Ancient Inequality
Good Questions, Bad Data
Is inequality largely a
byproduct of the Industrial Revolution? Or, were
pre-industrial incomes as unequal as they are
today? How does inequality in today’s least
developed, agricultural countries compare with
that in ancient, agricultural societies dating
back to the Roman Empire? Did some parts of the
world always have greater income inequality than
others? Was inequality augmented by colonization? These questions have yet to be answered, for want
of sufficient data.
Simon Kuznets was skeptical of attempts to
compare income inequalities across countries when
he was writing in the 1970s. In his view, the
early compilations assembled by the International
Labor Organization and the World Bank referred to
different population concepts, different income
concepts, and different parts of the national
economy. To underline his doubts, Kuznets once
asked (rhetorically) at a University of Wisconsin
seminar “Do you really think you can get good
conclusions from bad data?” Economists with
inequality interests are indebted to Kuznets for
his sage warning.
[1] We are even
more indebted to Kuznets for violating his own
warning when, earlier in his career, he famously
conjectured about his Kuznets Curve based on a
handful of very doubtful inequality observations. His 1954 Detroit AEA Presidential Address mused on
how inequality might have risen and fallen over
two centuries, and theorized about the sectoral
and demographic shifts that might have caused such
movements. Over the last half-century, economists
have responded enthusiastically to his postulated
Kuznets Curve, searching for better data, better
tests, and better models.
As we have said, Kuznets based his hypothetical
Curve on very little evidence. The only country
for which he had good data was the United States
after 1913, on which he was the data pioneer
himself. Beyond that, he judged earlier history
from tax data taken from the United Kingdom since
1880 and Prussia since 1854 (1955:4). For these
three advanced countries, incomes had bec ome less
unequal between the late nineteenth century and
the 1950s. He presented no data at all regarding
earlier trends, yet bravely conjectured that
“income inequality might have been widening from
about 1780 to 1850 in England; from about 1840 to
1890, and particularly from 1870 on in the United
States; and from the 1840s to the 1890s in
Germany” (1955:19). For poor, pre-industrial
countries, he had only household surveys for India
1949–1950, Sri Lanka 1950, and Puerto Rico 1948
(1955:20). These are all bad data judged by the
standards Kuznets himself applied in the 1970s. They are also bad data judged by modern World Bank
standards since those three surveys from the
mid-twentieth century would now be given low
grades on the Deininger-Squire scale assessing the
quality of income distribution data (Deininger and
Squire 1996:567–571). Meanwhile, world
inequalities have also changed. The mid twentieth
century convergence of incomes within industrial
countries that so impressed Kuznets has been
reversed, and the gaps have widened again.
We have reason, therefore, to ask anew whether
income inequality was any greater in the distant
past than it is today. This paper offers five
conjectures about inequality patterns during and
since ancient pre-industrial times. First, income
inequality must have risen as hunter-gathers
slowly evolved into ancient agricultural
settlements with surpluses above subsistence. Inequality rose further as economic development in
these early agricultural settlements gave the
elite the opportunity to harvest those rising
surpluses.
[2] Second, and
surprisingly, the evidence suggests that the elite
failed to exploit their opportunity fully since
income inequality did not rise anywhere near as
much as it could have. While potential inequality
rose steeply over the pre-industrial long run,
actual inequality rose much less. Third, in
pre-industrial times, overall inequality was
driven largely by the gap between the rural poor
at the bottom and the landed elite at the top. The
distribution of income among the elite themselves,
and their share in total income, was only weakly
correlated with overall inequality. Fourth,
ancient pre-industrial inequality seems to have
been lower in crowded East Asia than it was in the
Middle East, Europe, or the world as settled by
Europeans. Only in China (and Singapore) since the
1980s have East Asian national inequalities
matched those of other regions. Yet, it was no
higher in pre-industrial Latin America than in
pre-industrial Western Europe. Fifth, while there
is little difference in conventionally measured
inequality between modern and ancient
pre-industrial societies, there are immense
differences in our new, less conventional measure:
the share of potential inequality actually
achieved today is far less than was true of
pre-industrial times.
Our data are subject to all the concerns that
bothered Kuznets, other economists, and the
present authors. Our income inequality statistics
exploit fragile measures of annual household
income, without adjustment for taxes and
transfers, life-cycle patterns, or household
composition. None of our ancient inequality
observations would rate a “1” on the
Deininger-Squire scale. Yet, like Gregory King in
the 1690s and Simon Kuznets in the 1950s, we must
start somewhere. Section 2 begins by introducing
some new concepts that we use for the analysis—the
inequality possibility frontier and
the
inequality extraction ratio ,
measures of the extent to which the elite extract
the maximum feasible inequality. These new
measures open the door to fresh interpretations of
inequality in the very long run. Section 3
presents our ancient inequality evidence. Section
4 explores the determinants of ancient
inequalities and extraction ratios. Section 5
examines income gaps between top and bottom, and
the extent to which observed inequality change
over the very long run is driven by those gaps as
opposed to the distribution of income among those
at the top or the top’s income share. We conclude
with a research agenda.
The Inequality Possibility Frontier
and the Extraction Ratio
The workhorse for our empirical analysis of
ancient inequalities is a concept we call the
inequality possibility frontier . While the idea is simple enough, it has,
surprisingly, been overlooked by previous
scholars. Suppose that each society, including
ancient non-industrial societies, has to
distribute income in such a way as to guarantee
subsistence minimum for its poorer classes. The
remainder of the total income is the surplus that
is shared among the richer classes. When average
income is very low, and barely above the
subsistence minimum, the surplus is small. Under
those primitive conditions, the members of the
upper class will be few, and the level of
inequality will be quite modest. But as average
income increases with economic progress, this
constraint on inequality is lifted; the surplus
increases, and the maximum possible inequality
compatible with that new, higher, average income
is greater. In other words, the maximum attainable
inequality is an increasing function of mean
overall income. Whether the elite fully exploit
that maximum or allow some trickle-down is, of
course, another matter entirely.
To fix
ideas intuitively, suppose that a society consists
of 100 people, 99 of whom are lower class. Assume
further that the subsistence minimum is 10 units,
and total income 1050 units. The 99 members of the
lower class receive 990 units of income and the
only member of the upper class receives 60. The
Gini coefficient corresponding to such a
distribution will be only 4.7 percent.
[3] If total income about doubles over time to 2000
units, then the sole upper class member will be
able to extract 1010 units, and the corresponding
Gini coefficient will leap to 49.5. If we chart
the locus of such maximum possible Ginis on the
vertical axis against mean income levels on the
horizontal axis, we obtain the
inequality
possibility frontier (IPF).
[4] Since any progressive transfer must reduce
inequality measured by the Gini coefficient, we
know that a less socially segmented society would
have a lower Gini.
[5] Thus, IPF is
indeed a
frontier .
The
inequality possibility frontier can
be derived more formally. Define s=subsistence
minimum, μ=overall mean income, N=number of people
in a society, and ε=proportion of people belonging
to a (very small) upper class. Then the mean
income of upper class people (yh) will be
Equation 1
where we assume as before that the (1–ε)N
people belonging to lower classes receive
subsistence incomes.
Once we document
population proportions and mean incomes for both
classes, and assume further that all members in a
given class receive the same income,
[6] we can calculate any standard measure of
inequality for the potential distribution. Here we
shall derive the IPF using the Gini
coefficient.
The Gini coefficient for n
social classes whose mean incomes (y) are ordered
in an ascending fashion (yj > yi), with
subscripts denoting social classes, can be written
as in equation (2)
Equation 2
where πi=proportion of income received by
i –th social class, pi=proportion of
people belo nging to
i –th social
class, Gi=Gini inequality among people belonging
to
i –th social class, and L=the
overlap term which is greater than 0 only if there
are members of a lower social class
(
i ) whose incomes exceed those of
some members of a higher social class
(
j ). The first term on the right-hand
side of equation (2) is the within component
(total inequality due to inequality within
classes), the second term is the between component
(total inequality due to differences in mean
incomes between classes) and L is, as already
explained, the overlap term.
Continuing with our
illustrative case, where all members of the two
social classes (upper and lower) have the mean
incomes of their respective classes, equation (2)
simplifies to
Equation 3
Substituting (1) for the income of the
upper class, and s for the income of lower class,
as well as their population shares, (3) becomes
Equation 4
where G* denotes the maximum feasible
Gini coefficient for a given level of mean income
(μ). Rearranging terms in (4), we simplify
Equation 5
Finally, if we now express mean income as
a multiple of the subsistence minimum, μ=αs (where
α≥1), then (5) becomes
Equation 6
Equation (6) represents our final
expression for the maximum Gini (given α) which
will chart IPF as α is allowed to increase from 1
to higher values. For example, when α=1 all
individuals receive the same subsistence income
and (6) reduces to 0, while when α=2, the maximum
Gini becomes 0.5(1–ε). Let the percentage of
population that belongs to the upper class be
one-tenth of 1 percent (ε=0.001). Then for α=2,
the maximum Gini will be 49.95 (once again,
expressed as a percentage), we can easily see that
as the percentage of people in top income class
tends toward 0, G* tends toward (α–1)/α. Thus, for
example, for α=2, G* would be 0.5. The
hypothetical IPF curve generated for α values
ranging between 1 and 5 is shown in Figure 1. Figure 1. Derivation of the Inequality
Possibility Frontier
The derivative of the maximum Gini with
respect to mean income (given a fixed subsistence)
is
Equation 7
In other words, the IPF curve is
increasing and concave. Using (7), one can easily
calculate the elasticity of G* with respect to α
as 1/(α–1). That is, the percentage change in the
maximum Gini in response to a given percentage
change in mean income is less at higher levels of
mean income.
The
inequality possibility
frontier depends on two parameters, α and
ε. In the illustrative example used here, we have
assumed that ε=0.1 percent. How sensitive is our
Gini maximum to this assumption? Were the
membership of the upper class even more exclusive,
consisting of (say) 1/50th of one percent of
population, would the maximum Gini change
dramatically? Taking the derivative of G* with
respect to ε in equation (6), we get
Equation 8
Thus, as ε falls (the club gets more
exclusive), G* rises. But is the response big? Given the assumption that mean income is twice
subsistence and that the share of the top income
class is ε=0.001, we have seen that the maximum
Gini is 49.95. But if we assume instead that the
top income group is cut to one-fifth of its
previous size (ε=1/50 of one percent), the Gini
will increase to 49.99, or hardly at all. G* is,
of course, bounded by 50. For historically
plausible parameters, the IPF Gini is not very
sensitive to changes in the size of the top income
class.
The assumption that all members of the
upper class receive the same income is convenient
for the derivation of the IPF, but would its
relaxation make a significant difference in the
calculated G*? To find out, we need to go back to
the general Gini formula given in (2). The
within–group Gini for the upper class will no
longer be equal to 0.
[7] The overall
Gini will increase by επhGh where h is the
subscript for the upper (high) class. The income
share appropriated by the upper class is
Equation 9
and the increase in the overall G* will
therefore be
Equation 10
This increase is unlikely to be
substantial. Consider again our illustrative
example where α=2 and ε=0.001. The multiplication
of the last two terms in (10) equals 0.0005. Even
if the Gini among upper classes is increased to
50, the increase in the overall Gini (ΔG*) will be
only 0.025 Gini points. We conclude that we can
safely ignore the inequality among the upper class
in our derivation of the maximum Gini. Moreover,
note that maximum feasible inequality is derived
on the assumption that the size of the elite tends
towards an arbitrarily small number. That
arbitrarily small number can be one, in which
case, of course, inequality within the elite must
be nil. This inference should not imply a
disinterest in actual distribution at the top;
indeed, we will assess the empirical support for
it in section 5.
The inequality possibility
frontier can also serve as a measure of inequality
with a clear intuitive economic meaning. Normally,
measures of inequality reach their extreme values
when one individual appropriates the entire income
(not simply all the surplus). Such extreme values
are obviously just theoretical and devoid of any
economic content since no society could function
in such a state. That one person who appropriated
the entire income would soon be all alone
(everyone else having died), and after his death
inequality would fall to zero and the society
would cease to exist. The inequality possibility
frontier avoids this irrelevance by charting
maximum values of inequality compatible with the
maintenance of a society (however unequal), and
thus represents the maximum inequality that is
sustainable in the long run. Of course, those at
subsistence may revolt and overturn the elite,
suggesting that the subsistence level is itself
endogenous to more than just equilibrating
Malthusian physiological forces.
[8]
The Data: Social Tables and Pre-Industrial
Inequality
Income distribution data based
on large household surveys are almost never
available for any pre-industrial society. In lieu
of surveys, we derive seventeen of our twenty-nine
estimates of ancient inequalities from what are
called social tables (or, as William Petty called
them more than three centuries ago,
political arithmetick ) where various
social classes are ranked from the richest to the
poorest with their estimated population (family or
household head) shares and average incomes.
[9] Social tables are particularly useful in
evaluating ancient societies where classes were
clearly delineated, and the differences in mean
incomes between them were substantial. Theoretically, if class alone determined one’s
income, and if income differences between classes
were large while income differences within classes
were small, then all (or almost all) inequality
would be explained by the between-class
inequality. One of the best social table examples
is offered by Gregory King’s famous estimates for
England and Wales in 1688 (Barnett 1936; Lindert
and Williamson 1982). King’s list of classes
summarized in Table 1 is fairly detailed (31
social classes). King (and others listed in Table
1) did not report inequalities within each social
class, so we cannot identify within-class
inequality for 1688 England and Wales.
However, within-class inequalities can be
roughly gauged by calculating two Gini values: a
lower bound Gini1, which estimates only the
between-group inequality and assumes within-group
or within-social class inequality to be zero; and
a higher Gini2, which estimates the maximum
inequality compatible with the social tables
grouped data assuming that all individuals from a
higher social group are richer than any individual
from a lower social group. In other words, where
class mean incomes are such that yj > yi, it also
holds true that ykj > ymi for all members of
group j, where k and m are subscripts that denote
individuals. Thus, in addition to between-class
inequality Gini2 includes some within-class
inequality (see equation 2), but under the strong
assumption that all members of a given social
class are poorer or richer than those respectively
above or below them.
[10] (The overlap
component L from equation (2) is by construction
assumed to be zero.) The differences between the
two Ginis are in most cases very small, as the
lion’s share of inequality is accounted for by the
between-class component (see Table 2). This means
that our Ginis will be fairly good estimates of
inequality for (i) class-structured societies and
(ii) societies whose social tables are fairly
detailed, that is include many social classes. If
(i), then the overlap should be expected to be
fairly small, as (say) all members of nobility are
richer than all artisans, and the latter than all
farmers. Similarly, when social tables are
detailed (a topic we discuss below), the
definitions become fairly precise, and the overlap
is less. At the extreme, a social table such that
each individual represents a “social class” would
make the overlap equal to zero.
Our Gini would be downward biased in cases
where social tables present only a few classes but
in reality the social structure is finely
gradated—in that case, both Gini1 and Gini2 would
miss lots of “overlap” inequality. However, we
believe that such cases are unlikely. Why? When
authors of social tables created these tables,
their interest was in the salient income cleavages
they observed around them. If a society was
strongly stratified, it seems likely that these
observers would present estimated average incomes
for only a few groups; if in contrast a society
was less stratified, it seems likely that the
observers would tend to supply estimates for many
more social groups (as King and Massie did for
England and Wales). Thus, the number of social
groups is likely to vary across societies, and the
co-existence of a finely class-gradated society
with a social table containing only a few social
classes is very unlikely.
For two cases (South Serbia 1455 and Levant
1596), we have used Ottoman location-specific tax
surveys. These surveys allow us to estimate mean
income per settlement. In these two cases,
settlements (hamlets, villages, towns) are the
units of observation and building blocks for our
estimates of inequality: they play the same role
played by social or professional classes in all
other cases. Although these two surveys are
methodologically different, the wealth of
information they provide leads us to believe that
their inequality estimation is of similar or equal
quality as the class-based estimations.
[11]
Table 1 lists twenty-nine pre-industrial
societies for which we have calculated inequality
statistics. (Detailed explanations for each income
distribution are provided in the Appendix 1.)
These societies range from early first-century
Rome (Augustan Principate) to India in the year of
independence from Britain in 1947.Since we
assume, somewhat conservatively, an annual
subsistence minimum of $PPP 300,
[12] and with GDI per capita ranging in
our sample from about $PPP 450 to just above $PPP
2000,
[13] α ranges from about 1.5 to 6.8. A
GDI per capita of $PPP 2000 is a level of income
not uncommon today, and it would place 1732
Holland or 1801–1803 England and Wales in the 40th
percentile in the world distribution of countries
by per capita income in the year 2000. With the
possible exception of 1732 Holland and 1801–1803
England, countries in our sample have average
incomes that are roughly comparable with
contemporary pre-industrial societies that have
not yet started significant and sustained
industrialization. The urbanization rate in our
sample ranges from 2 or 3 percent (South Serbia
1455, Java 1880) to 45 percent (Holland 1561). Population size varies even more, from an
estimated 80,000 in South Serbia 1455 and 237,000
in Levant 1596 to 350 million or more in India
1947 and China 1880.
The number of social classes into which
distributions are divided, and from which we
calculate our Ginis, varies considerably. They
number only three for 1784–99 Nueva España
(comprising the territories of today’s Mexico,
parts of Central America, and parts of western
United States) and 1880 China. In most cases, the
number of social classes is in the double digits. Understandably, large numbers of groups are found
in the case of occupational censuses: thus, the
data from the 1872 Brazilian census include 813
occupations, and the Levantine census includes
average incomes for more than 1400 settlements. The largest number of observations is provided in
the famous 1427 Florentine (Tuscan) census where
income data for almost 10,000 households are
available. As we shall see below, these large
differences in the number of groups have little
effect on the measured Gini1 and Gini2 values.
The estimated inequality statistics are
reported in Table 2. The calculated Gini2’s
display a very wide range: from 24.5 in China 1880
to 63.5 in Nueva España 1784–1799 and 63.7 in
Chile 1861.
[14] The latter
figure is higher than the inequality reported for
some of today’s most unequal countries like Brazil
and South Africa.The average Gini2 from these 29
data points is 44.3, while the average Gini from
the modern counterpart countries is 40.6
[15] These are only samples, of course,
but there is very little difference on average
between them, 44.3(ancient) – 40.6(modern
counterparts) = 3.7.
[16] In contrast,
there are very great differences within each
sample: 58.8 (Brazil 2002) – 26.0 (Japan 2002) =
32.8 among the modern counterparts, while 63.5
(Nueva España 1784–1799) – 24.5 (China 1880) = 39
among the ancient economies. In short, inequality
differences within the ancient and modern samples
are many times greater than are differences
between their averages.
The Gini estimates are plotted in Figure 2
against the estimates of GDI per capita on the
horizontal axis. They are also displayed against
the inequality possibility frontier constructed on
the assumption of a subsistence minimum of $PPP
300 (solid line). In most cases, the calculated
Ginis lie fairly close to the IPF. In terms of
absolute distance, the countries farthest below
the IPF curve are the most “modern” pre-industrial
economies: 1561–1808 Holland and the Netherlands,
1788 France, and 1688–1801 England and Wales.
How do country inequality measures compare with
the maximum feasible Ginis at their estimated
income levels? Call the ratio between the actual
inequality (measured by Gini2) and the maximum
feasible inequality the
inequality
extraction ratio , indicating how much of
the maximum inequality was actually extracted: the
higher the
inequality extraction
ratio , the more (relatively) unequal the
society.
[17] The median and mean inequality
extraction ratios in our ancient sample are 74.2
and 74.9 percent, respectively. Thus, almost
three-quarters of maximum feasible inequality was
actually “extracted” by the elites in our
pre-industrial sample. To put a more positive spin
on it, the elites did not want, or were unable, to
extract the last one-quarter of maximum feasible
inequality. The countries with the lowest ratios
are 1924 Java and 1811 Kingdom of Naples with
extraction ratios of 48 and 54 percent,
respectively. In these cases, the elite left about
half of the maximum feasible inequality on the
table for the non-elite.
Three estimated Ginis are equal to or slightly
greater than the maximum Gini implied by the IPF
(given level of income): Moghul India 1750 (an
extraction ratio of 113 percent), Nueva España
1790 (an extraction ratio of 106 percent) and
Kenya in 1927 (an extraction ratio of 100
percent). Recalling our definition of the IPF,
these cases can only be explained by one or more
of the following four possibilities: inequality
within the rich classes is very large; the
subsistence minimum is overestimated; the
inequality estimate is too high; and/or a portion
of the population cannot even afford the
subsistence minimum. We have already analyzed and
dismissed the first two possibilities. The third
possibility is unlikely; as our estimates of
inequality are calculated from a limited number of
social classes, they are likely to be biased
downwards, not upwards. The last possibility
offers the most plausible explanation. In the case
of Moghul India and Nueva España, a portion of the
population might have been expected to die from
hunger or lack of elementary shelter. But poor
people’s income often does, in any given month, or
even year, fall below the minimum and they survive
by borrowing or selling their assets. Still, the
same individuals cannot, by definition, stay below
subsistence for long. Such societies were not
viable since the population could not be
sustained. The fact that the only two such
societies in our sample, 1750 Moghul India and
1790 Nueva España, were both notoriously
exploitative seems to support the fourth
explanation.
The observations for England and Wales, and
Holland/Netherlands—the only countries for which
we have at least three pre-industrial
observations—are connected to highlight their
historical evolution of inequality relative to the
IPF. Between 1290 and 1688, and particularly
between 1688 and 1759, the slope of the increase
of the Gini in England and Wales was significantly
less than the slope of the IPF. Thus, the English
extraction ratio dropped from about 69 percent in
1290, to 57 percent in 1688 and to about 55
percent in 1759. However, between 1759 and 1801,
the opposite happened: the extraction ratio rose
to almost 61 percent. Or consider
Holland/Netherlands between 1732 and 1808. As
average income decreased (due to the Napoleonic
wars), so too did inequality, but the latter even
more so. Thus, the extraction ratio decreased from
around 72 to 68 percent.
The
inequality possibility
frontier allows us to better situate these
ancient inequality estimates in the modern
experience. Using the same framework that we have
just applied to ancient societies, the bottom
panel of Table 2 provides estimates of inequality
extraction ratios for some 25 contemporary
societies. Brazil and South Africa have often been
cited as examples of extremely unequal societies,
both driven by long experience with racial
discrimination, tribal power and regional dualism. Indeed, both countries display Ginis comparable to
those of the most unequal pre-industrial
societies. But Brazil and South Africa are several
times richer than the richest ancient society in
our sample, so that the maximum feasible
inequality is much higher than anything we have
seen in our ancient sample. Thus, the elites in
both countries have extracted only a little more
than 60 percent of their maximum feasible
inequality, and their inequality extraction ratios
are about the same as what we found among the less
exploitative ancient societies (1801–1803) England
and Wales, and (1886 Japan).
In the year 2000, countries near the world
median GDI per capita (about $PPP 3500) or near
the world mean population-weighted GDI per capita
(a little over $PPP 6000), had maximum feasible
Ginis of 91 and 95 respectively. The median Gini
in today’s world is about 35, a “representative”
country having thus extracted just a bit less than
40 percent of feasible inequality, vastly less
than did ancient societies. For the modern
counterparts of our ancient societies, the ratio
is just under 44 percent (Table 2). China’s
present
inequality extraction ratio
is almost 46 percent, while that for the United
States is almost 40 percent, and that for Sweden
almost 28 percent. Only in the extremely poor
countries today, with GDI per capita less than
$PPP 600, do actual and maximum feasible Ginis lie
close together (2004 Congo D. R., and 2000
Tanzania).
[18] Compared
with the maximum inequality possible, today’s
inequality is
much smaller than that
of ancient societies.
It could be argued that our new
inequality extraction ratio measure
reflects societal inequality, and the role it
plays, more accurately than any actual inequality
measure. For example, Tanzania (denoted TZA in
Figure 3) with a relatively low Gini of about 35
may be less egalitarian than it appears since
measured inequality lies fairly close to its
inequality possibility frontier
(Table 2 and Figure 3). On the other hand, with a
much higher Gini of almost 48, Malaysia (MYS) has
extracted only about one-half of maximum
inequality, and thus is farther away from the IPF. This new view of inequality may be more pertinent
for the analysis of power and conflict in both
ancient and modern societies.
Another implication of our approach is that it
considers inequality and development jointly. As a
country becomes richer, its feasible inequality
expands. Consequently, even if recorded inequality
is stable, the
inequality extraction
ratio must fall; and even if recorded
inequality goes up, the extraction ratio may not. This can be seen in Figure 4 where we plot the
inequality extraction ratio against GDI per capita
for both ancient societies and their modern
counterparts. The farther a society rises above
the subsistence minimum, the less will economic
development lift its
inequality possibility
frontier , and thus the
inequality
extraction ratio will be driven more and
more by the rise in the Gini itself. This is best
illustrated by the United States where the maximum
feasible inequality already stands at a Gini of
98.6. Economic development offers this positive
message: the
inequality extraction
ratio will fall with GDI per capita growth
even if measured inequality remains constant. However, economic decline offers the opposite
message: that is, a decline in GDI per capita,
like that registered by Russia in the early stages
of its transition from communism, drives the
country’s maximum feasible inequality down. If the
measured Gini had been stable, the
inequality extraction ratio would
have risen. If the measured Gini rose (as was
indeed the case in Russia), the
inequality
extraction ratio would have risen even more
sharply. Rising inequality may be particularly
socially disruptive under these conditions.
Explaining Pre-Industrial Inequality and the
Extraction Ratio
Using this information from
ancient societies, can we explain differences in
observed inequality and the extraction ratio? We
have available, of course, the Kuznets hypothesis
whereby inequality tends to follow an inverted U
as average real income increases. Although Kuznets
formulated his hypothesis explicitly with a view
toward the industrializing economies (that is,
with regard to economies that lie
outside our sample), one might wonder
whether the Kuznets Curve can be found among
pre-industrial economies as well. In addition to
average income and its square, Table 3 includes
the urbanization rate, population density and
colonial status (a dummy variable). The regression
also includes a number of controls for
country-specific eccentricities in the data: the
number of social groups available for calculating
the Gini, whether the social table is based on tax
data, and whether the social table for a colony
includes income for the colonizers. The Kuznets
hypothesis predicts a positive coefficient on
average income and negative coefficient on its
square. We also expect higher inequality for the
more urbanized countries (reflecting a common
finding that inequality in urban areas tends to be
higher than in rural areas: Ravallion et al. 2007), and for those that are ruled by foreign
elites since powerful foreign elites are presumed
able to achieve higher extraction ratios than
weaker local elites, and since countries with weak
local elites but large surpluses to extract will
attract powerful colonizers (Acemoglu, Johnson and
Robinson 2001).
The regression results readily confirm all
expectations. Both income terms are of the right
sign, and significant at less than 1 percent
levels, strongly supporting a (conditional)
pre-industrial Kuznets Curve. The sign on
urbanization is, as predicted, positive, but since
it competes with population density, its
significance is somewhat lower. Still, each
percentage point increase in the urbanization rate
(say, from 10 percent to 11 percent) is associated
with an increase in the Gini by 0.35 points. Colonies are clearly much more unequal: holding
everything else constant, a colony would have a
Gini about 12–13 points higher than a non-colony.
Dno_foreign is a dummy variable that
controls for two observations (South Serbia 1455
and Levant 1596) that were colonies but where
their ancient inequality surveys did not include
the incomes and numbers of colonizers at the top. This is therefore simply another control for data
eccentricity, and its negative sign shows that
being a colony, and not having colonizers included
in the survey, reduces recorded inequality
considerably (almost 10 points) compared to what
one might expect.
[19] In summary,
being a colony was a major determinant of measured
inequality. Excluding South Serbia 1455 and Levant
1596, the measured Gini2 ranges between 24.5 for
China 1880 and 63.7 for Chile 1861 (Table 2), that
is, the spread is 39.2 percentage points, and the
colony effect is 13.6/39.2=35 percent of that
spread, a big influence indeed.
The number of social groups that we use in our
inequality calculations does not seem to affect
the Gini values. In the regression analysis of the
extraction ratio, we shall experiment with
different upward-adjusted values of the Gini (and
hence higher values of the extraction ratio) to
find out if our results are sensitive to the way
Ginis were calculated, and, in particular, to the
difference in the number of social groups used in
the calculation.
Population density is negatively associated
with inequality (in all formulations, including
those not shown here) and is significant. According to regression 1 (Table 3), an increase
in population density by 10 persons per square
kilometer (equivalent to an increase in population
density from that of the early nineteenth century
Naples to England and Wales) is associated with a
1 Gini point decrease. One might have thought that
the introduction of a dummy variable for more
densely populated Asian countries would have
caused the effect of density to dissipate. This is
not the case, as shown by regression 2 (Table
3).
[20] Thus, inequality is associated
with lower population density and lower labor-land
ratios, at least in our sample. If this effect
holds for larger samples, what might explain it? Conventional economics gave us a strong prior
which has been rejected: higher labor-land ratios
in agrarian systems imply higher rents per hectare
and lower labor productivity, and thus more
inequality. Although we cannot explore competing
explanations for this density result with our
ancient inequality evidence, we can list some
likely candidates. Here are two, with opposite
causal chains. First, where land was scarce, land
intensive products, like food grains, should have
been expensive, especially in ancient times when
there was no global grain market. Expensive grains
implied the necessity of more nominal income to
purchase a subsistence quantity of foodstuffs, and
thus the appearance of lower measured inequality
(and extraction ratios). Second, less exploitative
societies, which arose for reasons we do not know,
might have allowed higher subsistence (lower
inequality and extraction ratios), bigger survival
rates, larger populations, and thus greater
density.
When exploring the determinants of the
extraction ratio, theory is less helpful. A simple
plot of the extraction ratio against ln GDI per
capita displays a negative and statistically
significant relationship (see Figure 5). In
regression 4 (Table 3), the extraction ratio is
regressed against much the same variables as with
the Gini.
[21] Income is
negatively (and significantly) associated with the
extraction ratio,
[22] while being
a colony and being more urbanized are both
associated with higher extraction ratios. Having a
colonial elite—with everything else the same—is
associated with a very large 16.2 point increase
in the extraction ratio. The introduction of
population density (regression 5, Table 3) renders
both income and urbanization rate statistically
insignificant. The positive effect of being a
colony remains and the coefficient even increases
(to 25 extraction ratio points). Similar to the
inequality result, greater population density is
strongly associated with lower extraction ratios. The result persists even after we eliminate
observations for Java (regression 6), although
only at the 5 percent significance level. Figure 6
plots population density against the residuals
from regression 6 (which omits the two
observations from Java: see footnote 20). As can
be seen, the relationship is still strongly
negative.
To explore the sensitivity of these results to
the issue of measurement, we introduce three
additional computations of the Gini. First, we use
Deltas’ (2003) correction whereby the measured
Gini is adjusted by the n/n–1 ratio, where n is
the number of social groups.
[23] Second, we
use information from the bootstrapped standard
errors of the Gini. As expected, standard errors
are generally greater the fewer the number of
social groups.
[24] We thus
adjust our measured Ginis by adding, in one case,
½ of standard error, and in the other case, one
standard error.
[25] The
regressions (reported in Appendix 4) show that all
the main results carry over. The only notable
change is that the coefficient on population
density, in a formulation that omits the two
observations from Java, is significant only around
the 10 percent level. Simultaneously, the role of
higher income in reducing the extraction ratio,
particularly when Gini is revised upward a lot
(measured Gini + one standard error), becomes
stronger. We conclude that the population density
results are not fully robust to some alternative
upward Gini adjustments
combined with
the elimination of the two extreme population
density observations.
When we draw together the analyses of
inequality and the extraction ratio, the picture
that emerges is this: the Gini follows contours
that are broadly consistent with the Kuznets Curve
hypothesis (a rise and then a turn-around to
falling inequality) even in pre-industrial
societies, but the extraction ratio tends to fall
as income increases, with no turn-around. In other
words, while inequality at first increases as
income per capita rises, it does not increase to
the full extent made possible by the larger
surplus, so that the extraction ratio falls. In
addition, higher population density puts downward
pressure both on the Gini and the extraction
ratio. Its effect is particularly strong in the
latter case so that both income and urbanization
become insignificant. Finally, colonies record
very high inequality and extraction ratios
throughout.
[26]
The data also shed light on the historical
persistence of inequality. First, it does not
appear that ancient Asia was significantly less
unequal when we control for other factors, such as
population density. When the Asian dummy is added
to regression 2, its coefficient is negative, but
it is not significant. That is, population density
may be sufficient to identify why ancient Asia had
lower levels of inequality. Some have argued this
result is driven by the absence of scale economies
in rice cultivation (Jones 1981; Bray 1986), but
we have already offered other possibilities as
well.
Second, Stanley Engerman and Kenneth Sokoloff
(1997, 2000) have offered a hypothesis to account
for Latin American growth underachievement during
the two centuries following its independence which
appeals to the region’s persistent inequality
since 1492. Their thesis begins with the plausible
assertion that high levels of income inequality,
and thus of political power, favor rich landlords
and rent-seekers, and thus the development of
institutions which are compatible with the former
but incompatible with economic growth. Their
thesis argues further that high levels of Latin
American inequality have their roots in the
natural resource endowments present after Iberian
colonization five centuries ago. Exploitation of
the native population and African slaves, as well
as their disenfranchisement, reinforced the
development of institutions incompatible with
growth. Engerman and Sokoloff had no difficulty
collecting evidence which confirmed high
inequality, disenfranchisement and lack of
suffrage in Latin America compared with the United
States. Oddly enough, however, their thesis has
never been confronted with inequality evidence for
the industrial leaders in northwestern Europe. It
would be damaged if we can show that inequality in
England, Holland and France, prior to their
industrial revolutions, was greater than or equal
to that of Latin America, while during and after
their industrial revolutions the former three led
the world economically and the latter lagged
behind (e.g. Maddison 2003, Prados de la Escosura
2004).
Table 2 presents inequality information for
pre-industrial Western Europe (that is, prior to
1810) and for pre-industrial Latin America (that
is, prior to 1875). For the former, we have
observations from 1788 France, 1561 and 1732
Holland, and 1688, 1759, and 1801 England-Wales. For the latter, we have Nueva España 1790, Chile
1861, Brazil 1872, and Peru 1876. Engerman and
Sokoloff coined their hypothesis in terms of
actual inequality. According to that criterion,
their thesis must be rejected. That is, the
(population weighted) average Latin American Gini
(48.9) was lower than that of Western Europe
(52.9), not higher.
[27] True, the
variance in the Gini is considerable within both
regions, but it is not true that pre-industrial
Latin America was unambiguously more unequal than
pre-industrial Western Europe. However, Latin
America was poorer than Western Europe, and poorer
societies have a smaller surplus for the elite to
extract. Thus,
feasible inequality
was lower in Latin America (range of 59.9–62.4
versus European range of 77.7–79.8). As it turns
out,
extraction rates were
considerably higher in Latin America than in
Western Europe. Thus, while measured inequality
does not support the Engerman-Sokoloff thesis, the
extraction rate does. This suggests a new question
to be added to the long run growth debate: Why was
the
extraction rate so much higher in
Latin America? Was it simply because they were
colonized?
What Components Are Driving Overall Income
Distribution?
How much of the inequality
observed in ancient societies can be explained by
the economic distance between the average rural
landless peasant at the bottom and the average
rich landed elite at the top? How much can be
explained by the distribution among the elite at
the top? And how much can be explained by the
income share held by all the elite at the top?
Life at the Top: Income Distribution
Involving the Elite
An impressive amount of recent
empirical work has suggested that the evolution of
the share of the top 1 percent yields a good
approximation to changes in the overall income
distribution in modern industrial societies
(Piketty 2003, 2005; Piketty and Saez 2003, 2006;
Atkinson and Piketty forthcoming). These studies
find that most of the action takes place at the
top of the income distribution pyramid and that
changes or differences in the top 1 percent income
share account for much of the changes or
differences in overall inequality (Leigh 2007). These top share studies have also been performed
on poor pre-modern India (since 1922: Banerjee and
Piketty 2005), Indonesia (since 1920: Leigh and
van der Eng 2006) and Japan (since 1885: Moriguchi
and Saez 2005). So, are differences in the share
of the top 1 percent also a good proxy for
differences in overall income distribution in
ancient pre-industrial societies?
The income share of the top 1 percent is
estimated here under the assumption that top
incomes follow a Pareto distribution. Our approach
is basically the same as that recently used by
Anthony Atkinson (forthcoming) and by others
writing before him (see the references in Atkinson
forthcoming).
[28]
Table 4 reports the estimated income share of
the top 1 percent of recipients, and the cut-off
point, that is the income level (relative to the
mean) where the top one percent of recipients
begins. The countries are listed in descending
order according to the top 1 percent share. In
contrast with modern studies, the correlation
between the top 1 percent share and the Gini is
small (+0.18) and statistically insignificant.
[29] This implies that differences in
overall inequality are not reflected by
differences in the top percentile share very well. Consider, for example, the Roman and Byzantine
empires. Their estimated Ginis are very similar
(39.4 and 41.1) but the top percentile share in
Byzantium (30.6, the highest in our sample) is
almost twice as great as in Rome (16.1).
The poor correlation between the top 1 percent
and overall inequality in the ancient
pre-industrial sample is also supported by more
evidence. Table 4 also reports modern counterparts
to our ancient economies as well as a few other
modern countries. Among the modern counterparts,
those with the highest top 1 percent share
(Mexico, Brazil) display values that are equal to
the average for the ancient economies (about 14
percent of total income). Relatively low top 1
percent shares (from the UK at 7 percent to the
Netherlands at 3.6 percent) plus low cut-off
points (characteristic of advanced societies)
announces modern distributions where the richest 1
percent are not extravagantly rich nor extremely
different from the population average.
[30] We have already noted that Gini
coefficients in ancient and contemporary poor
societies are quite similar, so the difference in
the average top 1 percent shares between ancient
and modern societies implies further support for
the view that the link between top income shares
and overall inequality is very weak between
ancient and modern societies.
Life at the Bottom: The Unskilled Rural Wage
Relative to Average Income
For fourteen of the
twenty-nine observations in our ancient inequality
sample, we can measure the economic distance
between the middle of the distribution and
landless labor by computing the ratio of average
income per recipient (y) to that of landless,
unskilled rural laborer (w). Figure 7 plots the
relation between the overall Gini and the y/w
ratio.
[31] The correlation between y/w and
the Gini is positive and significant (0.52). The
estimated relationship also implies an elasticity
of the Gini with respect to y/w of 0.35: thus, for
every 10 percent increase in y/w, the Gini rose by
3.5 percentage points. Low measured inequalities
in China 1880 and Naples 1811 (Ginis of 24.2 and
28.4: Appendix 2) were consistent with small gaps
between poor rural laborers and average incomes
(y/w of 1.32 and 1.49: Appendix 2), or with a
rural wage two-thirds to three-quarters of average
income. High measured inequalities in Nueva España
1784–1799 and England 1801–1803 (Ginis of 63.5 and
51.4) were consistent with large gaps between poor
rural laborers and average incomes (y/w of 4.17
and 2.94), or with a rural wage only one-quarter
to one-third of average income. There appears to
be only one possible outlier to the otherwise
tight relationship in Figure 7, British India in
1947. The overall relationship suggests that the
Gini correlates more closely with the gap between
poor landless labor and the landed elite, than
with the top 1 percent share: to repeat, Gini has
a significant correlation with y/w, but an
insignificant 0.02 correlation with the share
received by the top 1 percent.
[32]
New Inequality Insights and an Agenda for
the Future
Our exploration of ancient
pre-industrial experience has uncovered three key
aspects of inequality which had not been
appreciated before.
First, income inequality in pre-industrial
countries today is not very different from
inequality in distant pre-industrial times.
[33] In addition, the variance of
inequality among countries then and now is much
greater than any difference in average inequality
between them then and now.
Second, the
extraction ratio —how
much of potential inequality was converted into
actual inequality—was significantly bigger then
than now. We are persuaded that much more can be
learned about inequality in the past
and the present by looking at the
extraction ratio rather than just at
actual inequality. The ratio measures just how
powerful, repressive and extractive are the elite,
its institutions, and its policies. Regression
analysis suggests that colonies are much more
unequal and have far higher extraction rates. In
addition, ancient pre-industrial societies passed
through a Kuznets Curve, inequality rising steeply
until the beginning of modern economic growth. Economic development also tends to diminish the
extraction ratio. This latter finding suggests
that even in pre-industrial societies the elite do
not fully exploit their opportunity to capture
more of the rising surplus as average incomes
increase. While we do not explore them here, there
must be factors that kept the extraction ratio
from increasing, or actually lowered it, long
before the appearance in the twentieth century of
universal suffrage and the rise of the welfare
state. Once the analysis control for these and
other factors, there is no evidence left to
support the view that high inequality has always
been a special characteristic of Latin America, or
that low inequality has always been a
characteristic of Asia. Finally, greater
population density is correlated with lower
inequality.
Third, our ancient pre-industrial inequality
sample does not reveal any significant correlation
between the income share of the top 1 percent and
overall inequality, unlike recent twentieth
century findings for industrial and
post-industrial societies. Pre-industrial
societies could and did achieve high inequality in
two ways: in some, a high income share of the
elite coexisted with a yawning income gap between
it and the rest of society, with small income
differences among the non-elite; in others, those
at the very top of the income pyramid were
followed below by only slightly less rich and then
further down the line toward something that
resembled a middle class. Why were some ancient
societies more hierarchal while others more
socially diverse? While this paper has explored
inequality over two millennia, it has not explored
the social structure underpinning that inequality,
its determinants, and its impact. We plan to
pursue this issue in future work.
Footnotes
His Wisconsin seminar paper
became a classic (Kuznets 1976).
This result resembles
Frederic Pryor’s (1977:197 and 2005:40) finding
that among remote foraging and agricultural
communities an index of wealth inequality seems to
rise with an index of “economic development.” The
rise in inequality seems to be tied to a rise in
“centric” (regressive) taxes and tributes.
Throughout this paper, we
report Ginis as percent and thus here as 4.7
rather than 0.047.
The IPF concept was first
introduced in Milanovic 2006.
The reader can verify this
by letting one subsistence worker’s income rise
above subsistence to 20, and by letting the
richest person’s income be reduced to 1000. The
new Gini would be 49.49.
This is already assumed for
the lower classes, but that assumption will be
relaxed later for the upper classes.
For the lower class,
within-group inequality is zero by assumption
since all of its members are taken to live at
subsistence.
Note that in the special
case where subsistence is zero, G* rises to the
maximum value of 1 (or 100 in percentage terms). To see this, let α→∞ in equation (6) (which is the
case if s=0) and apply L’Hospital’s rule.
As far as we can determine,
the compilers of the social tables did include
income in kind produced by the consuming
households themselves. Looking at the English
source materials in particular, we find that
Gregory King and others sought to know what
different people consumed, and tied their income
estimates to that. In addition, the tax returns
they often used for their estimates seem to
include assessments of owner-occupied housing.
Gini2 is routinely
calculated for contemporary income distributions
when the data, typically published by countries’
statistical offices, are reported as fractiles of
the population and their income shares. In that
case, however, any member of a richer group must
have a higher income than any member of a poorer
group. This is unlikely to be satisfied when the
fractiles are not income classes but social
classes as is the case here. The Gini2 formula is
due to Kakwani (1980).
As explained above, both
approaches underestimate inequality by assuming
that the mean income of each group (social in one
case, settlement in the other) hold for all
members of that group. It could be argued that the
downward bias is greater in the case of
settlements (which may be economically more
diverse within) than in the case of social classes
(e.g. most nobles tend to be richer than most
peasants). However, a very large number of
settlements for which the means are available in
the Ottoman surveys provides an offsetting
influence to that bias: the informational content
of having mean incomes for more than 1,000
settlements may be greater than having mean income
estimates for half a dozen social classes.
This is less than
Maddison’s (1998:12) assumed subsistence minimum
of $PPP 400 which, in principle, covers more than
physiological needs. Note that a purely
physiological minimum “sufficient to sustain life
with moderate activity and zero consumption of
other goods” (Bairoch 1993:106) was estimated by
Bairoch to be $PPP 80 at 1960 prices. Using the US
consumer price index to convert Bairoch’s estimate
to international dollars yields $PPP 355 at 1990
prices. Our minimum is also consistent with the
World Bank absolute poverty line which is 1.08 per
day per capita in 1993 $PPP (Chen and Ravallion
2007:6). This works out to be about $PPP 365 per
annum in 1990 international prices. Since more
than a billion people are calculated to have
incomes less than the World Bank global poverty
line, it is reasonable to assume that the
physiological minimum income must be less. One may
recall also that Colin Clark 1957:18-23, in his
pioneering study of incomes, distinguished between
international units (the early PPP dollar) and
oriental units, the lower dollar equivalents which
presumably hold for subtropical or tropical
regions where calorie, housing and clothing needs
are considerably less than those in temperate
climates. Since our sample includes a fair number
of tropical countries, this gives us another
reason to use a conservatively low estimate of the
physiological minimum.
All dollar data, unless
indicated otherwise, are in 1990 Geary-Khamis PPP
dollars.
South Serbia 1455 Gini is
even lower (20.9) but the survey excludes Ottoman
landlords. We shall make adjustment for such
omission in the empirical analysis below.
The modern counterpart
countries are defined as countries that currently
cover approximately the same territory as the
ancient countries (e.g. Turkey for Byzantium,
Italy for Rome, Mexico for Nueva España, modern
Japan for ancient Japan, and so on).
The hypothesis of equality
of the two means is easily accepted (t test
significant at 22 percent only).
The term “relative” is
used here,
faute de mieux , to
denote conventionally calculated inequality in
relation to maximum possible inequality at a given
level of income, not whether the measure of
inequality itself is relative or absolute.
Actually, the extraction
ratio for Congo is in excess of 100 percent. It is
very likely that Congo’s real income ($PPP 450 per
capita) is underestimated. But even so, the
extraction ratio would be close to 100 percent.
If colonies with no
information on colonizers were a random draw from
all the statistical population of all colonies
(which of course they are not), we would expect
the two coefficients to be the same but, of
course, of opposite sign.
True, when we eliminate
the two Java observations, a region with the
highest population density in our sample and with
relatively low inequality, the negative
coefficient on population density begins to lose
its statistical significance at conventional
levels (although barely so, since it is still
significant at 5.3 percent).
We no longer include
survey controls (number of groups or a dummy for
tax-based source) since we have seen that they do
not make a difference in the calculations of the
Gini.
Including income squared
reveals no significant curvature (results not
shown here).
Deltas adjustment for
small-sample Ginis is derived for the “usual” case
where Gini is estimated from the ordered fractile
data (and where the overlap component between the
fractiles is, by construction, zero). We apply it
here in a somewhat different context (where
incomes of various social groups may overlap).
The correlation
coefficient is -0.46.
Because our measured Ginis
do not include the “overlap” component, they
underestimate “true” Ginis.
With one exception, the
data sources use the gross national income
accounting convention, which measures global
incomes for residents of a place. Thus the
estimates include as “Indian” those British
citizens resident in India, whereas those resident
in Britain getting incomes from India are included
in the British income distribution. The one
exception is the estimate for the Roman Empire,
which unavoidably aggregates the colonizing and
colonized populations together (and for many
reasons, Roman Empire may be considered a single
political entity).
The same is true of the
unweighted average.
The estimation procedure
is explained in detail in Appendix 3. There we
list several caveats necessitated by the fact that
our social tables are different from the usual
income distribution data sources.
The correlation between
the top 1% share and Gini coefficient among the
modern comparators given in Table 4 is +0.97 (and
statistically significant at less than 0.1
percent).
The data for modern
societies are calculated from household surveys
that are, we believe, closer counterparts to our
social tables than the top income shares
calculated from tax data. The latter almost
uniformly give higher values: for the developed
countries, they range from about 5 to almost 15
percent of
gross (pre-tax) income. We
present these data for completeness in Table 4.
See also Appendix 2. This
simple y/w index has been shown to be a good proxy
for inequality among nineteenth and twentieth
century poor economies (Williamson 1997,
2002).
This 0.02 correlation
refers to the 26 cases in Table 4. When we reduce
the sample to the same 14 cases used for y/w, the
correlation between the top 1 percent share and
the overall Gini becomes negative 0.21.
However, it seems likely
that any measure of lifetime income (as opposed to
annual income used here) inequality would confirm
that ancient pre-industrial inequality was higher
than modern pre-industrial inequality. After all,
there has been an immense convergence in mortality
and morbidity by social class in even poor
countries since the First Industrial Revolution in
Britain, and most of this was induced by elite
policy towards cleaner cities and public health. See Milanovic, Lindert and Williamson 2007 section
6.
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