differences, in particular the increasingly strong
performance of Asian economies (such as the Asian tigers and more recently India and
China).
Explaining the development of inter-country differences in economic growth is
therefore of fundamental importance for understanding the long term evolution of
global inequality. The literature suggests two different approaches to this. One if the
(neo)Marxian/dependencia view that inequality between (groups of ) countries is a
structural feature of global capitalism; Wallerstein (1974), for example, traces the
differentiation between the core and the periphery of the world economy back to the
16th century, and in essence argues that core and periphery are parts of the same system.
This interpretation, which was quite popular in the 1970s, sees the growing disparities
within the world economy during the 19th and first half of the 20th century as another
expression of global capitalism, and therefore predicts that inequality will not decline
strongly in the future.
The alternative approach that prevails in much of the literature about this topic is
that these processes of divergence and convergence are driven by the gradual diffusion
of the Industrial Revolution over the globe. Growing global inequality during the 18001950 period is dominated by the fact that the number of countries participating in
‘modern economic growth’ is only growing slowly. The Industria l Revolution began in
Great Britain in the late 18th century, spread to North America and Western Europe
during the first half of the 19th century, and since spread further to Eastern and Southern
Europe, to Japan and the Asian Tigers, and most recently, to large parts of mainland
Asia (see Dowrick and De Long 2003). This pattern of diffusion obviously has a strong
spatial element – industrialization seems to move from country to country – but was
also based on the ability of countries to develop the right institutions for
industrialization (as the success story of Japan illustrates).
In this paper we try to elaborate and test this diffusionist interpretation of the
development of global inequality. Our starting point is a paper by Robert Lucas (2000),
in which he presents a simplified model of this diffusion process, which he uses to
simulate the development of global inequality. He firstly assumes that the leading
economy (Great Britain) is growing at a constant rate of economic growth (of 2 per cent
per capita). The other countries that are member of the convergence club, have a growth
rate that is equal to this 2 percent plus a catch up factor that is proportional to the
percentage income gap between itself and the leader. This will cause all members of the
convergence club to eventually converge to the level of the leader. The final element of
the model is linked to the probability that country X will enter the convergence club at
some point in time. Lucas ignored the spatial and institutional dimensions of this
process and simply assumed that this probability was increasing slowly in time (from .1
to 3 percent), which generated a model that was more or less able to simulate the
development of world inequality (this increase from .1 to 3 percent was in tur n linked to
the general increase in income levels following Tamura (1996)).
This simplified model is the starting point of our paper. We would like to
establish if such a model of gradually diffusion of the process of industrialization is able
to explain the long term development of world inequality (and global economic growth)
in a more satisfactory way that the alternative view, which postulates the stability world
inequality. Our main focus is on empirically testing the Lucas model, using the
Maddison (2001) dataset about the growth of the world economy between 1820 and
2001. We concentrate on three predictions of the model:
the share of countries or the share of the world population that is
member of the convergence club (i.e. as rich as the leading economy or
growing more rapidly that it) is increasing in the long term, and these
shares shows a logistic curve approaching 100% in the long run;
global inequality (between countries) increases until more than 50% of
countries/world population is member of the convergence club;
afterwards, inter-country global inequality will begin to decline (see the
appendix for a proof of this);
the growth rate of world GDP also will increase during the first phase
of the diffusion process (because the leader is growing at a constant
rate of 2% per annum, but increasing numbers of countries will join the
convergence club and initially grow even faster than 2%), until again a
certain point is reached – when the majority of countries has converged
– that the growth of world GDP will start to decline again; in the
extremely long run, when all countries have converged, the growth rate
of GDP per capita of the world population will be 2% per annum, the
same as that of the leading country.
In the simulation by Lucas (2000) the turning point in both world inequality and the
growth rate of world GDP is reached between 1950 and 2000, when indeed more than
50% of the world population is member of the convergence club.
An important assumptions of the Lucas model is that once countries have joined the
convergence club they will continue to converge; there is no exit from the convergence
club, whereas the neo-marxian interpretation will probably assume that – after some
point – exit will equal entrance to the convergence club, creating the stabile degree of
inequality they consider to be characteristic for global inequality.
We study long term patterns; being a member of not of the convergence club is related
to the long-term performance of an economy (one cannot assess convergence or no nconvergence of individual countries on the basis of the growth experience during short
periods of time). As a result, the number of periods for which this can be studied is
rather limited; following Maddison we distinguish the following periods for which we
define and measure membership of this club: 1820-1870, 1870-1913, 1913-1950, 19501973 and 1973-2001 (1780-1820 is sometimes added to the analysis). This we then use
to study entrance and exit: which factors determine the spread of ‘modern economic
growth’ (i.e. the entrance of countries to the convergence club), and – a factor ignored
by Lucas – why do some countries leave the convergence club? Two kinds of factors
seem to play a role here: spatial patterns (countries near other countries that grow
rapidly will be stimulated to grow rapidly as well), and institutional factors (which
institutions determine the joining or the leaving of the convergence club?).
2. Data and sources
The main source of data is Maddison (2003). The dataset containing population and per
capita GDP data (in 1990 Geary-Khamis International USD) is available on- line at
http://www.ggdc.net/maddison/Historical_Statistics/horizontal- file.xls. Since the data
had a lot of missing observations before 1870, and especially during the first decades of
the 19th century, these had to be filled in by interpolation. For the interpolation of
population we used a log- linear method, that is, it was assumed that the growth rate of
population was even during the missing periods. The GDP per capita was linearly
interpolated. The missing GDP data was calculated from the interpolated population and
GDP per capita.
Countries where there was no initial data on the GDP and population in 1820
(developing countries, and predominantly in Africa) required a further assumption: here,
in the absence of more information, we used the average of the continent to fill in the
missing initial observation. A disadvantage of this approach is that some African
countries may sometime seem to have experienced very high economic growth between
1820 and 1870, while in fact it is just the continental average that proved to be too low
in their cases. Therefore, all developing countries are subject to the limitation that they
cannot enter the convergence club before 1871.
For similar reason, we omitted three Middle Eastern countries, Kuwait, The
United Arab Emirates, and Quatar. According to the Maddison dataset, in these
countries the per capita GDP was between 16000 and 30000 USD (at 1990 prices) in
1950, while in the same time the region had an average of 1776 $ only. These outliers,
and their erratic behavior significantly biased the calculations of average GDP, growth
and variance.
We also made adjustments to the estimates for China, following the critical
review of Maddison’s estimates by Holz (2006), who in our view convincingly shows
that the adjustment Maddison made to the official estimates of the growth of GDP
between 1978 and 1995 – by substracting 2.78% annually – is unfounded. We return to
the official growth rates for this period (by adding again 2.78% annually). The result of
this is that, whereas according to the Maddison estimates China between 1949 and 1978
is one of the most dynamic economies in the world – and part of the convergence club –
the revised estimates show a much lower rate of growth between 1949 and 1978, and
China in those years in not part of the convergence club. The decision to follow Holz
therefore has important consequences for the results of this paper.
Summing up, the dataset contains annual data of GDP per capita and population
of 139 countries representing almost 100% of world population and world GDP (the
whole Maddison dataset covers 142 countries).
3. The dynamics of the convergence club
Dowrick and De Long (2003) already carried out a classification of countries based on
their place in the convergence club. Their definition of convergence club is, however,
based on conventions rather than on objective factors. In their view, a country enters the
convergence club when it assimilates the institutions, technologies and productivity
levels typical of North-western Europe. The main problem with such classification is
that it is necessarily based on secondary literature (which covers not all of the countries
of the world and may be subjective), and basically just put our European or NorthAmerican perception of development and being developed in writing: the more Western
you look, the more developed we will think you are.
But this may not necessarily be advantageous. For example, the DowrickDeLong classification fixes the position of Western-Europe within the convergence
club, even though, by applying an alternative classification system, one may find that
most of Western Europe dropped out of the convergence club after 1973. Now either we
put an emphasis on institutional system, or we face the reality that there are no reserved
seats in the convergence club. As an alternative, we offer an alternative classification,
based on economic indicators. One may argue with good reason that our approach also
based on simplifications, but this was necessary to remain more or less objective.
Criteria of the convergence club
The period between 1820 and 2001 was divided into five sub-periods: 1820-1870, 18711913, 1914-1950, 1951-1973, and finally 1974-2001 (coinciding with the development
phases of capitalism by Maddison, 1991). For each period, each country had to meet at
least one of the following two requirements in order to be counted as member of the
convergence club.
1. The requirement of growth demands that a country had to grow faster on average than
the technological leader (the United Kingdom before until 1914, and the USA
afterwards).
2. The requirement of high level of income requires that a country has at least 80% of
the GDP per capita of the technological leader (in other words: it is already converged).
The second condition allows the long-run per capita income within the convergence
club differ by 20%, which is important as country-specific differences (institutional
background, geographical factors, size) may cause the log-run per capita output to differ
and therefore one should not expect a perfect convergence. We intervened in the
classification twice:
First, as mentioned and reasoned in Section 2, no developing country was allowed to be
member of the convergence club before 1871. Secondly, if a country was a member of
the convergence club both in the periods 1870-1914 and 1951-1973, it was
automatically counted as member between 1914 and 1950, as well. We consider
membership of the convergence club to be a long-term feature of an economy, which is
not affected by exogenous shocks as occurred during the 1914-1945 period. This also
means that our estimates of membership of the convergence club after 1973 are
preliminary, and only the future can tell if North-Western Europe (countries such as
France, Germany, Belgium, The Netherlands and Sweden), whose performance during
the post 1973 period does not allow us to include them in the convergence club, will
only temporarily underperform or permanently leave the club. The same applies to the
(formerly) planned economies of Eastern Europe and the (former) USSR, which also
leave the club in the post 1973 period, but may re-enter or perhaps, with the benefit of
hindsight, never ‘really’ have left it. Membership of the convergence club in the post
1973 is therefore a lower bound estimate.
Changes in the convergence club
The results from the classification based on the above- mentioned criteria is summarized
in Table 1
Table 1
Entries to and departures from the convergence club
Period
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
Entries to the club
Belgium, the Netherlands, Switzerland, the UK, Ireland,
Australia, New Zealand, Canada, USA
Austria, Denmark, Finland, France, Germany, Italy,
Norway, Sweden, Greece, Spain, Albania, Bulgaria, exCzechoslovakia, Hungary, Poland, Romania, exYugoslavia, ex-USSR, Argentina, Chile, Mexico,
Uruguay, Venezuela, Trinidad and Tobago, Japan,
Hong Kong, Singapore, Sri Lanka, Israel, Lebanon,
Syria, Palestine, Algeria, Gabon, Ghana, Mauritius,
Namibia, Reunion, Seychelles, South Africa
Brazil, Peru, Jamaica, Morocco
Portugal, Costa Rica, Dominican Republic, Costa Rica,
Nicaragua, Panama, Puerto Rico, Indonesia, Philippines,
South Korea, Thailand, Taiwan, Malaysia, Mongolia,
North Korea, Bahrain, Iran, Iraq, Oman, Saudi Arabia,
Turkey, Yemen, Angola, Botswana, Côte d'Ivoire,
Guinea Bissau, Lesotho, Malawi, Mauritania, Nigeria,
Swaziland, Togo, Tunisia, Zimbabwe, Equatorial
Guinea, Libya, São Tomé and Principe
Chile, China, India, Burma, Pakistan, Sri Lanka,
Vietnam, Cape Verde, Egypt, Mauritius, Seychelles
Departures from the club
None
None
Argentina, Chile, Uruguay, Lebanon, Ghana, Mauritius,
Namibia, Seychelles, South Africa
New Zealand, Venezuela, Sri Lanka, Morocco
Belgium, France, Germany, the Netherlands, Sweden,
Australia, Albania, Bulgaria, ex-Czechoslovakia,
Hungary, Poland, Romania, ex-Yugoslavia, ex-USSR,
Brazil, Mexico, Peru, Costa Rica, Ecuador, Jamaica,
Nicaragua, Panama, Trinidad and Tobago, Philippines,
Mongolia, North Korea, Bahrain, Iran, Iraq, Israel, Saudi
Arabia, Syria, Turkey, Yemen, Algeria, Angola, Côte
d'Ivoire, Gabon, Guinea Bissau, Malawi, Mauritania,
Nigeria, Reunion, Swaziland, Togo, Zimbabwe, Libya,
São Tomé and Principe
As Table 1 indicates, the membership to the convergence club changed quite a lot
during the last two centuries. As it is found by other studies, the periods 1871-1913 and
1951-1973 were especially favourable for the world convergence, while the period
1974-2001 was almost catastrophic: countries that had been members of the club since
1820 or 1871, such as Belgium, France, Germany, the Netherlands, Australia, and
Sweden lose their position. The reason is that their average growth rates remained
below that of the USA long enough to lag behind in terms of per capita income by more
than 20%. 1 Obviously, as we argued in the introduction of this section, there is no
guarantee that one remains in the club (the only exceptions are the UK before and the
USA after 1914).
Figure 1 reports the number of countries in- and outside the convergence club. It should
be noted that the only period when the number of convergence countries exceeds the
1
The story of Western Europe exiting the convergence club after 1973 is rather complicated though, and
we have not found a good solution for it; until the mid 1990s slow growth was linked to a slow increase
(or even decrease) of labour input per capita, possible as a result of a different choice between leisure and
income as in the US combined with increases in unemployment, early retirement etc. in Western Europe;
in fact, labour productivity may have even increase faster there than in the US (Crafts 2004); since the
mid 1990s however, productivity growth in the US has inrceased rapidly, mainly as a result of the ICT
revolution, whereas Western Europe in general did not witness a similar growth spurt in productivity; so
from the mid 1990s onwards there is a clear ’falling behind’; for that reasons we stuck to the results of
working with the Maddison dataset; at some point in the future it will be possible though to study these
two periods seperately: 1973-1995 and 1995-2020, and see how this changes our classification.
number of countries outside the club is the “golden age” of economic growth, 19501973.
Figure 1
Number of countries in and outside the convergence club
140
130
Convergence club
Rest of the World
120
99
95
100
90
77
80
62
60
49
44
1871-1913
1914-1950
40
40
20
9
0
1820-1870
1951-1973
1974-2001
Looking at Figure 1, it is very difficult to say anything regarding how the convergence
club is likely to grow in the future. If we take the average of the last two periods (which
are very short individually) we obtain that there were 58-59 convergence countries in
the 1950-2001 period. It seems therefore, that even though the convergence club
managed to grow considerably in the last two centuries, the speed of its expansion
slowed down quite significantly.
The following maps visualize the expansion of the convergence club between 1820 and
2001:
Using our data we can calculate the ex-post (observed) chances of joining and leaving
the convergence club.
Figure 2
Ex-post chances (in terms of countries)
chance of being in the club
60%
55.4%
chance of joining the club
50%
chance of leaving the club
40%
35.3%
28.8%
30%
34.5%
31.7%
28.8%
26.6%
20%
10%
6.5% 6.5%
7.9%
6.5%
0.0%
0.0%
2.9%
2.9%
0%
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
The results are not surprising: the chance of joining the convergence club was especially
high in the 1871-1913 and the 1950-1973 periods. One can also argue that the pre-1974
period was also favourable for preserving the achieved status; the chance of drop-out
was marginal. The post-1973 period, on the other hand, saw a massive increase of the
chance of leaving, but as argued before, since membership of the convergence club is a
long-term affair, our assessment of the 1973-2001 period may change in the future.
Looking at the number of countries entering and leaving the converge nce club does not
really us the whole story – the significance of a small country like Belgium falling out
of the convergence club is very different from the joining of the same club by big
countries like India and China. Again, we have to look at what this means in terms of
the world population.
Figure 3
Share of the world population in- and outside the convergence club
100%
Convergence club
94,1%
y = 0,1226x + 0,012
2
R = 0,8888
Rest of the World
90%
Linear (Convergence club)
80%
70%
61,8%
63,3%
61,9%
60%
52,8%
47,2%
50%
36,7%
40%
38,2%
38,1%
30%
20%
10%
5,9%
0%
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
The share of the world’s population experiencing convergence to the
technological leader increased steadily in the last 180 years, especially between 1870
and 1913, and again after 1973, when India’s and China’s joining to the club could
more than counterbalance the effect of several countries’ convergence failure. On
theoretical grounds it has been argued that global inequality would stop to increase once
more than 50% of the world’s population is part of the convergence club; so we will
expect a decline of global inequality and a decline in the growth of global GDP in the
final decades of the 20th century. On ground of five periods, it is not easy to draw any
conclusion about the speed of the convergence process, but at least it is obvious, that
from this perspective, convergence seems to have been a sustained process – in spite of
the fact that many countries dropped out of it after 1973. A simple regression line
linking the five periods – assuming the share of world population that is converging is
growing at a constant rate per period – results in the estimate that 100% convergence
will have to wait until the second half of the 21th century (in period 8, 1974-2001 is
period 5). 2 Perhaps more important is the fact that the share of world population
converging is not showing the kind of logistic curve as predicted by the diffusionist
approach; in particular the jump between 1820-1870 to 1870-1913 is too steep in
comparison with the relatively modest gains that were achieved during the 20th century.
Figure 4 presents the ex-post chances in terms of the world population of being,
joining and leaving the convergenc e process. Until the last period (1973-2001) the
2
There are several ways to determine when total convergence takes place. The first one is to accept the
slope of the regression line in Figure 3, and argue that the share of convergence countries increases by
12.3% per period on average. Since the average length of a period is 36.4 years, total convergence occurs
about 3x36.4=109.2 years after 2001, thus in the first decades of the 22th century. If, like in the text, we
assume that the length of a period remains 25 years, the total convergence comes around 2076.
Another way is to calculate the annual growth rate of the share of convergence countries in the
population. First we determine the middles of the first and the fifth periods, which are 1845 and 1988
respectively. Since 56% growth took place during this 143 years, the annual growth rate was 0.39%.
Using this, it can be calculated that the complete convegrence would occur in 2085.
differences with the chances in terms of countries are not very large: the chance to leave
is quite small (before 1973), to enter are highest in 1871-1913 and fall to a much lower
level between 1914 and 1950 etc. What is really different is the last period, when the
chance to enter has increased to more than 80% (so more than 80% of the world
population which was still ‘underdeveloped’ before 1973, entered the convergence club
after 1973), whereas at the same time the chance to leave has also risen quite
dramatically.
Figure 4
Ex-post chances (of terms of world population)
chance of being in the club
90%
82,2%
80%
chance of joining the club
70%
chance of leaving the club
61,9%
60%
47,2%
50%
36,7%
40%
45,1%
38,2%
29,7%
30%
19,8%
20%
10%
5,9% 5,9%
0,0%
0,0%
3,6% 4,3%
3,4%
0%
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
4. The long-term development of world GDP
Now that we have established that in the second half of then 20th century the share of
the world population converging has increased to more than 50%, we can see how this
relates to the growth of world GDP (per capita). There are two ways to measure this.
The first one is the usual procedure, by weighting the various growth rates of the
different countries by their share in world GDP. Rich countries have a bigger impact on
growth rates than poor ones – the United States, for example, with less than 300 million
inhabitants, weights more heavily than China and India combined (with more than 2.3
billion). In theory rapid growth of world GDP may mean that only a small fraction of
world population experiences an increase in their real income. A second approach is to
weight countries on the basis their population size; it measures the average growth of
real income as ‘experienced’ by the world population. The difference between the two
indicators is also very interesting: when rich countries on average grow faster than poor
ones, the first (GDP weighted) estimate of the development of per capita world GDP
will grow more rapidly than the second, population weighted estimate, meaning that
income disparities between countries increase. Similarly, when the population weighted
GDP per capita increase faster than the GDP weighted, income disparities will tend to
decline.
Figure 5 presents the estimates of the two series; additionally, the unweighted
average GDP per capita is also given. Figure 6 shows the annual growth rates of the two
series. At the beginning of the 19th century the differences between the three series are
very small; the GDP weighted series grows much more rapidly, causing a ‘great
divergence’ to appear between the two ways of measuring global income levels. This
gap is one way of measuring global inequality (the pattern found here is very similar to
the one identified by estimating the coefficient of variation weighted by population in
the next section). Figure 6 also demonstrates than until the final quarter of the 20th
century income disparities on a global scale continued to increase, as the growth rate of
the GDP weighted world GDP was larger than that of the population weighted. As
Table 2 shows, the differences was relatively stable during the 19th century, increased
during the first half of the 20th century – indicating that on average poor countries were
more affected by the instability of the world economy than rich ones (Table 2) – but
declined sharply after 1950, when both growth rates became more or less the same.
Looking at the trends in Figure 6 it appears that the decline in the growth rate of GDP
weighted world GDP after 1973 has been faster than the fall in the population based
growth rates, but differences between the two series are rather small.
Figure 5
The average GDP per capita of the world, 1820-2001 (US 1990 dollars)
1990 G-K USD
16000
unweighted
14000
weighted by GDP
12000
weighted by population
10000
8000
6000
4000
2000
0
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Figure 6
Two estimates of the growth of world GDP per capita, 1820-2001
10%
8%
weighted by GDP
weighted by population
Polinom. (weighted by GDP)
6%
Polinom. (weighted by
population)
4%
2%
0%
1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-2%
-4%
-6%
-8%
-10%
Table 2
Average annual growth rate of the GDP per capita
1820-1870
1871-1913
1914-1950
1950-1973
1974-2001
Weighted by GDP
1.11%
1.70%
1.81%
2.70%
1.44%
Weighted by population
0.53%
1.22%
1.01%
2.67%
1.47%
Difference
0.58%
0.48%
0.80%
0.03%
-0.03%
These patterns seem to confirm the assumptions of the Lucas model: there is a gradual
acceleration of the growth of world GDP – broken by the exogenous shocks of the
1914-1950 period – followed by a deceleration of growth at the end of the 20th century.
Moreover, the two patterns distinguished here – based on weighting by GDP and by
population – seem to confirm the prediction of the model in terms of the development of
global inequality as well. We will now review the trends in global inequality more in
detail.
5. Global inequality
These tentative results can easily be verified by calculating different measures of
inequality on the basis of the amended Maddison dataset. We concentrate on the
coefficient of variation, which is the standard deviation divided by the average and
therefore measures relative inequality. A problem with these measures is that countries
vary in size and therefore cannot be seen as single observations, and should have an
impact on the standard deviation and the coefficient of variation related to their size.
Moreover, as we already saw, this size can be either measured in terms of population
and in terms of total GDP, and this choice may have implications for the results. So we
get three different ways of measuring the development of inequality: the unweighted
coefficient of variation (all countries have the same impact), and coefficients of
variation weighted by population and weighted by GDP. This can moreover be done in
two ways: when calculating the coefficient of variation we can divide the standard
deviation by the average global GDP (per capita) – which is usually weighted by GDP –
or we can divide the standard deviation by the related average – so the unweighted
standard deviation is divided by the unweighted average GDP per capita, and the
standard deviation which uses population weights is divided by the average GDP per
capita weighted by population size. The second procedure, which is in our view the
correct one, gives the results of Figure 7.
Figure 7
The coefficient of variation of global inequality (GDP per capita), 1820-2001
coefficient of variation
160%
unweighted
140%
weighted by GDP
weighted by population
120%
100%
80%
60%
40%
20%
20
00
19
90
19
80
19
70
19
60
19
50
19
40
19
30
19
20
19
10
19
00
18
90
18
80
18
70
18
60
18
50
18
40
18
30
18
20
0%
Figure 7 shows how strongly the results of measuring the development of global
inequality are dependent on the measure used. The GDP-weighted coefficient of
variation increases only until the 1880s, stabilizes after 1880, shows a strong declining
trend during the post-1945 Golden Age, and, remarkably, an increase again after the
mid 1980s. Probably the best measure of world inequality is the population weighted
coefficient of variation, which shows an almost continuous growth between 1820 and
1930; the rate of increase, which peaks in the mid 1800s, declines after 1860 (Figure 8).
The depression of the 1930s causes a sudden decline in inequality, followed by an
equally sudden upsurge during the Second World War – in both cases global inequa lity
seems to be driven to a large extent by the leading country, the US, which suffers
disproportionally during the 1930s, and recovers very strongly during the war period.
The fast recovery of many countries after 1945 leads to certain decline in inequality, but
after the mid 1950s global inequality stabilizes at a much higher level than before 1929,
and hardly seems to change anymore (in contrast to the large changes in the GDP
weighted series). The very rapid development of China and India in recent years have
not lead to a strong decline in inter-country inequality so far (which is a bit contrary to
expectations).
Figure 8 Change in the coefficient of variation of per capita world GDP
(weighted by population), 1820-1901
0.100
0.080
0.060
0.040
0.020
0.000
1821
1831
1841
1851
1861
1871
1881
1891
1901
1911
1921
1931
1941
1951
1961
1971
1981
1991
2001
-0.020
-0.040
-0.060
-0.080
-0.100
Figure 9
The standard deviation of global inequality (GDP per capita) 1820-2001 (in 1990 USD)
std. deviation
12000
10000
unweighted
weighted by GDP
8000
weighted by population
6000
4000
2000
20
00
19
90
19
80
19
70
19
60
19
40
19
50
19
20
19
30
19
00
19
10
18
80
18
90
18
70
18
60
18
50
18
40
18
30
18
20
0
The striking differences between these two ways of measuring global inequality are to a
large extent the result of the diverging development of per capita GDP sketched in the
previously (see Figure 5). In 2000, for example, per capita global GDP weighted by
GDP is more than twice the level of per capita GDP weighted by population (almost
15.000 1990 dollars versus about 6.000 dollars). As Figure 9 demonstrates, the standard
deviations of global inequality measured in the three ways suggested here, do not differ
that much in the very long; in fact, weighting by GDP even gives a slightly stronger
increase than weighting by population.
At this point we remind the reader that Lucas’s simulation focuses on the betweengroup sources of income inequality in his theoretical model. In fact, however, total
variance can be decomposed into two parts:
The between-group variance, that is the variance resulting from the difference between
the average per capita income of the convergence club and average of the rest of the
world.
The within-group variance, resulting from different growth rates and income levels of
members of the same group (convergence or non-convergence).
It is clear that the between- group variance will start to decrease when the share of
convergence countries exceeds a threshold value (probably at some point when more
than 50% of the countries are converging, and the number of countries which is not
converging is declining rapidly). We cannot say the same about the within- group
variance, though. Lucas assumes that the within group variance of the non- members of
the convergence club is zero, all countries remaining at a ‘minimum’ level of GDP per
capita. This is, of course, not very realistic. The inequality within the convergence club
will depend on the convergence process itself: it will increase strongly initially, but
again there will be a tendency – once more than 50% of countries converge – for this
part of global inequality to decline.
Table 3 has the standard deviation and coefficient of variance in- and outside the
convergence club. It can be concluded that until about 1950, the inequality within the
convergence club increased faster than in the rest of the world. The trend reversed later,
and while inequality among non-convergence countries seems to increase both in
absolute and relative terms, the coefficient of variance actually decreased within the
convergence club.
Table 3
Standard deviation and coefficient of variance of the unweighted per capita GDP in- and
outside the converge nce club (1990 G-K USD and percentage)
Std. deviation in the
convergence club
Coefficient of
variance in the
convergence club
Std. deviation
outside the
convergence club
396
1054
1741
3225
5799
30.81%
61.97%
64.16%
88.61%
79.37%
335
410
677
1766
4927
1820-1870
1871-1913
1914-1950
1950-1973
1974-2001
Coefficient of
variance outside
the convergence
club
46.91%
49.90%
61.59%
92.19%
116.03%
Table 4 reports the results from the decomposition of total standard deviation into
between- and within- group components.
Table 4
Standard deviation of the per capita GDP and its components (1990 G-K USD)
1820-1870
Between-Group
std. deviation
141
Within-Group
std. deviation
336
Total std. deviation
364
1871-1913
1914-1950
1950-1973
1974-2001
420
751
857
1385
701
1117
2656
5153
817
1346
2791
5336
In absolute terms both components of variance seem to have increased in the last 180
years: there is no sign of any reduction in inequality. From our perspective it is more
interesting to see how the coefficient of variance (different components of the std.
deviation divided by the world average per capita income) and its components changed
over time (Figure 10).
Figure 10
The coefficient of variance and its components
120%
Between Group
100%
93%
Within Group
101% 104%
97%
84%
Total
72%
80%
69%
62%
60%
45% 49%
47%
37%
40%
30%
27%
19%
20%
0%
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
As Figure 10 suggests, until about 1950 both the within- and between-group coefficient
of variance contributed to the growth of the total coefficient of variance. On the other
hand, the between-group coefficient of variance started to decrease after World War 2.
We have found the reversed U-curve, hence, but it exists only in relative terms, that is,
if the standard deviation is divided by the mean: the between-group component of std.
deviation seems to have grown slower than the per capita GDP.
Figure 11 shows the share of the between- and within- group components within the
total sum of square. It is clear that the cross-country differences are increasingly
responsible for the increasing dispersion, and the difference between the convergence
club and the rest of the world plays a secondary, diminishing role. A theoretical model
that tries to forecast inequality (total variance) by focusing on the between-group
component of variance only is therefore increasingly inaccurate and basically useless
after World War 2.
Figure 11
Share of the different components in the total sum of square
100%
85.1%
90%
80%
Between Group
93.3%
90.6%
Within Group
73.5%
68.9%
70%
60%
50%
40%
26.5%
30%
20%
31.1%
14.9%
9.4%
10%
6.7%
0%
1820-1870
1871-1913
1914-1950
1951-1973
1974-2001
6. The development of the convergence club
One of the limitations of the Lucas model is that it does not really explain why countries
join the convergence club; he only assumes that the chance to converge increases over
time. There is a growing literature suggesting that this process is determined by
geographical and institutional forces.
The importance of spatial patterns in economic development is the main topic of New
Economic Geography (see for example Krugman, 1991; Krugman and Venables, 1995).
Gallup et al. (1998), for example, argue that after holding institutional factors fixed,
geographical factors still play an important role in development through affecting
transaction and transportation costs. They find that location and climate have strong
relationship with income levels, and argue that geographical factors affect the choice of
institutions. We operationalize this by formulation two hypotheses:
Hypothesis 1: Distance from the economic center of the World Economy is important
determinant of the chances of a country to join the convergence club. (geographical
distance from London in km - dist); we selected London because Great Britain is the
original starting point of the process of industrialization, from which it spread.
Hypothesis 2: Having at least one neighbor that already member of the convergence
club increases the chance of joining to the club; we measured whether a country had one
or more neighbours being members of the convergence club. (oneneigh and moreneigh
variables)
The literature suggesting that institutions cause economic growth is enormous (see
North 1982 for a general statement of the argument). An important dimension is the
quality of government. Mauro (1995), for example, finds that corruption lowers
investments, while an efficient bureaucracy may be beneficial. He also finds that corrupt
governments tendentiously spend less on education, which establishes a link between
the general state of institutions and the formation of human capital. A similar conclusion
is reached by Rodrik et al (2002) and Dollar and Kraay (2003). Acemoglu et al (2002)
point at the role of European colonization in the “reversal of fortune”: regions where
colonizers established extractive institutions later lagged behind in development.
Another set of institutions – ‘communism’ or a centrally planned economy – has also
been subject to much debate; did communism hinder economic development in (for
example) Russia and Eastern Europe, or make it possible to industrialize rapidly and
enter the convergence club, as Allen (2003) has argued for the Soviet Union?
The direction of causality between welfare and institutions is not obvious,
however. Lipset (1960) argues that rising welfare paired with the improvement of
human capital leads to better institutions and conflict solving mechanisms. His view is
opposed by Przeworski and Limongi (1993, 1994, 2004), who state that changes in
political institutions are basically not determined by economic development, that is
democracy may rise in any country independently whether it is wealthy or not. There is
no endogeneity thus, but higher income may help to preserve democracy. These two
hypotheses are of high importance for any empirical research in this area, since if Lipset
is right, the coefficients from the regressions analyzing the relationship between
institutions and economic growth are likely to be biased. Glaeser et al. (2004) find that
the causality link cannot be easily determined, and the positive relationship between
democracy and economic performance is not necessarily general: autocratic regimes
may foster economic growth up to the point enough human capital is accumulated for a
change in political system to take place. Milanovic (2005), similarly to this paper, relies
on the Maddison and the PolityIV datasets to test the hypothesis whether higher income
increases the chance of changing to democracy. He points out that the relationship
between democracy and income depends largely on out definition what democracy is. If
we are very narrow in our hypothesis, there is a positive relationship between income
and democracy and Lipset’s hypothesis can be justified. If the previously achieved level
of democracy is taken account with, though, the level of income loses its importance.
This leads us to formulate the following hypotheses:
Hypothesis 3: Political institutions are important determinants whether a country
converges to the leader. We measure the quality of policy using the PolityIV variable
from (http://www.cidcm.umd.edu/inscr/polity/) (a high number means more democratic
regime).
Hypothesis 4: Communism – i.e. a centrally planned economy – was an instrument for
entering the convergence club (a communism dummy should have a positive sign)
Hypothesis 5: Colonization has a negative impact on a country’s chance to converge.
(colony variable) 3
A variable that is at the crossroads between institutions and geography is the settler
dummy. 4 Acemoglu et.al.(2002) argues that Europeans introduced different institutions
depending on the hospitability of environment and the wealth of the subdued region. In
hospitable but poor regions they founded settler colonies with more European- like
3
Since the Polity IV dataset follows the historical changes in borders and countries, we had to adjust it to
the Maddison dataset that projects today’s countries back in time. This was especially required for
developing countries that did not exist or were colonies before World War 2. For the extrapolation of the
missing data, we used the following strategy: colonies were given the same polity score as their
metropoles. (The additional, probably negative, effect of colonization is captured by the colony dummy in
the regressions.) For countries that were independent, we used the scores of similar countires. For
example in South-East Asia, we used the Chinese score (-6), while in case of the African tribal kingdoms,
we took the average of China (-6) and Turkey(-10): -8.
4
USA, Canada, Australia, New Zealand, Argentina, Brazil, Chile, Uruguay, South Africa, Hong Kong.
institutions, while in rich or hostile areas they rather applied extractive institutions.
Acemoglu et al. suggest these institutional differences were decisive in the later
development of the ex-colonies, leading to the large-scale differences in welfare
observed today. The expected sign of the settler coefficient is positive.
Specification
Yi,t = α0 + α1polity i,t + α2 lndist i + α 3oneneigh i,t + α 4moreneigh i,t +
+α5communism i,t + α 6settleri + α 7colonyi,t + ηi + τt + ε i,t
(1.)
Yi,t = {memberi,t , joini , t ,leavei,t }
where ?i, and t t denote the country, and period specific unobserved effects, and ei,t is the
error-term assumed to be i.i.d.. We assume the strict exogeneity of the regressors.
The variables are summarized in the following table:
Variable
memberi,t , join i,t , leavei,t
polityi,t
lndisti
oneneighi,t
Description
Variable
Description
Binary dependent variables
1 if country i was member
of/joined/left the convergence
club in period t, 0 otherwise
Polity score of country i in
period t ranging between -10
and +10.
Logarithm of the distance of
country i from London in km.
1 if country i had at least one
neighbor in the convergence
club in period t, 0 otherwise
moreneighi,t
1 if country i had more
than one neighbor in the
convergence club in
period t, 0 otherwise
1 if country i was
colony, 0 otherwise
communismi,t
settleri
colonyi,t
1 if country i was a
settler colony
1 if country i was a
colony in period t, 0
otherwise
We estimated equation (1.) in both random-effect and fixed-effect specification. In the
fixed-effect specification we applied the method suggested by Mundlak (1978). 5 This
allows us to estimate the coefficients of the time- invariant regressors as well. The
results for the different periods are summarized in the next table. The marginal impacts
are calculated at the mean of the dependent variable. 6 Originally, we planned to apply
different colony dummies for different metropoles to capture the difference in colonial
policies, but since these turned out to be insignifcant (with t- statistics near zero), or
were sometimes dropped, we opted for using a single colony dummy.
The chance of being in the convergence club
5
Instead of subtracting the country specific mean of variables from both sides (Within-Group
transformation), he suggests using these means as regressors. These coefficients are not reported in the
tables as they have no economic importance. The advantage of the method is that it requires no
transformation of the data, and it is possible to estimate the coefficients of time -invariant regressors. Their
presence, however, marginally increases the pseudo-R2 .
6
We used the logit function of the Stata, together with the mfx function that calculates the marginal
impacts with significance tests. We opted not to use xtlogit, because it does not calculate robust tstatistics, and has the tendency to drop dummy variables on ground that they predict perfect success or
failure, even though theoretically these variables are also important.
Table 2 reports the estimation results for the dependent variable “member”. This
equation is used to identify the main determinants of membership in the convergence
club. We do not experience with regressions containing less variables, because these
would just show the effect of the omitted variable bias.
Table 5.
Results from equation (1.), the dependent variable is the membership dummy
Variable
1820-2001
Random-Effect
Marginal
effect in
%
1.5% ***
1820-2001
Fixed-Effect Mundlak
Marginal effect in
%
0.082**
-0.037
-0.6%
(2.67)
(-1.23)
lndisti
-0.927***
-0.17***
-0.961***
-0.16***
(-5.04)
(-4.31)
oneneighi,t
0.819***
15.2% ***
-0.052
-0.9%
(2.67)
(-0.13)
moreneighi,t
1.222***
26.3% **
1.179**
23.7% **
(3.03)
(2.47)
communismi,t
-0.326
-5.5%
-1.680**
-17 %***
(-0.65)
(-1.97)
settleri
1.889***
43%
1.028**
21.1% *
(3.29)
(1.95)
colonyi
-1.066**
-16.7% ***
-0.124
-3.2%
(-2.53)
(-0.24)
Constant
4.639***
2.594
(3.09)
(1.39)
1870-1913
2.268***
49.3% ***
3.725***
72.8% ***
(5.16)
(5.86)
1914-1950
1.370***
29.2% ***
2.940***
60.8% ***
(3.05)
(4.51)
1951-1973
2.872***
60.9% ***
4.977***
84.4% ***
(6.08)
(6.91)
1974-2001
1.570***
34% ***
3.547***
70.5% ***
(3.37)
(5.32)
Pseudo R2
0.38
n.a.
0.43
n.a.
Note: heteroscedasticity and serial correlation robust t-statistics are reported in parentheses. *,**,***
denote a coefficient significant at 10, 5, 1 percent level of significance. In case of lndist, elasticity is
reported in marginal effect column.
polityi,t
It is important to see the difference between a random-effect and a fixed-effect
specification: if the regressors could capture all country-specific differences (cultural,
institutional, geographical), the random-effect specification should suffice. This is not
the case, however: there are still important unobserved country-specific effects present. 7
It may sound strange, but after these unobserved effects are taken care of, institutional
variables (polity and colony) seem to play no role in determining the chance of a
country to enter and remain in the convergence club (we must, however, separately
check in the next sub-section whether these have any impact on the chance of joining
the club). The exceptions are the settler coefficient which is significant at 10% and
positive, suggesting that ex-settler colonies still performs quite well on average, and the
7
A fixed-effect panel specification cannot solve all the problems regarding omitted variables (unobserved
country-specific effects), since it is based on the assumption that these affects do not change over time. If
there are country-specific factors that are unobserved and change over time, they will still cause an
omitted variable bias. The longer the time -dimension of a panel is, the more chance we have that the
unobserved effects also change over time. This is obviously a limitation of analysing secular processes
with a panel regression.
communism dummy - state-socialism seems to lead to failure in the long-run by
reducing the chance of remaining in the club by 17%.
The impact of geographical forces is stronger though. Being not too far from the
economic center of the world (lndist), and being embedded in a “block” of convergence
countries (moreneigh) has positive impact on the chance to converge to the leader.
It seems that our model could not capture several important time-varying aspects of
development, because there are highly significant period-specific effects: 1951-1973
seems to have been especially fortunate periods for convergence.
The chance of joining the convergence club
In Table 6 we report the results from the regression that attempt to capture the main
factors determining the chance to join the convergence club. Unlike in the previous
regression, now the only question is what causes a country to enter the club, but we
neglect the determinants of what help a country to preserve her position within the club.
Table 6.
Results from equation (1.), the dependent variable is the “join” dummy
Variable
1820-2001
Random-Effect
Marginal
effect in
%
-0.4% **
1820-2001
Fixed-Effect Mundlak
Marginal
effect in
%
-0.9% ***
-0.045**
-0.108***
(-2.27)
(-3.22)
lndisti
-0.047
-0.004
-0.040
-0.003
(-0.65)
(-0.65)
oneneighi,t
0.642*
5.9% *
0.688
5.9%
(1.90)
(1.45)
moreneighi,t
0.379
3.7%
0.498
4.7%
(1.11)
(0.78)
communismi,t
-1.530*
-7.8% ***
-2.147**
-8.4% ***
(-1.87)
(-2.00)
settleri
0.074*
7.4% *
0.324
3%
(1.89)
(1.08)
colonyi
-0.349
-2.8%
-0.209
-1.7%
(-0.96)
(-0.41)
Constant
-2.635***
-3.198***
(4.02)
(-4.11)
1870-1913
1.818***
24.7% ***
2.218***
31% ***
(3.55)
(3.81)
1914-1950
-0.817
-6%
-0.370
-2.8%
(-1.19)
(-0.48)
1951-1973
1.700***
22.1% **
2.013***
27.2% **
(3.14)
(3.12)
1974-2001
-0.130
-1.1%
0.223
1.95%
(-0.23)
(0.35)
Pseudo R2
0.19
n.a.
0.21
n.a.
Note: heteroscedasticity and serial correlation robust t-statistics are reported in parentheses. *,**,***
denote a coefficient significant at 10, 5, 1 percent level of significance. In case of lndist, elasticity is
reported in marginal effect column.
polityi,t
In the long-run, being democratic does not ensure that a country starts to converge, what
is more too much democracy may even decrease the chance (negative polity
coefficient). Before rejecting these results on theoretical grounds, let us not forget that
most convergence countries (European countries as well) were less democratic when
they joined the convergence club than they are now. There are examples, especially
from Asia, that less democratic nations sometimes can pursue an efficient development
policy (South Korea and Indonesia are cases in point, not to mention communist China).
The magnitude of the effect of the political system is very low, however, and does not
seem to be a decisive factor. Unlike in the case of membership, we find that
geographical factors do not affect the chance of joining the club in the long-run either.
This means, that entering the club is not an impossible goal for any countries in the
world, the re are no “doomed” countries. Preserving their status, however, is much more
difficult when one is not member of a block of converging countries as we saw
previously (Argentina is perhaps the best illustration). The results do not seem to
confirm any of the two opposing theories: convergence seems to be almost independent
of the political system with the sole exception of state-socialism, which seems to be
very counterproductive and does not have the effect postulated by Allen (2003) for the
Soviet Union. The period dummies indicates that the environment was increasingly
favourable for joining the convergence club in the periods 1870-1913, and 1951-73.
The chance of leaving the convergence club
Now we arrive to the very important question, namely that what determines the chance
of a country to lose its position within the club. Table 7. has the results.
Table 7.
Results from equation (1.), the dependent variable is the “leave” dummy
Variable
1914-2001
Random-Effect
Marginal
effect in
%
0%
1914-2001
Fixed-Effect Mundlak
Marginal
effect in
%
0%
-0.030**
-0.000
(-0.94)
(-0.00)
lndisti
0.247
0.012
0.107
0.0014
(0.91)
(0.31)
oneneighi,t
0.437
0.6%
0.646
0.9%
(0.99)
(1.03)
moreneighi,t
-2.096**
-1.7% **
-1.769
-1.5% *
(-2.18)
(-1.54)
communismi,t
3.487***
28.2% *
3.810**
38.1%
(4.06)
(2.48)
settleri
1.130*
2.6%
1.597***
4.4%
(1.90)
(2.61)
colonyi
0.341
0.5%
0.424
0.6%
(0.38)
(0.33)
Constant
.5.777**
-5.437*
(-2.59)
(-1.80)
1951-1973
-0.773
-0.9%
-0.793
-0.8%
(-0.58)
(-0.55)
1974-2001
3.871***
23.6% ***
3.845***
22.2% **
(5.97)
(4.85)
Pseudo R2
0.44
n.a.
0.45
n.a.
Note: heteroscedasticity and serial correlation robust t-statistics are reported in parentheses. *,**,***
denote a coefficient significant at 10, 5, 1 percent level of significance. In case of lndist, elasticity is
reported in marginal effect column.
polityi,t
It seems that the political system (insignificant polity coefficient) has little to do with
the success of a country, but may be important determinant of its failure (communism).
Wealthy, democratic European countries (France, Germany, the Benelux countries,
Sweden) may also lose their position, similarly to their poor African counterparts. A
possible explanation is that more democratic nations can find it difficult to adapt their
social security systems and welfare institutions to changing environment. Here the
stabilization process may take a long time, and during this time even a wealthy country
may lag behind the leader (USA).
Being close to a block of convergence club (significant ne gative moreneigh coefficient)
seems to offer a marginal protection from losing position, but this is not guarantee, as
we saw in case of Western Europe after 1974.
7. Conclusion
In this paper we have developed and tested the idea that the development of global
inequality can be analysed as driven by the diffusion of the process of industrialization
in the past two centuries. We used Lucas (2000) model as an elegant (but perhaps rather
simple) way to operationalize this idea. The competing approach to global inequality,
which we kept in the back of our mind but was not developed in more detail, is that the
world economy is characterized by relative stable relationships core and periphery. We
used a (slightly extended) version of the Maddison (2001) dataset to test the ideas of the
Lucas model. The predictions of the model were threefold: (1) the share of countries or
the share of the world population that is converging is constantly increasing, and these
shares show a logistic curve approaching 100% in the long run; (2) global inequality
(between countries) increases until more than 50% of countries/world population is
member of the convergence club; afterwards, inter-country global inequality will begin
to decline; and (3) the growth rate of world GDP will also increase during the first phase
of the diffusion process until the majority of countries is converging, after which the
growth of world GDP will start to decline again (until in the very long run they are all
growing at the rate of the leading country).
Our main results are as follows. The ‘bad news’ is that the share of countries
converging is not growing consistently in time, in particular because after 1973 many
countries seem to leave the convergence club, because they grow at a slower rate than
the US and/or have a income per capita that is lower than 80% of the leading country.
The failure of many countries to continue being member of the convergence club (as
defined here) is probably the most striking ‘problem’; or put differently, the Lucas
model does not allow countries to leave the convergence club, but in practice they do,
and in particular many did after 1973. We have to be a bit cautious of course, because
we do not know their long term performance after 1973; only in the 2020s or 30s, after
another period of 30 years, can we really assess if this was a structural phenomenon or
just a temporary set back, caused, for example, by the desintegration of the communist
world and the transition problems faced by the centrally planned economies (many of
which left of convergence club after 1973). Similarly, it is still rather early to judge the
economic performance of the Western European countries (such as the Netherlands), or
countries such as Australia that also left the club after 1973; between 1973 and the mid
1990s Western Europe increased its labour productivity faster than the US. At the same
time its labour force and labour input grew much more slowly than in the US, causing a
slower growth of per capita GDP. Whether this was a voluntary choice – the result of
different preferences for leisure versus income – or the result of bad institutions and
incentives in Western Europe is still a matter of debate.
The ‘good news’ is that the share of the world population converging is growing
over time, and has continued to increase after 1973 (when a few very big countries such
as India and China joined the club). In that – more important – respect our data seem to
be consistent with the predictions of the Lucas model, albeit that the share of the world
population converging does not show the logistic growth curve that results from the
model. During the 19th century this appeared to be the case, but the world wars and
great depression of the 1930s ‘breaks’ the pattern found, and led to a near-stabilization
of the share of the world population converging, whereas one would have expected - on
the basis of the 19th century pattern – a further, even accelerated growth of that share.
The convergence club (in terms of world population) again expanded consistent ly after
1945 (although this is to some extent also dependent on the classification of China,
which does not enter the convergence club until 1973), as a result of which in the most
recent period (1974-2001) more than 60% of world population is converging (and this
excludes a large part of Western Europe and Australia, which discontinued converging
after 1973).
Global inequality (between countries) seems to move more or less in line with
the expectations of the Lucas model. It increased strongly in the century and a half after
the start of the Industrial Revolution, and only began to stabilize in the second half of
the 20th century (see Boltho and Toniolo (1999) for a similar result). We could also
establish that the increase in global inequality was most rapid during the middle decades
of the 19th century – when only a few countries industrialized rapidly – and already
began to slow down during the first phase of globalization after 1870 (which was indeed
a very successful period of the spread of ‘modern economic growth’) (although it
should be added that the data for the pre 1913 period are much weaker than for the 20th
century). But, in spite of the fact that more than 60% of the world population is now
part of the ‘convergence club’, we see no signs of a continuing decline of global
inequality yet. In fact, the new growth spurt set in by the US after the mid 1990s, and
the continuing bad performance of Africa (and Latin America, and GOS countries),
seems to counterbalance the strong performance of East and South-Asian countries such
as India and China. Also the prediction that the growth of world GDP is most rapid
when about 50% of world population is converging, appears at first sight to be
consistent with the facts as reconstructed here, in view of the acceleration of growth
after 1945. But the post 1973 slowing down of world growth cannot be easily explained
in there terms – such a slowing down might only happen when a large majority of the
world population is close to convergence, which obviously is not the case (yet).
The most obvious problem with the Lucas model is that it does not explain why
countries enter (or leave) the club. We have tried to find out which spatial and
institutional factors determine this process. It can be concluded that geography plays a
very important role in this – that closeness to London and having neighbors who are
also part of the convergence club are important factors in determining once position –
being a member or not. It proved more difficult to establish the role played by
institutions – only communism was consistently a negative factor in terms of the chance
of being or becoming a member of the convergence club, and also increased the chance
to leave the club.
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Appendix
Derivation of between-group variance
The between-group variance is a component of total variance which results from the
difference between the average per capita GDP of the two country groups: the
convergence club and the rest of the world. The average per capita GDP of the whole
world ( ytw ) in year t equals:
ytw = E ( ytw ) = λt ytc + (1 − λt ) ytr (A.1.)
where ?t is the share of convergence countries within all countries of the world, ytc and
ytr denote the average income of the convergence club and the rest of the world in year
t. Using that the variance of the worlds average income is directly calculable form
(A.1.) one may write:
V ( ytw ) = E ( ( ytw )2 ) − ( E( ytw ) ) = λt ( ytc ) + (1 − λt ) ( ytr ) −  λt ytc + (1 − λt ) ytr  (A.2.)
Taking the first derivative of (A.2.) according to ? yields:
2
∂V ( ytw )  c 2
= ( yt ) + ( ytr )  (1 − 2λt ) + ytc ytr (4λt − 2) (A.3.)


∂λt
The first order condition for a maximum requires (A.3.) being equal to zero, which is
true only if ?t =0.5. The second order derivative of (A.2.) with respect to ?t is negative.
This finding indicates that holding all other factors fixed, the between-group variance
should start to decrease when the share of convergence countries exceeds 50%.
This result applies to the standard deviation and all logarithmic versions as well, as
these are all monotonous transformations.
The between-group coefficient of variance may behave differently though. Rewriting
(A.2.) yields the formula for between-group coefficient of variance:
2
2
E ( ( ytw ) 2 ) − ( E ( ytw ) )
2
CV ( y ) =
w
t
E ( ytw )
2
2
λt ( ytc ) + (1 − λt ) ( ytr ) −  λt ytc + (1 − λt ) ytr 
=
λt ytc + (1 − λt ) ytr
2
2
2
(A.4.)
the first derivative with respect to ?t is:
c
r
c
r
λt yt + (1 − λt ) yt ) ⋅ yt − yt
(
∂CV ( ytw )
=
c
r 2
∂λt
2  λt yt + (1 − λt ) yt  ⋅ λt (1 − λt ) (A.5.)
2
λt ytc + (1 − λt ) ytr  ⋅ λt (1 − λt ) ≠ 0
The FOC leads to the following equation:
λt ytc + (1 − λt ) ytr = 0 (A.6.),
from which one can express the ?t at which the between- group coefficient of variance
reaches its maximum λtmax :
1
λtmax =
(A.7.)
ytc
1+ r
yt
The second order derivative of (A.4.) is negative if we assume that all parameters are
strictly positive, which means that λtmax determines a maximum indeed.
Equation (A.7.) tells us that the maximum of the between-group coefficient of
variance depends on the ratio of the average per capita aggregate incomes of the
convergence club and the rest of the world. In other words, it is determined by the
welfare bonus of the convergence club. As ytc > ytr , it is evident that 0 < λtmax < 0.5 ,
that is a decrease of the between-group coefficient of variance always precedes that
of the between-group variance.