WPS5044
Policy Research Working Paper 5044
Global Inequality and the Global Inequality
Extraction Ratio
The Story of the Past Two Centuries
Branko Milanovic
The World Bank
Development Research Group
Poverty and Inequality Team
September 2009
Policy Research Working Paper 5044
Abstract
Using social tables, the author makes an estimate of determinants of global inequality have become differences
global inequality (inequality among world citizens) in in mean country incomes rather than inequalities within
the early 19th century. The analysis shows that the level nations. The inequality extraction ratio (the percentage
and composition of global inequality have changed of total inequality that was extracted by global elites) has
over the past two centuries. The level has increased, remained surprisingly stable, at around 70 percent of the
reaching a high plateau around the 1950s, and the main maximum global Gini, during the past 100 years.
This paper--a product of the Poverty and Inequality Team, Development Research Group--is part of a larger effort in the
department to study inequality in its historical perspective. Policy Research Working Papers are also posted on the Web
at http://econ.worldbank.org. The author may be contacted at bmilanovic@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
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Global inequality and the global inequality extraction ratio:
The story of the past two centuries
Branko Milanovic1
World Bank Research Department, Washington
School of Public Policy, University of Maryland at College Park
JEL classification: D31, N30
Key words: global inequality, history, inequality extraction ratio
Number of words: around 6,900
1
Paper presented at the XV World Economic History Congress, Utrecht, May 3-8, 2009. I am grateful to
Alberto Chilosi for the discussion of the issues raised in the paper, and to Daron Acemoglu, Peter Lambert
and Peter Lanjouw for very useful comments. The views expressed here are author's own views and
should be attributed to the World Bank or any affiliated organizations.
Introduction: Pre-industrial global inequality
The studies of global, and a fortiori, global pre-industrial inequality are a relatively recent
phenomenon and they are few in number. Obviously, the reason is the lack of household
survey data that are needed to estimate global inequality, that is, income distribution
across all individuals in the world. The lack of household surveys and their variable
quality are problems that plague even contemporary studies of global inequality. They
are much more severe for studies of past inequality. But even the very concept of global
inequality--that is, of measuring and comparing incomes of (theoretically) all individuals
in the world--is a new one, both because the idea of such a study had to wait for a more
advanced stage of globalization to take hold, and because it crucially depends on the
availability of purchasing power parity estimates that are needed to convert incomes
expressed in national currency into a single global numeraire.
There are only two long-run empirical historical studies of global inequality. The first and
seminal work was done by François Bourguignon and Christian Morrisson in their 2002
American Economic Review paper which estimated global inequality from 1820 to 1992.
The estimates were made at more or less regular 20-year intervals. The Bourguignon-
Morrisson approach relied on two building blocks. The mean incomes of countries were
taken from Maddison (2004 or earlier) while 33 income distributions of uneven quality
and coverage were put together by Christian Morrisson to represent various parts of the
globe. "Similar" countries were allocated the same income distribution, coming from a
country for which such data were available. This has, for obvious reasons, led to many
simplifications. In addition, Bourguignon and Morrisson used in many cases the 20th
century distributions to "interpolate" (backward predict) the 19th century distributions for
the countries for which 19th century data were unavailable. Thus, the number of data
points (fractiles of the distributions) which they show for each benchmark year, say,
1820, 1850 etc. (33 "countries" times 11 fractiles 2) are not all really independent and
2
For 33 "representative" distributions, Bourguignon and Morrisson give 11 data points per country (nine
bottom deciles and two top ventiles). However, these are the already "processed" data and it is not clear
how many actual independent data points the authors had. For example, if only a Gini is available for a
given country/year and the authors assume a lognormal distribution, then there is not a single fractile
2
contemporary data points but estimates based on posterior data.3 Although their approach
was in several respects less than ideal, it was, at that time, perhaps the only possible since
historical income distributions are so scarce.
More recently, Baten, Foldvari, van Leeuwen, and van Zanden (2009) [in the rest of the
text BFLZ] have expanded and improved on the Bourguignon and Morrisson approach by
using for the countries for which actual income distribution data were lacking either (i) an
estimate of inequality based on the evolution of the unskilled wage/GDP ratio,4 or (ii) by
substituting for the missing income distributions, the data on the distribution of individual
heights. For (i), if unskilled wage-to-GDP ratio increases, the assumption is that income
inequality declines; for (ii), if there is a strong correlation between distribution of
individual heights and distribution of income, then we can "enrich" the dataset on
countries' income distributions by adding the data on countries for which we possess the
distributions of heights.5 In that way, the Bourguignon-Morrisson "backward projections"
are not used at all. The other building block of the exercise, the reliance on Maddison's
GDP per capita data, remained.
In this paper, I proceed to do three things. First, I use social tables from thirteen 18th and
19th century countries to estimate global inequality for the early 19th century. Social
tables have not been used for such a purpose before. Second, I present a story of global
inequality between the beginning of the 19th and the beginning of the 21st century that at
its two end-points relies on my own estimates, and uses Bourguignon-Morrisson or BFLZ
estimates for the years in-between. Third, I apply the concept of the inequality extraction
ratio (used earlier by Milanovic (2006), and Milanovic, Lindert and Williamson (2009)
within country-wide framework) to the global scale. In other words, I ask how close was
global inequality to its maximum feasible amount during the last two centuries. I
conclude the paper with some speculative notes.
datum, but just an overall statistic like the Gini, available. It is also possible, that, basing themselves on
published quintiles, Bourguignon and Morrisson estimated deciles.
3
The point was made by Baten, Foldvari, van Leeuwen, and van Zanden (2009)
4
The approach was pioneered by Williamson (1998). It was used most recently by Prados de la Escosura
(2008).
5
The approach was introduced by Baten (2000).
3
1. Global inequality in the early XIXth century
The data. Let us start with the two building blocks. For GDP per capita, I too use
Maddison's data for all countries for which they are available. I do this, to some extent,
faute de mieux because Maddison's data may be in the need of serious revisions on
account of new, and for China, India, Indonesia, etc., dramatically different, estimates of
the domestic price levels by the 2005 International Comparison Project. The upward
revisions of domestic price levels led to the corresponding reduction of these countries'
current PPP (purchasing power parity) "real" incomes. This level change then
"percolates" (carries over) to the historical income levels which are calculated by
applying past domestic real growth rates to the 2005 level.6 However, since these
revisions have not yet been done by Maddison or anyone else (and they would need to be
massive), I use Maddison's 2004 GDP per capita data expressed in Geary-Khamis 1990
international dollars.
The second building block, the income distribution data, comes from the social tables for
13 countries that have been calculated by different authors and put together within a
single framework by Milanovic, Lindert and Williamson, MLW, (2009). The social
tables are our unique source of information about income distribution in preindustrial
societies where neither household surveys nor tax censuses were conducted. Following
upon the first one created by Gregory King for England and Wales in 1688, social tables
list salient social classes and give estimates of their average income (by class) and
number of people or households who belong to it. Some are more detailed than others,
and cover the entire range of the of income pyramid, from the top (e.g. high nobility) to
the bottom (vagrants and beggars). Others are, of course, more parsimonious or simple
and may include just a few classes (say, nobility, merchants and urban population, and
farmers). MLW (2009) studied preindustrial inequality using thirty such social tables,
some of which were created by the contemporary authors and others by economic
historians. (Detailed explanation of all social tables is available in an annex to MLW
paper.)
6
See Milanovic (2009).
4
For the "early" 19th century I use the "time window" of 1750-1880. The time window is
wide. This is due to the fact that, in order to have a sufficiently comprehensive coverage
of the world, I need to include both India and China. Now, the social table for the Moghul
India is available for the year 1750, while the first social table for China is for the year
1880. The dates of these two social tables therefore frame our time window. In-between,
from Europe, I have social tables from Old Castille 1752, France 1788, England and
Wales 1801, the Netherlands 1808, and Kingdom of Naples 1811; from Latin America, I
have Nueva Espaa (Mexico) 1790, Chile 1861, Brazil 1872 and Peru 1876. Finally,
there is an additional social table from Asia (Java 1880), and one from Africa (Maghreb
1880).
In reality, as this list makes clear, the future advanced (developed) countries have their
social tables up to the early 19th century only. That was intentionally done in MLW
paper, which dealt with pre-industrial inequality, so as to limit the investigation to not yet
industrialized countries. As is conventionally believed, after the end of the Napoleonic
wars, Great Britain, France, Belgium and the Netherlands were already engaged in
industrialization. But for other countries, MLW collected social tables up to a much later
date (since these countries were still preindustrial). In the context of this paper, it means
that one can argue that treating the whole sample as giving a snapshot of pre-industrial
global inequality, around early to mid 19th century, does not involve a significant bias.
This is because GDP per capita of countries that enter our sample at later dates (the three
Latin American countries, Maghreb, Java and China) registered no appreciable economic
progress between the early 19th century and 1860-1880 when they enter the sample.
According to Maddison (2004), China's GDP per capita decreased from $PPP 600 in
1820 to $PPP 530 in 1870 (no datum for 1880 is given). For Indonesia, the change was
from $PPP 612 in 1820 to $PPP 654 in 1880. For Brazil, it was from $PPP 647 in 1820 to
$PPP 718 in 1870. Since most of global inequality after 1820 was driven by fast growth
of the industrializing nations while economies and income distributions of other nations
were basically stagnant between the early 19th century and 1870-1880 when they enter
5
the sample, we can assume that our sample gives a reasonable snapshot of global
inequality around 1820.
The social tables from the period 1750-1880 include 650 million people. According to
Maddison, total world population moved from almost 1 billion in 1820 to 1.1 billion in
1850 to 1.2 billion in 1870. Therefore an average population at any point between 1750
and 1880 can be estimated at around a billion. Our time-window therefore comprises
around 2/3 of the world population living at any point between 1750 and 1880.
How are average social group incomes converted into equivalent 1990 PPPs? The 13
social tables that we use have in total 591 social groups or classes. That means that we
have average incomes, expressed in national currencies, for 591 social groups. (One such
social table for England and Wales 1801-03 is given in the Annex.) These national
currency income per social group are converted into 1990 PPP dollars using (i)
Maddison GDP per capita data and, (ii) for the countries for which Maddison's data are
unavailable, the ratio between average income and the subsistence minimum with the
latter priced at $PPP 300 per year. According to the first method, the social class income
estimates are made by linking overall national currency mean income (calculated across
all social groups) to GDP per capita in 1990 international prices from Maddison. To
explain: from the social table for (say) Brazil in 1872, we calculate that the average per
capita income is 311 milreis. From Maddison's (2004) GDP per capita data, we know
that the estimated GDP per capita for Brazil in 1872 is $PPP 721. By linking the two, we
obtain the conversion ratio of 1872 milreis into 1990 international dollars (1 milreis is
worth $PPP 2.3 of year 1990). This then enables us to directly convert average milreis
income of every social class into its 1990 $PPP equivalents. For some data prior to 1820,
the procedure is different. When we do not have Maddison's GDP per capita data, we
need to get an estimate of the subsistence minimum in local currency (of the time). Thus,
for example for the Kingdom of Naples 1811, the estimated subsistence minimum is 31
ducats per capita annually (from Melanima 2000). Since the subsistence minimum is by
assumption priced at $300 PPP dollars at 1990 prices, we again directly get the
conversion factor (1 ducat from year 1811 = $PPP 9.67 in year 1990). Using this
6
conversion factor, we convert mean contemporary ducat incomes of each social class into
1990 $PPP equivalents.
We thus obtain $PPP-equivalent average incomes for all 591 social groups that are
included in our sample. The number of groups and their population sizes vary between
the countries. The number of social groups ranges from only 3 for China in 1880 and
Nueva Espaa in 1790 to 375 for Brazil 1872. The average number of social groups per
country is 45 (without Brazil, the average number of groups drops to 18). On average,
therefore the number of groups is sufficiently large to provide a reasonable estimate of
overall inequality within each nation. 7Although a small number of groups biases the
national Gini downward, the bias need not be strong if the social structure of a society is
not very complex. For example, if most of peasants lived at, or near, the subsistence
minimum in China around 1880, then the fact that we have only three social groups for
China, need not imply a strong downward bias to the calculated inequality. (The
presumption is also that the authors of social tables divided each society into salient and
sufficiently income-differentiated groups, so that most of country's inequality is captured
by income differences between social groups.)
Global inequality around 1820. The average income for our sample is $PPP 600. The
country with the highest mean income is England and Wales 1801-03 with $PPP 2000,
the country with the lowest, Moghul India in 1750 with $PPP 530.
Inequality indices for the sample are given in Table 1. The global Gini works out as 38.5.
Table 1 also compares this result with Bourguignon and Morrison calculations for 1820.
The Gini of 38.5 is significantly lower than the Bourguignon-Morrison value of 50. An
obvious reason is smaller coverage of our dataset. As mentioned above, it provides the
coverage for 2/3 of the world population that has, on average, lived during that period.
But if for all the missing countries, we supplement our data with the data from
7
However, for the discussion of this point see Milanovic, Lindert and Williamson (2009).
7
Bourguignon and Morrisson (16 countries)8, we increase the coverage to about 90
percent, the number of independent data points to 767, and the global Gini goes up to
43.3. This will be our estimate for the early 19th century global inequality. It is not far
from the BFLZ (2009) estimate of 47 (see their Table 4). As I shall argue below,
Bourguignon and Morrisson estimate of Gini 50 for 1820 seems implausibly large.
In comparison with today's inequality, global inequality in the period 1750-1880 was
much lower. The most recent global inequality estimate, calculated from individual
household survey data around year 2002, is 65 Gini points, using the "old" PPPs which
are based on the same ("old") benchmark as the 1990 PPPs used by Maddison. If we use
the more recent PPP values (from the 2005 International Comparison Project), the global
Gini is 70.7. The increase is due to a significant reduction of GDPs per capita or average
household incomes for China, India and several other Asian countries (see Milanovic,
2009).
It is interesting to focus on the highest incomes in our sample. Incomes above $PPP
70,000 per capita, which would place such individuals into the top global percentile
today, are registered in the Netherlands, Java (which was a Dutch colony then), Chile and
(a practically negligible number) in Brazil. The total number of people with such high
incomes is minute however. It was less than 5,000 (out of 650 million people). Yet it is
clear that enormously rich people, by today's standards, lived then too.
8
The "countries" are Austria-Czechoslovakia-Hungary, Australia-Canada-New Zealand, the Balkans, Ivory
Coast-Ghana-Kenya, Germany, Egypt, Japan, Korea-Taiwan, Nigeria, Philippines-Thailand, Poland,
Russia, Scandinavia, Turkey, USA and South Africa.
8
Table 1. Global (Concept 3) inequality in early 19th century
This paper Bourguignon and BFLZ (2009)
Morrisson (2002)
1750-1880 1750-1880 Countries 1820 1820
Countries with social tables plus
with social distribution data from
tables only BM (year 1820)
(1) (2) (3) (4)
Gini 38.5 43.3 50.0 47.0
Theil (0) 60.9 57.9 52.2 n.a.
Average income of 600 646 652* 687
population included (in
1990 $PPP)
Total population 650 861 1057* 921
included (in m)
Population coverage (%) ~66 ~90 ~100 >90****
Number of countries*** 13 29 33 40
Number of independent 591 <767 <<363** n.a.
data points
Note: The difference in total population in Columns (2) and (3) stems from the fact that countries with
social tables enter population in column (2) with their actual populations in the year when the social table
was created while in Column (3) they enter with their populations in year 1820. Thus in Column (2) India's
population is 182 million and in Column (3) it is 209 million.
* Calculated directly from the Bourguignon-Morrisson tables, Data_WD19.xls (supplied by the authors
separately from the paper). The 100 percent coverage by Bourguignon and Morrisson has to be taken with a
grain of salt since the data were "forced" (through generous use of estimates) to cover 100 percent of the
population.
** See footnote 2 above.
*** The number of countries is not fully comparable. For example, Bourguignon and Morrisson, treat
Bangladesh/Pakistan and India as two countries; we treat them as one as the 1750 data refer to the entire
subcontinent.
*** BFLF (Table 4) give 88 percent for their coverage but that number seems to be based on a somewhat
higher estimate of the world population in 1820 than we use here.
9
2. The changing composition of global inequality, 1820-2002
While the social tables and (obviously) the survey data for the early 19th century are not
fully available so that global inequality must always be estimated quite approximately,
Maddison's GDP data allow us to compute with much more precision Concept 2
inequality. Concept 2 or international population-weighted inequality is an inequality
index computed across GDPs per capita of countries at a given point in time, where each
country's GDP per capita is weighted by country's population (see Milanovic, 2005).
Concept 2 and Concept 3 (or global) inequality are, in the case of Gini, linked as in
relation (1). Concept 2 inequality also represents the between component of global
inequality. This is inequality that would exist if each individual had mean income of
his/her country, i.e., all individual country distributions were egalitarian. The within
component (the part of global inequality due to income inequalities within each country)
is the rest of expression (1).
1 n n n
Global inequality =
( y
i j i
j yi ) pi p j Gi i pi L
i
(1)
Concept 2 inequality
where yj = mean income or GDP per capita of country j, pj = population share of country
j, j = income share of country j (country j-th share in global income), = global average
per capita income, and L = overlap term (which can be treated as part of the within
component; it is greater than zero any time there are people from a poorer country that
are better off than some people from a mean-richer country).
The difference between the Concepts 2 and 3 consists of intra-national inequality or, in
other words, of the within component. Today, the between component--on account of
huge differences in mean incomes between the countries--represents at least 85 percent
of global inequality. 9 But was this the case in the past?
9
See Milanovic (2005).
10
Table 2 provides Concept 2 computations for four dates in the 19th century for which
Maddison provides a sufficient number of countries' GDPs per capita. We focus on years
1820 and 1870 when Maddison's data provide an almost full coverage of the world.
Between these two dates, the Gini coefficient more than doubles from about 15 to 32.
This reflects the well known phenomenon of income divergence that started in the 19th
century. Concept 2 inequality continued to rise throughout the beginning of the 20th
century, then stabilized at a rather high plateau of 55-60 Gini points between the end of
World War II and fairly recently It has been decreasing in the past 20 years thanks to
high growth rates of China and India.10
As the last two columns in Table 2 show, today's Concept 2 international inequality can
be estimated at 60 to 63 Gini points, depending on whether we use GDPs per capita or
survey means. This is some 7 Gini points higher than what we get when we use "old"
PPPs. As already mentioned, this is because the new PPPs imply lower real incomes for
China, India, Indonesia and a number of other Asian countries.
What is striking is not solely that Concept 2 inequality was much lower in 1820 than now
but that the composition of global inequality was so much different.11 Using our estimate
of global inequality in the early 19th century of around Gini 43 points, we see that
Concept 2 inequality represented then only 35 percent of global inequality: 15.2 Gini
points out of 43 Gini points. (If we use Theil, the percentage is even smaller.) Today
when global inequality is about 65-70 Gini points, 12 Concept 2 inequality accounts for
80 to 90 percent of global inequality measured by the Gini (see line 10 in Table 2). Using
the Theil index, the share of population-weighted international inequality rises from 8
percent in 1820 to between 61 and 74 percent now (see the last line in Table 2).
10
This can be seen if we compare the data for 1980 and the first column for 2002 which is based on "old"
PPPs (see Table 2).
11
It should be noted that in the 19th century, we calculate Concept 2 inequality across only 60 countries
while today we do it over twice as many. This imparts an upward bias to the latter.
12
See Milanovic (2009). The "correct" 2002 global inequality is 70 Gini points, but I also use Gini of 65
derived from the "old" PPPs because of compatibility with Maddison's historical data based on the "old"
PPPs.
11
Table 2. Concept 2 international population-weighted inequality and global inequality
Using Maddison's GDP per capita and 1990 PPPs Using WDI Using Using WDI
GDPs and household GDPs and
"old" survey means 2005
benchmark and 2005 benchmark
PPPs benchmark PPPs
PPPs
1820 1850 1870 1913* 1929 1950 1960 1980 2002 2002 2002
(1) Concept 2 Gini 15.2 25.9 31.9 44.3 48.0 55.0 54.0 56.8 52.6 63.0 59.9
(2) Concept 2 Theil 4.55 12.0 17.1 32.6 39.3 54.4 53.5 62.7 50.6 77.2 69.2
(0)
(3) Global average 689 916 911 1,599 1,941 2,111 2,778 4,520 7,099 3,665 8,123
income (in $PPP)
(4) Total population 941 623 1,178 1,666 1,775 2,518 3,030 4,423 5,775 5,802 6,004
included (in m)
(5) Estimated world 1,057 1,201 1,266 1,719 2.042 2,518 3,030 4,423 6,172 6,172 6,172
population
(6) Population 89 52 93 97 87 100 100 100 94 94 99
coverage (4)/(5)
(in %)
(7) Number of 53 24 63 66 53 141 141 141 114 120 153
countries
(8) Global inequality 43 53.2 56.0 61.0 61.6 64.0 63.5 65.7 65.4 70.7 70.7
(Gini points) (50) (53) (58) (62) (65) (64) (65)
(9) Global inequality 58 48.5 54.4 66.8 69.0 77.5 76.6 85.0 82.5 104.8 104.8
(Theil 0)
(10) Share of
between inequality in 35 49 57 73 78 86 85 86 80 89 85
global Gini (1)/(8)
(11) Share of
between inequality in 8 25 31 49 57 70 70 74 61 74 66
global Theil (2)/(9)
Sources: All Concept 2 statistics calculated from Maddison's 2004 data, except for 2002, calculated from World Development Indicators (WDI) and World Income Distribution (WYD) database.
Estimated global population from Bourguignon and Morrisson (2002, Table 1).Global inequality estimates (line 8) for the period 1850-1980 are from Bourguignon and Morrisson (on top) and from
Baten, Foldvari, van Leeuwen and van Zanden (between brackets). Global inequality for the year 1820 as calculated here; for 2002, from Milanovic (2009).* Bourguignon and Morrisson population
and global inequality data are for the year 1910. [2002 values calculated from my global_new.dta, except 2002 with 1990 PPPs calculated from world2002.dta.]
12
We can summarize the results by writing out the composition of global inequality
in the early 19th and 21st century as follows:
Early 19th century: Inequality between individuals in the world: Gini around 43.
= 35 percent due to differences in average country incomes (15 Gini points)
+ 65 percent due to within-national income differences (28 Gini points).
Early 21st century: Inequality between individuals in the world: Gini around 70.
= 85-90 percent due to differences in average country incomes (60-63 Gini)
+ 10-15 percent due to within-national income differences (7-10 Gini points).
These two simple relationships describe the change that has occurred globally during the
last two centuries: inequality between individuals is much higher today than 200 years
ago, but more dramatically--its composition has totally reversed: from being
predominantly driven by within-national inequalities (that is, by what could be called
"class" inequality), it is today overwhelmingly determined by the differences in mean
country incomes (what could be called "location" or citizenship-based inequality). This
latter, "locational", element was "worth" 15 Gini points in the early 19th century; it is
"worth" 60-63 Gini points today.
The evolution of the share of between inequality in global inequality is shown in Figure
1. The calculations are based on Milanovic's estimates of global inequality for 1820 and
2002, and Bourguignon and Morrisson's for all points in-between. With BFLZ estimates
of global inequality, which are for the 19th century lower by about 3 Gini points than
Bourguignon and Morrisson's (see Table 2), the share of between-country inequality in
the 19th century would be slightly higher. The trend would not be affected however.
13
Figure 1. Share of between-country inequality in global inequality:
Selected years, 1820-2002 (in percent of global Gini)
100
80
60
40
20
0
1820 1850 1870 1913 1929 1950 1960 1980 2002
Note: Based on Milanovic's estimates of global inequality for 1820 and 2002, and Bourguignon
and Morrisson for all points in-between. Concept 2 inequality is calculated from Maddison (2004)
data. Source: See Table 2.
14
3. Did global inequality extraction ratio decline?
Definition of the inequality extraction ratio. MLW (2009) have developed the concept of
the inequality possibility frontier. Simply put, this is the maximum Gini that is
achievable at a given level of mean income provided that all population but an
infinitesimally small elite live at least at the subsistence minimum. To understand the
concept intuitively, imagine a society whose mean income is just barely above
subsistence. Then the maximum Gini, however small the elite (at the extreme, the elite
could be composed of one individual), cannot be high because a vast majority (99.999%
etc.) of bilateral income comparisons that enter into the creation of Gini will yield zeros
(since all other individuals but the elite have the same, subsistence, income). As the
average income grows, the constraint on the maximum Gini is relaxed. The inequality
possibility frontier, the locus of maximum Ginis as mean income rises, is given by
equation (2):
1
G ( )* (1 ) (2)
where = average income of a community expressed in terms of subsistence, G* =
maximum feasible Gini, and = the share of the elite in total population. Clearly as 0,
(2) simplifies to:
1
G ( )* (3)
Thus, for example, if the average income of a community is twice the subsistence, the
maximum feasible Gini will be 50 ((2-1)/2 expressed in percentage terms). But if, as in
modern rich societies, the average income is some 100 times the subsistence, than the
maximum feasible Gini is 99, very close to what we tended to regard (before the
introduction of G*) as the maximum Gini regardless of average income level.
15
A similar calculation can be done for Theil(0). For Theil(0), the maximum feasible
inequality is:
T ( )* ln( ) (4)
The ratio between the actual (measured) Gini, G, and the maximum feasible Gini (G/G*)
gives the inequality extraction ratio which can be interpreted as the share of maximum
inequality extracted by the elite. (The same, of course, holds for the T/T* ratio.) Clearly,
as that percentage increases, the elite can be said to have been more successful in
extracting the surplus. The approach has been applied by MLW to 30 pre-industrial
societies, running from the Imperial Rome in year 14 to Siam and Kenya in 1927.13 The
average extraction ratio over these 30 societies is 75 percent. For seven societies (six of
them colonies), the extraction ratio was around 100 percent--that is, the inequality was
pushed close to its maximum level, compatible with the physiological survival of the
society. (Note that the Gini can even exceed the maximum if some people temporarily
survive at less than the subsistence. In the medium term, the extraction ratios above 100
percent are possible only if population decreases.)
The stylized, but also very consistent picture, for modern developed societies is that of a
decreasing inequality extraction ratio with rising mean per capita income. For example,
for England and Wales (later United Kingdom) for which we have the most complete
data series, the inequality extraction ratio drops from 70 percent in 1290 (when England's
was 2.1) to about 55 percent in 1688 and 1759 ('s of respectively 4.7 and 5.9), briefly
increases to 60 percent in 1801 (=6.7), and then begins a more or less steady decline to
38 percent today (=66). 14 In other words, over the last century, inequality in developed
countries generally decreased, or even when it went up, it increased less than the
maximum feasible inequality.
13
And quite exceptionally India in 1947, at the independence from Britain.
14
See MLW (2009, Table 2).
16
Global results. Now the question can be asked: Can the same methodology be applied
globally? The answer is yes, but with one important caveat. When this methodology was
applied to individual countries, it made sense also in implicitly assessing how rapacious
or successful was the elite in extracting the surplus. Combined with an analysis of class
structure of a given society (e.g., the share of the middle classes), it provided an insight
into the social and political structure of a polity. At the global level, however, there is no
single elite and no single government (then or now), and the application of the
methodology makes sense certainly in an accounting sense, but perhaps much less as a
tool that would enable us to gain further insight into the social structure of a given society
(with society being here "the globe"). Yet, perhaps depending on one's perspective (e.g.,
taking a "world-systems" perspective) the global inequality extraction ratio could be seen
as more than an accounting tool. In effect, the results obtained below will, to some extent,
lead us to pose, if not to answer, that question.
The "accounting" part is useful because we may want to know whether the low measured
Gini in the early 19th century (around 43 Gini points) can in part be "explained" by the
overall low level of global income. Or differently, whether the increase in global
inequality that we observe in the last two centuries is associated with the removal of the
constraint that low income sets to the maximum feasible inequality.
Using the data on global average income (GDP per capita) from Table 2 (line 3) and
assuming the subsistence minimum to be $PPP 300 (as in Milanovic, Lindert and
Williamson, 2009) we can directly calculate G* and T* (see Table 3).
17
Table 3. Global inequality extraction ratio, 1820-2002
Using Using Maddison GDP per capita at 1990 PPPs, and Bourguignon-Morrisson global inequality Using 2002
Maddison estimates WDI GDPs and
GDP data 2005 benchmark
and PPPs and
Milanovic
global
Milanovic
inequality global inequality
estimate estimate
1820 1850 1870 1913 1929 1950 1960 1980 2002
(1) Global average GDP
per capita (in $PPP)
689 916 911 1599 1941 2111 2778 4520 5886
(2) Global average
income to subsistence 2.30 3.05 3.04 5.33 6.47 7.04 9.26 15.07 19.62
(ratio)
(3) Maximum feasible
Gini (in %)
56 67 67 81 85 86 89 93 95
(4) Maximum feasible
Theil (in %)
83 112 111 167 187 195 223 271 298
(5) Estimated global Gini 43 53.2 56.0 61.0 61.6 64 63.5 65.7 70.7
(6) Estimated global
Theil(0)
58 49 54 67 69 78 77 85 105
(7) Estimated global Gini
inequality extraction ratio 77 79 83 75 73 75 71 70 73
(5/3; in %)
(8) Estimated global
Theil inequality
extraction ratio (6/4; in
70 43 49 40 37 40 34 31 35
%)
Sources: 1820-1980 global average income calculated from Maddison's data; global Gini from Maddison and Bourguignon (2002) who base themselves on Maddison's data (all
data in 1990 PPPs). 2002, global income calculated from World Development indicators (in 2002 PPPs, based on the benchmark 2005 ICP). Global inequality for 2002 calculated
from Milanovic World Income Distribution (WYD) database; all in 2002 PPPs, based on the benchmark 2005 ICP. Therefore, the PPPs used for year 2002 differ from Maddison's
1990 Geary-Khamis PPPs by US CPI increase between 1990 and 2002 (38 percent) as well as by major revisions in relative price levels that occurred in 2005 International
Comparison Project. The data for 2002 ($PPP 5886) correct for the former (that is, formally they are expressed in 1990 international prices) but cannot correct for the latter.
18
The striking fact, revealed by these numbers, is that the Gini-based global inequality
extraction ratio today is at about the same level as in the early 19th century. If we use
Bourguignon and Morrison's historical data, it could be said to have remained stable over
the last two hundred years with the exception of a moderate tick up around 1850-1870
(Figure 2).15 With BFLZ (2009) data, the Gini inequality extraction ratio in 19th century
is somewhat higher, and accordingly is higher too than it is today. If we use the Theil-
based inequality extraction ratio, today's values are significantly lower than those of the
early 19th century, but after 1910, there is little downward movement (Figure 3). For the
last one hundred years, we do not see any compelling evidence that there was a decline in
the global inequality extraction ratio, measured either by the Gini or Theil index. What
has happened is that the actual global Gini has risen pari passu with the maximum
feasible Gini thus broadly keeping the inequality extraction ratio constant (see Figure
4).16
Combining this with the earlier finding that the composition of global inequality has
shifted from being "caused" by internal factors, like domestic income distribution, to
"external" like differences in mean country incomes, we can conclude that the main
"inequality extractors" today are not (within)-national elites, but an elite which is
basically composed of the citizens of rich countries.
15
The result also shows why the Bourguignon-Morrisson estimate of Gini 50 for global inequality in 1820
is implausibly high. Using their own global mean income of $PPP 652, it can be shown that the maximum
feasible Gini could be only 54 points and that the inequality extraction ratio would have to be greater than
90 percent. This cannot be totally rejected but seems implausibly high in light of the results for the
subsequent years.
16
The "extraction" levels are quite different depending on whether we use Gini- or Theil-based measures.
However, our concern here is not with the levels as such but with changes in the levels and in that respect
both Gini- and Theil-based extraction ratios are in agreement for the period of the last one hundred years.
Note that the Theil index is much more sensitive to the extreme values than the Gini. Thus the maximum
feasible Theil increases faster as goes up than the maximum feasible Gini. It can be readily verified from
equations (3) and (4) that the slope of Gini-based Inequality Possibility Frontier is 1/2 while the slope of
Theil-based Inequality Possibility Frontier is 1/. Thus the former is more concave (see Figure 4).
19
Figure 2. Global Gini inequality extraction
ratio 1820-2002 (in percent)
90 100
80
70
60
50
40
30
20
10
0 BFLZ
1800 1850 1900 1950 2000
year
Note: Bars based on the data from Table 3. Dots based on global inequality calculations of Baten,
Foldvari, van Leeuwen, and van Zanden (2009). [From summary_utrecht.dta. ]
Figure 3. Global Theil inequality extraction
ratio 1820-2002 (in percent)
90 100
20 30 40 50 60 70 80
global extraction ratio -- theil
10
0
1800 1850 1900 1950 2000
year
.
Source: Table 3.
20
We can summarize the change that occurred over the last century as follows:
Early 20th century: Global mean income was 5.3 times the
subsistence. Maximum feasible global Gini was 81 points
while the actual global Gini was 61. Thus, actual inequality
"exhausted" ¾ of maximum inequality. (Using Theil index
that proportion was 40 percent.)
Early 21st century: Global mean income is 19.6 times the
same physiological subsistence. Maximum feasible global
Gini is 93 while the actual global Gini is around 70. Thus,
actual inequality "exhausted" (still) some ¾ of maximum
inequality. (Using Theil index that proportion is 35
percent.) Whether we use Gini or Theil to calculate global
inequality indices, the level of inequality extraction has
remained remarkably stable between 1900 and 2002.
21
Figure 4. Global inequality frontier and global inequality, 1820-2002
Gini Theil
100
400
inequality possibility frontier
80
300
2002
1950 1960 1980
1913929
1 inequality possibility frontier
60
g lo b a l g in i
global theil
1870
1850
200
1820
40
100
2002
20
1980
1950 1960
1
1913929
1820
1870
1850
0
0
1 6 11 16 21 26 1 6 11 16 21 26
global income to subsistence global income to subsistence
Note: All global average incomes, including for 2002 expressed in 1990 PPP (see note to Table 3). [From summary_utrecht.dta. ]
22
Why is world income distribution such that during the last century, the rich have
extracted a constant of about 70 percent of global (Gini) maximum feasible inequality?
This is a question that, due to its complexity, cannot be answered in this paper. However,
regarding the future we may hazard some projections. Since global mean income is
already quite high, almost 20 times the subsistence, the increase in the maximum feasible
Gini will be quite limited. This means that the only venue for the reduction in global
inequality extraction ratio remains an effective reduction in measured global inequality.
For it to go down, inter-country differences in mean incomes must decrease, and in
particular those between poor and rich populous countries. Thus, both global inequality
and global inequality extraction ratio fundamentally depend on what I called elsewhere
(Milanovic 2005), the relationship within the triangle of China, India and the United
States. If the mean-normalized absolute distance between China and India, on the one
hand, and the US, on the other, decreases, then we are likely to observe favorable
developments in this century. 17
17
Note that for the Gini to go down, it is not sufficient that China grows faster than the US. China must
grow sufficiently fast to reduce the absolute distance, normalized by world mean income, with the United
States. Suppose that the world mean income is constant, and US grows by 1 percent per capita per annum.
For the US-China Gini component to be reduced, China needs to grow by 10 percent per capita per annum
(since its mean per capita income is about 1/10th of the US level).
23
4. Conclusions
Several conclusions can be made.
1. Global inequality around 1820 was probably 43-45 Gini points rather than 50 points as
estimated by Bourguignon and Morrisson (2002). The latter value would have implied an
unlikely high inequality extraction ratio of around 90 percent.
2. Global inequality increased from 43-45 Gini points in the early 19th century to some
65-70 Gini points today. Even more remarkable is that the composition of global
inequality changed from being driven by class differences within countries to being
driven by locational income differences (that is, by the differences in mean country
incomes). The latter accounted for only 15 Gini points around 1820, but account for more
than 60 Gini points today.
3. Although the inequality extraction ratios have steadily and often dramatically
decreased within individual countries as they developed in the course of the last two
centuries (see MLW, 2009), the global inequality extraction ratio has only mildly
declined since its 19th century level and has remained broadly stable in the last 100 years.
4. This means that global inequality has increased at about the same rate as the maximum
feasible inequality (the latter's increase being determined by the rise in mean global
income), leaving the (Gini-based) global inequality extraction ratio at around 70 percent.
5. The implication of (a) changing composition of global inequality, and (b) stable
inequality extraction ratio is that the main "inequality extractors" today are citizens of
rich countries rather than individual national elites as was the case 200 years ago.
24
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"World Income Inequality, 1820-2000", mimeo. Available at
http://www.wehc2009.org/programme.asp?day=1&time=2.
Bourguignon, Francois and Christian Morrisson (2002), "The size distribution of income
among world citizens, 1820-1990", American Economic Review, September, pp.
727-744.
Maddison, Angus (2004), "World population, GDP and GDP per capita, 1-2000 AD".
Available at http://www.eco.rug.nl/~Maddison/
Maddison, Angus (2007), Contours of the world economy, 1-2030: Essays in macro-
economic history, Oxford: Oxford University Press.
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http://www.helsinki.fi/iehc2006/papers3/Malanima.pdf
Milanovic, Branko (2005), Worlds Apart: Measuring International and Global
Inequality, Princeton: Princeton University Press.
Milanovic, Branko (2006), "An estimate of average income and inequality in Byzantium
around year 1000," Review of Income and Wealth 52 (3).
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note on global inequality calculations using the 2005 ICP results", International
Review of Health Services, No. 3, pp. 421-429..
Milanovic, Branko, Peter H. Lindert and Jeffrey G. Williamson (2009), "Preindustrial
inequality", mimeo. Available at http://econ.worldbank.org/projects/inequality.
Previous version published as "Measuring ancient inequality", National Bureau of
Economic Research Working Paper No. 13550 and World Bank Working Paper
No. 4412, November 2007.
Prados de la Escosura, Leandro (2008), "Inequality, poverty and the Kuznets curve in
Spain, 1850-2000", European Review of Economic History, vol. 12, pp. 287-324.
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25
ANNEX: Social table for England and Wales 1801-03
Social group Number of Percentage of Per capita Income in terms
people population income of per capita
(in £ per annum) mean
Paupers 1040716 11.5 2.5 0.11
Persons imprisoned for debt 10000 0.11 6 0.27
Laborers in husbandry 1530000 16.9 6.9 0.31
Hawkers, pedlars, duffers 4000 0.04 8 0.36
Laborers in mines, canals 180000 1.99 8.9 0.41
Vagrants 175218 1.94 10 0.46
Artisans, mechanics, laborers 2005767 22.16 12.2 0.56
Clerks and shopmen 300000 3.31 15 0.68
Freeholders, lesser 600000 6.63 18 0.82
Farmers 960000 10.6 20 0.91
Innkeepers and publicans 250000 2.76 20 0.91
Lesser clergymen 50000 0.55 24 1.09
Dissenting clergy, itinerants 12500 0.14 24 1.09
Education of youth 120000 1.33 25 1.14
Military officers 65320 0.72 27.8 1.27
Common soldiers 121985 1.35 29 1.32
Naval officers 35000 0.39 29.8 1.36
Shopkeepers and tradesmen 372500 4.11 30 1.37
Tailors, milliners, etc. 125000 1.38 30 1.37
Confined lunatics 2500 0.03 30 1.37
Freeholders, greater 220000 2.43 36.4 1.66
Marines and seamen 52906 0.58 38 1.73
Lesser offices 52500 0.58 40 1.82
Engineers, surveyors, etc. 25000 0.28 40 1.82
Merchant service 49393 0.55 40 1.82
Keeping houses for lunatics 400 0.004 50 2.28
Theatrical pursuits 4000 0.04 50 2.28
Liberal arts and sciences 81500 0.9 52 2.37
Law, judges to clerks 55000 0.61 70 3.19
Eminent clergymen 6000 0.07 83.3 3.8
Gents 160000 1.77 87.5 3.99
Shipowners, freight 25000 0.28 100 4.56
Higher civil offices 14000 0.15 114.3 5.21
Lesser merchants, by sea 91000 1.01 114.3 5.21
Building & repairing ships 1800 0.02 116.7 5.32
Warehousemen, wholesale 3000 0.03 133.3 6.08
Manufacturers 150000 1.66 133.3 6.08
Knights 3500 0.04 150 6.84
Esquires 60000 0.66 150 6.84
Educators in universities 2000 0.02 150 6.84
Baronets 8100 0.09 200 9.12
Eminent merchants, bankers 20000 0.22 260 11.86
26
Social group Number of Percentage of Per capita Income in terms
people population income of per capita
(in £ per annum) mean
Spiritual peers 390 0.004 266.7 12.16
Temporal peers 7175 0.08 320 14.59
Total 9053170 100 21.93 1
Source: Milanovic, Lindert and Williamson (2009, Appendix 1).
27