Chad Jones' two methods for predicting future World Income Distribution and their criticisms

Chad Jones uses two different methods in predicting how the
World Income Distribution (WID) will evolve in the future. The
first approach he uses is based on the findings of the Solow
model, which Jones then uses to say that it is up to the
fundamentals of a country such as its savings rate and
population growth rate, that determines how fast it will grow in
the future. He plugs in the fundamentals he finds of a country
from 1988 to project the future levels of income distribution,
and determine whether or not there has been change and in what
direction (increase or decrease). The criticism of this approach,
however, is that it assumes that the fundamentals of savings rate
and population growth rate, for example, are fixed at 1988
levels.
The second approach Jones takes is not reliant on the Solow
model, and is rather called the Markov Transitional Matrix.
Essentially, Jones here classifies the data he has, either within a
country's household income distribution as we learned in class
or across different countries, as bottom tier, middle tier, or top
tier. Then, depending on how much of the data falls outside of
the central diagonal formed by the data, Jones determines
whether the country or countries experiences an
increase/decrease/stagnation in income distribution levels in the
future. The criticism about this approach, however, is that it
assumes that the distributions of growth rates across countries
would stay constant in the future as they were in the period
between 1960 and 1988, which is a very big detail to assume
and would skew the findings coming out of this approach.
Lant Pritchett also tries to explain the idea of convergence
through two separate methods. Because the only evidence that
existed at the time was based on OECD countries or more
rich/developed countries, Pritchett attempts to influence the
literature by accounting for the poorer countries. He does this
by finding what the lowest level of GDP/capita is in our modern
day by looking at the poorest of countries in our time. He then

assigns this level to countries that data could not be found for in
the past, because Pritchett states that countries could not exist if
they did not even meet this threshold for GDP/capita. This
number is $250. The second method he uses is to prove that
assigning this $250 for poor countries in the past is not
outrageous. He does this by determining the relationship
between caloric consumption and GDP/capita and then finding
what the basic number of calories needed to survive was, which
was around 2,400 calories. Pritchett then plugged 2,400 into his
relationship between caloric consumption and GDP/capita to
back out what the level of GDP/capita would be in countries
who only managed to meet 2,400 calories/day, which was the
minimum subsistence level. The number he got for GDP/capita
using this method was between $250-$280, which confirms his
ability to plug this in for poor countries that did not have data
in the past. A criticism of this approach is that there will never
a feasible way to determine convergence, because regardless of
the minimum GDP/capita you place for the poor countries,
empirically the model will show that the poor countries can
never and will never catch up to the richer countries. We saw
this in the last example in class, when countries were placed at
$100, they still weren't reaching the 2% growth rate that rich
countries were reaching yearly, symbolizing that these poorer
countries could not catch up regardless of their low GDP/capita
levels.
Journal of Economic Perspectives—Volume 11, Number 3—
Summer 1997—Pages 19–36
On the Evolution of the World Income
Distribution

Charles I. Jones
H
ow rich are the richest countries in the world relative to the
poorest? Are
poor countries catching up to the rich countries or falling
further be-
hind? How might the world income distribution look in the
future?
These questions have been the subject of much empirical and
theoretical work over
the last decade, beginning with Abramovitz (1986) and Baumol
(1986), continuing
with Barro (1991) and Mankiw, Romer and Weil (1992), and
including most re-
cently work by Quah (1993a, 1996). This paper provides one
perspective on this
literature by placing it explicitly in the context of what it has to
say about the shape
of the world income distribution. We begin in the first section
by documenting
several empirical facts concerning the distribution of GDP per
worker across the
countries of the world and how this distribution has changed
since 1960.1
The main part of the paper attempts to characterize the future of
the world
income distribution using three different techniques. First, we
use a standard
growth model to project the current dynamics of the income
distribution forward,
assuming the policies in place in each country during the 1980s
continue. One can
interpret this exercise as forecasting the near-term income

distribution. The results
indicate that the near-term income distribution looks broadly
like the current dis-
tribution. However, there are some notable exceptions,
primarily at the top of the
income distribution, where a number of countries are predicted
to continue to
converge toward and even overtake the United States as the
richest country in the
world.
Second, we exploit insights from the large literature on cross-
country growth
1For a related review of the facts, see Parente and Prescott
(1993) and Jones (forthcoming).
• Charles I. Jones is Assistant Professor of Economics, Stanford
University, Stanford, Cali-
fornia. His e-mail address is [email protected]
20 Journal of Economic Perspectives
regressions following Barro (1991) and Mankiw, Romer and
Weil (1992). An im-
portant finding of this literature is that one can interpret the
variation in growth
rates around the world as reflecting how far countries are from
their "steady state"
positions. Korea and Japan have grown rapidly because their
steady state positions
in the income distribution are much higher than their current
positions. Venezuela
has grown slowly because the reverse is true. We use this

insight to provide a second
way of predicting where countries are headed based on current
policies.
Finally, we step back and consider how the steady states toward
which countries
are headed are themselves changing. The evidence from the last
30 years suggests
that growth miracles are occurring more frequently than growth
disasters and that
the relative frequency of miracles has increased. Projecting
these dynamics forward
indicates that the long-run world income distribution involves a
substantial im-
provement in the incomes of many countries. For example in
1960, 60 percent of
countries had incomes less than 20 percent of incomes in the
richest country. In
the long run, the empirical results indicate that the fraction of
"poor" countries
will fall from 60 percent to only 27 percent.
Facts
Before examining several facts about the world income
distribution, it is worth
pausing for a moment to consider which definition of income to
use. GDP per
capita seems like a natural definition if one is interested in an
important determi-
nant of average welfare. However, in many developing
countries, nonmarket pro-
duction is quite important, leading GDP per capita to understate
true income in
these countries. A coarse correction for this problem is to focus
on GDP per worker.

Both the numerator and the denominator then correspond to the
market sector.
To the extent that wages are equalized at the margin between
the market and
nonmarket sectors, this is a natural measure of income, and it is
the one employed
in most of this paper.
The world distribution of GDP per worker has changed
substantially during
the post-World War II period. Figure 1 plots the density of GDP
per worker relative
to the United States in 1960 and 1988 for 121 countries.2
Roughly speaking, the
more countries there are at a particular level of income, the
higher the density will
be at that point in the figure. The 121-country sample, which
includes all countries
for which Summers and Heston (1991) report real GDP per
worker in both years,
will make up the "world" for the purposes of this paper. The
most notable
omissions are several Eastern European economies and several
economies in the
Middle East for which data are not reported in 1960.
A number of features in this figure deserve comment. First, the
distribution is
2 T h e data are from the Penn World Tables Mark 5.6 update of
Summers and Heston (1991) and
therefore are in principle corrected for differences in purchasing
power across economies. The density
estimates are computed using a Gaussian kernel with a
bandwidth chosen as .9AN–1/5 where A is the
standard deviation of the data and N is the number of

observations.
Charles I. Jones 21
Figure 1
World Income Distribution, 1960 and 1988
wide. In 1988, for example, the ratio of the income in the
richest country (the
United States) to the poorest country (Myanmar) was 35.
Second, the 1960 distri-
bution is single-peaked and looks roughly normal, although the
tails are too thick.
In contrast, the distribution in 1988 exhibits "twin-peaks," to
use the appellation
coined by Quah (1993a). This change reflects a shift in the mass
of the distribution
away from the middle and toward the ends. In particular, the
"hump" in the 1960
distribution between about 5 and 30 percent of U.S. income has
shifted upward
into the 20 to 65 percent range. Finally, the world income
distribution is wider in
1988 than it was in 1960, both at the top and at the bottom.
What cannot be seen in the figure is the general growth in GDP
per worker
throughout the world. Though this paper is almost entirely
about relative incomes,
it is important to remember that in absolute terms, income
growth is a prevalent
feature around the world. For example, U.S. GDP per worker
grew at an average

annual rate of 1.4 percent from 1960 to 1988. In other words, if
in Figure 1 we
plotted actual instead of relative incomes, the 1988 distribution
would be shifted
noticeably to the right. Nevertheless, not all countries
experienced positive growth.
GDP per worker actually declined from 1960 to 1988 in 11
percent of the countries.
Throughout this paper, we will consider incomes relative to
U.S. income; that
is, we will focus on the GDP per worker of the countries of the
world divided by
U.S. GDP per worker. The choice of the denominator is an
important one, and
U.S. income is chosen for several reasons. First, the United
States had the highest
GDP per worker in both 1960 and 1988, so the units of relative
income are readily
interpreted. Second, U.S. growth has been relatively steady over
this 30-year period.
Finally, it is natural to think of the U.S. economy as lying close
to the technological
frontier. Therefore, U.S. growth is probably a reasonable proxy
for the growth rate
of the technological frontier. These considerations indicate that
the U.S. economy
is "well-behaved" and that normalizing by U.S. income will not
distort our view of
the income distribution.

One drawback of Figure 1 is that individual countries cannot be
identified.
Figure 2 helps to address this concern by plotting GDP per
worker relative to the
United States in 1960 and in 1988 on a natural log scale.3
Changes in the world
distribution of income are then illustrated by departures from
the 45-degree line.
Countries with GDP per worker greater than about 15 percent of
U.S. income in
1960 typically experienced increases in relative income. These
countries corre-
spond to the shift in the mass of the income distribution toward
the top in Figure
1. On the other hand, many countries with relative incomes of
less than 10 or
15 percent in 1960 experienced a decrease in relative income
over this period. They
grew more slowly than did the United States and more slowly
than did most of the
countries above the 15 percent mark. These are the countries
that make u p the
peak at the lower end of the income distribution. One way of
interpreting these
general movements is that there has been some convergence or
"catch-up" at the
top of the income distribution and some divergence at the
bottom.
Figure 2 also allows us to identify the growth miracles and
growth disasters of
this 28-year period. Hong Kong (HKG), Singapore (SGP), Japan
(JPN), Korea
(KOR) and Taiwan (OAN) all stand out as growth miracles,
having increased their
relative incomes substantially. For example, Hong Kong,

Singapore and Japan grew
from about 20 percent of U.S. GDP per worker in 1960 to
around 60 percent in
1988. Korea rose from 11 percent to 38 percent. Several less
well known growth
miracles are also noteworthy. Relative income in Botswana
(BWA) increased from
5 percent to 20 percent, in Romania (ROM) from 3 percent to 12
percent, and in
Lesotho (LSO) from 2 percent to 6 percent.
A large number of the growth disasters—countries that
experienced large de-
clines in relative incomes—are located in sub-Saharan Africa.
Chad (TCD), for
example, fell from a relative income of 8 percent to 3 percent.
However, growth
disasters outside Africa are also impressive. For example,
Venezuela (VEN) was the
third richest economy in the world in 1960 with an income
equal to 84 percent of
U.S. income. By 1988, relative income had fallen to only 55
percent.
The facts about the world income distribution so far have
concerned the be-
havior of incomes in terms of countries. While this is a common
way to view the
data, it can be misleading: for example, if we drew national
borders differently—
for example, so that each of the 50 U.S. states were a separate
country—the shape
of the densities in Figure 1 would look different. An alternative
approach is to
weight each country by its population. The unit of observation
is then a person

instead of a country.4 The most important fact to note in this
regard is that roughly
40 percent of the world's population lives in China (23 percent
in 1988) and India
(17 percent in 1988). The experience of these two countries
largely determines
3 A complete guide to the country codes used in this figure can
be found on the World Wide Web at
http://www.stanford.edu/~chadj/growth.html.
4 O f course, this exercise says nothing about changes in the
income distribution within a particular
country.
On the Evolution of the World Income Distribution 23
Figure 2
Relative Y/L, 1960 vs. 1988
(log scale)
what happens to the "typical" poor person in the world. In
contrast, less than
10 percent of the world's population lives in the 39 countries
that make up sub-
Saharan Africa.
Figure 3 plots the density of GDP per worker relative to the
United States,
weighted by population. In comparing this figure to Figure 1,
one sees the over-
whelming importance of India and China. While the distribution
of countries has
exhibited some divergence at the bottom, the same is not true
for the distribution

weighted by population. Both China and India have grown faster
than the United
States in the last three decades, leading to some catch-up at the
bottom of the
income distribution weighted by population. The catch-up in the
top part of the
income distribution also remains evident in Figure 3.
The cumulative distribution of GDP per worker by population—
that is, the
area under the density—provides additional information that is
helpful in inter-
preting Figure 3. In terms of the cumulative distribution, 50
percent of the world's
population lives in countries in which GDP per worker is about
10 percent of that
in the United States. To be more exact, the income of the
country containing the
median person has improved from 8.1 percent of U.S. income in
1960 to
11.8 percent in 1988. Improvements for people higher up in the
distribution have
Figure 3
Density of GDP Per Worker Weighted by Population
been even more substantial. The 75th percentile of the
population lived in a country
with 22.5 percent of U.S. income in 1960, but 40.3 percent in
1988. The 90th
percentile of the population lived in a country with 59.2 percent

of U.S. income in
1960, and 79 percent in 1988.
The Assumption of Similar Long-Term Growth Rates
The remainder of this paper considers various techniques for
making state-
ments about the future shape of the world income distribution.
First, however, there
is an important issue to consider. The world income distribution
will only settle
down to a stable, nondegenerate distribution if all countries
eventually grow at the
same rate. Why? Well, suppose one thinks growth in Japan will
permanently be
higher than growth in the United States. In that case, the ratio
of Japanese to U.S.
income will diverge to infinity. If this is the way the world
works, one might be more
interested in the long-run distribution of growth rates than in
incomes. However,
I will argue here that in the long run, all countries are likely to
share the same rate
of growth.
This assertion may seem counterintuitive. After all, growth
rates of output
per worker over long periods of time do differ substantially, and
there may be
an initial inclination to believe that the endogenous growth
literature has pro-
vided ample evidence against this hypothesis. Nevertheless,
there are both con-
ceptual and empirical reasons to think that most countries are
likely to share
the same rate of growth in the long run. The conceptual reason

is most persua-
Charles I. Jones 25
sive and has been presented in several recent papers (Eaton and
Kortum, 1994;
Parente and Prescott, 1994; Barro and Sala-i-Martin, 1995;
Bernard and Jones,
1996). Following the recent endogenous growth literature, let us
assume that
the engine of growth is technological progress: output per
worker grows in the
long run because of the creation of ideas. Ideas diffuse across
countries, perhaps
not instantaneously, but eventually. Belgium does not grow only
or even largely
because of the ideas created by Belgians, but rather a
substantial amount of
growth in Belgian output per worker is due to ideas invented
elsewhere in the
world. In this framework, the fact that countries of the world
eventually share
ideas means that their incomes cannot get infinitely far apart.
All countries even-
tually grow at the average rate of growth of world knowledge,
as shown in each
of the papers cited above.
Which brings us to the empirical reason. What do we make of
the large em-
pirical variation in growth rates? Japan, for example, grew at an
average rate of
5.1 percent per year between 1960 and 1988 while the United
States grew only at

1.4 percent. Or consider an even longer horizon using the GDP
per capita data
reported by Maddison (1995). Over the century and a quarter
spanning 1870 to
1994, the United States grew at an average rate of 1.8 percent
per year while the
United Kingdom grew only at 1.3 percent.
In fact, such differences—even over 125 years—are not
inconsistent with the
hypothesis that all countries share a common long-run growth
rate. The resolution
of this apparent inconsistency is transition dynamics. To the
extent that countries
are changing position within the world income distribution,
their average growth
rate can be faster or slower than the growth rate of world
knowledge over any finite
period. This point is illustrated clearly by a closer look at the
U.S. and U.K. evidence
for the last century.
Figure 4 plots the log of GDP per capita in the United States
and United
Kingdom from 1870 to 1994 using the data from Maddison
(1995). As men-
tioned above, average growth in the United States has been a
half a percen-
tage point higher than in the United Kingdom over this 125-year
period. How-
ever, as the figure shows, nearly all of this difference is
accounted for by the
pre-1950 experience. Between 1870 and 1950, the U.S. economy
grew at
1.7 percent while growth in the United Kingdom was a
comparatively

sluggish 0.9 percent. This growth performance occurred as the
United States
overtook the United Kingdom as the world's richest country
around the turn
of the century. Since 1950, however, average growth rates have
been almost
identical, with the United States growing at 1.95 percent and the
United
Kingdom growing at 1.98 percent. Forecasters who in 1950
expected the large
growth differentials of the preceding 70 years to continue were
clearly
mistaken.
Similarly, the fact that Japan has grown faster than the United
States since 1950
says very little about whether or not these two economies will
grow at the same rate
in the long run. Rather, in a world where Japan and the United
States have a
common long-run growth rate, the experience of the last half-
century is evidence
that Japan is moving " u p " in the income distribution.
Figure 4
Income in the United States and United Kingdom
(log scale)
The Future of the Global Income Distribution

Under the assumption that all countries grow at the same
average rate in the
long run, there are a number of ways to make statements about
the eventual shape
of the income distribution. The remainder of this paper employs
three such tech-
niques. First, we examine the predictions generated from a
standard, well-known
growth model due to Solow (1956). Second, we use a prediction
based on transition
dynamics. And finally, we employ a statistical technique that
looks at the frequency
of growth miracles and growth disasters.
Projecting from Current Investment Levels
The Solow (1956) growth model predicts that the level of output
per worker
in an economy in the long run is a function of the rate of
investment in capital,
the growth rate of the labor force, and the level of technology.
5
Statements about
the future of the income distribution can be made if we can
make statements about
the future of investment rates, population growth rates, and
(relative) technology
levels. Notice that nothing really hinges on our following Solow
in assuming ex-
ogenously given and constant investment rates and population
growth rates. Pro-
vided these variables "settle down" in steady state to some
constant value (which
is nearly a definition of the steady state), what we really need

empirically is to be
5
Mathematically, y(t) = (s/(n + g + δ ) )
α / 1 - α
A ( t ) , where s is the investment rate, n is the population
growth rate, δ is the constant rate at which capital depreciates,
α is capital's share in production, and
A(t) is the level of labor-augmenting technology, which is
assumed to grow at the constant, exogenous
rate g.
able to predict where these variables are going to settle. The
Solow model then tells
us how to map these values into steady state incomes.
Jones (1997) follows this line of reasoning in a more general
model that in-
corporates human capital as well as physical capital. A simple
way of predicting
where investment rates and population growth rates will settle is
to assume that the
rates that prevailed in the 1980s will persist. Of course, this
simple method ignores
the fact that investment rates, for example, may be affected by
the transition dy-
namics of the economy. Moreover, what this exercise cannot
predict are underlying

changes in policy, which are presumably very important in the
actual evolution of
the income distribution. Still, this is a useful benchmark to
consider. Later sections
will address these other concerns.
Figure 5 plots steady state relative incomes based on this
forecasting exercise
against relative incomes in 1988 for 74 countries.6 Two features
of Figure 5 stand
out. First, broadly speaking, the 1988 distribution is quite
similar to the distribution
of steady states. Uganda (UGA) and Malawi (MWI) are not poor
because of tran-
sition dynamics. Rather, they are poor because investment rates
are low and tech-
nology levels are low. (Population growth rates are also high,
but a little analysis
illustrates that changes in population growth rates have
relatively small effects in
most neoclassical models.) Based on recent experience in the
1980s, there is no
reason to expect these broad features driving the world income
distribution to
change in the near future.
Second, this similarity is less pronounced at the top of the
income distribution,
where countries continue to "catch up" to the United States,
than it is at the
bottom. One notable exception is India (IND), which is
predicted to grow from a
relative income of 9 percent in 1988 to 13 percent based on
policies in place in the
1980s. Similarly, Malaysia (MYS), Korea, Hong Kong and
Singapore are all pre-

dicted to continue to grow faster than the United States during a
transition to
higher relative incomes, as are a number of OECD economies
like Spain (ESP),
Italy (ITA) and France (FRA). In fact, according to this
particular exercise, a
number of countries such as Singapore, Spain, France and Italy
are predicted to
surpass the United States in GDP per worker. While the exact
location of particular
countries is somewhat sensitive to assumptions, this general
feature that the United
States is not expected to retain its lead in output per worker is
robust. The expla-
nation is simple. Ignoring differences in technology for the
moment, differences
in income are driven by differences in investment rates in
physical and human
capital. The United States is one of the leaders in human capital
investment
(though not by much), but its investment rate in physical capital
is substantially
lower than are investment rates in a number of other countries.
A high U.S. tech-
nology level helps, but it is insufficient to compensate for the
lower U.S. investment
6Specifically, the exercise assumes a common capital share of
1/3 across countries. Educational attain-
ment is assumed to augment labor, and a common rate of return
to schooling of 10 percent is used.
Investment rates, schooling enrollment rates and population
growth rates from the 1980s and the level
of (labor-augmenting) total factor productivity from 1988 are
used in the computation. See Jones (1997)
for more details.

Figure 5
Steady State Incomes, Based on Current Policies
rate. It is largely these differences that are driving the
differences in incomes at the
top of the distribution.7
Transition Dynamics and Steady State Incomes
A second way of estimating the shape of the steady state income
distribution
exploits recent work in the cross-country growth literature.
According to this work,
one of the most persuasive explanations for why some countries
have grown faster
than others over long periods of time is transition dynamics.
The further a country
is below its steady state position in the income distribution, the
faster the country
should grow. I will refer to this as the principle of transition
dynamics. This principle
can be found in the Solow and Ramsey growth models, as well
as in models that
emphasize the importance of technology transfer and the
diffusion of ideas.8
7 Jones (1997) considers several scenarios to check the
robustness of these findings, including models
in which technology levels converge, a demographic transition
leads to identical population growth rates

around the world, human capital investment rates converge, and
physical capital flows internationally to
equalize returns.
8 O n l y the simplest growth models in which the dynamics are
driven by foregoing consumption to invest
output in physical capital, human capital, or research generally
obey the principle as written (for ex-
Charles I. Jones 29
According to this principle, the growth rate of the economy is
proportional to
the gap between the country's current position in the income
distribution and its
steady state position. In an unfortunate choice of terminology,
the factor of pro-
portionality is sometimes called the "speed of convergence."
This phrase uses the
word convergence in the mathematical sense of a sequence of
numbers converging
to some value. It describes the rate at which a country closes the
gap between its
current and steady state positions in the income distribution.
This use is unfortu-
nate because it seems to suggest that this equation has
something to do with dif-
ferent countries getting closer together in the income
distribution, which is not the
case (at least not directly). With this definition, the principle of
transition dynamics
can be stated as
Growth rate of relative income = Speed of convergence

× Percentage gap to own steady state.
For example, suppose a country has a GDP per worker relative
to the United States
of 0.4 and a steady state value equal to 0.5. This represents a 20
percent gap. If the
speed of convergence is 5 percent per year, then the country can
expect its relative
income to grow at 1 percent per year. Its actual GDP per worker
will then grow at
1 percent plus the underlying growth rate of world technological
progress (assum-
ing the United States has reached its steady state).9
This relation has been exploited by the cross-country growth
literature to ex-
plain differences in growth rates. The numerous right-hand side
variables included
in such regressions, in addition to the initial GDP per worker
variable, are an at-
tempt to measure the gap between initial income and the steady
state position of
the country in the world income distribution. A key parameter
estimated by these
regressions is the speed of convergence. For example, a number
of authors such as
Mankiw, Romer and Weil (1992) and Barro and Sala-i-Martin
(1992) have
documented using econometric techniques the well-known "2
percent" speed of
convergence. Other authors, however, have recently argued for
faster rates of con-
vergence.10 The standard Solow model implies a speed of
convergence of about 6
percent for conventional parameter values. Alternatively, in a
model that incorpo-

rates the diffusion of technology across countries, the speed of
convergence is re-
lated to the rate of diffusion.
In general, the authors in the cross-country growth literature
have not exam-
ined the shape of the steady state world income distribution
implied by their re-
gressions. However, the principle of transition dynamics
suggests a simple, intuitive
way to calculate the distribution of steady states. Instead of
using the principle to
ample, Mankiw, Romer and Weil, 1992). More sophisticated
models require more than one state variable
and cannot typically be reduced to so simple a formulation,
although a similar relation often holds,
either as an approximation or when applied to a slightly
different variable such as total factor productivity.
9Mathematically, the principle of transition dynamics is dlog
(t)/dt = λ(log * – log (t)) where is
relative income, * denotes the steady state value of relative
income, and λ is the "speed of convergence."
1 0
F o r example, see the work employing panel data of Islam
(1995) and Caselli, Esquivel and Lefort
(1996).
estimate speeds of convergence in a regression, we can simply
impose alternative
values. Then, data on growth rates from 1960 to 1988 and initial

incomes in 1960
can be used to back out the implied steady states.11 To the
extent that countries
roughly obeyed a stable principle of transition dynamics over
this 28-year period,
we can calculate the targets toward which they were growing.
Figure 6 reports the results of this exercise for several cases,
corresponding to
speeds of convergence of 2 percent, 4 percent and 6 percent. In
general, the steady
state distributions are determined as follows. Countries that
have grown faster than
the United States has over the 28-year period are predicted to
continue to increase
relative to the United States; countries that have grown more
slowly are predicted
to continue to fall. The extent to which the changes continue is
determined by the
speed of convergence. If this speed is slow, as in the first panel
of Figure 6, then
steady states must be far away in order to explain a given
growth differential, im-
plying large additional changes in the income distribution. On
the other hand, if
the speed is fast, say at 6 percent as in the last panel, then smal l
deviations from
the steady state can generate large growth differences; as a
result, the current dis-
tribution looks quite similar to the steady state distribution.
Looking more carefully at the first panel of the figure, the
steady state relative
incomes for a number of countries seem implausibly large with
a 2 percent speed
of convergence. A number of East Asian countries are predicted

to have incomes
of more than 150 percent of U.S. income. The explanation for
this prediction is
that these countries have grown very rapidly for 30 years; with
a very low speed of
convergence, the only way to obtain such rapid growth rates is
if the countries are
extremely far from their steady states. In contrast, the steady
states computed with
a 4 percent or a 6 percent rate of convergence seem more
reasonable.12
The Very Long-Run Income Distribution
So far, we have considered the future of the income distribution
under the
assumption that the policies currently in place in each country
continue, so that
countries are growing toward constant targets. This has a
number of advantages.
For example, it allows us to infer the position within the income
distribution toward
which each country is headed. It also has the flavor of
forecasting the near future.
However, much of the movement of countries within the income
distribution
presumably occurs as a result of policy changes within a
country (broadly inter-
preted to include institutional changes). Japan, for example, had
an income of
roughly 20 percent of that in the United States from 1870 until
World War II. After
the substantial reforms following World War II, we see
enormous increases in Jap-

1 1 To be more precise, we first integrate the equation in
footnote 9 and compute the average growth
rate, as in Mankiw, Romer and Weil (1992). The resulting
equation can be solved for * as a function
of the data.
1 2This result suggests one possible limitation of the exercise.
The calculation assumes that the growth
dynamics for 30 years are driven by a one-time increase in the
gap between current income and steady
state income. Instead, perhaps the steady states for these
economies have shifted upward several times
over the last 30 years. Some calculations reveal that this
alternative does not help as much as one might
suspect.
Figure 6
Steady States Implied by Transition Dynamics
anese relative income far beyond recovery back to the 20
percent level. On the
other side, there is the famous example of Argentina, a
relatively rich country dur-
ing the early part of the twentieth century, but with income in
1988 of only
42 percent of that of the United States. Much of this decline is
attributable to the
Table 1

Frequency of Growth Miracles and Growth Disasters
disastrous policy "reforms" of the Perón era (De Long, 1988,
and the references
there).
Predicting when and where such large changes in institutions
and economic
policies will occur is extremely difficult, if not impossible;
certainly, it requires de-
tailed knowledge of a particular economy. However, predicting
the frequency with
which such changes are likely to occur somewhere in the world
during a decade is
somewhat easier: we observe a large number of countries for
several decades and
can simply count the number of growth miracles and growth
disasters.
One way of making this count is provided in the first row of
Table 1. The 121
countries are classified according to how fast they grew from
1960 to 1988. The
somewhat arbitrary cutoffs for fast and slow growth are defined
as one percentage
point faster and slower than U.S. growth. Because its growth
rate is a reasonable
proxy for the growth rate of the world's technological frontier,
the United States is
a natural benchmark for this exercise. The first row of the table
clearly illustrates
one of the key facts about the world income distribution: rapid
growth has been
significantly more common over the last 30 years than slow
growth. For example,

40 percent of countries experienced fast growth over this
period, while only 15
percent of countries experienced slow growth. This general
result was also apparent
in Figure 2. Looking back at this figure, one sees that there are
more countries
moving up in the distribution than moving down. There are
more Italys than
Venezuelas.
The second part of the table divides countries into six intervals,
based on their
GDP per worker in 1960. For example, the intervals correspond
to countries with
income less than 5 percent of U.S. income, less than 10 percent
but more than 5
percent, and so on. The variable indicates a country's GDP per
worker measured
as a fraction of U.S. income. This part of the table documents
that fast growth and
slow growth occur at roughly the same frequency at the bottom
of the income
distribution; if anything, slow growth is more common. For
countries with incomes
Charles I. Jones 33
Table 2
World Income Distributions, Using Markov Transition Method
of more than 10 percent of U.S. GDP per worker, however, the
frequency of rapid
growth rises markedly. The clear implication is that once
countries make it out of

the lowest income categories, significant upward movements in
the income distri-
bution are much more common than large downward
movements.
Motivated by this data on the frequency of fast and slow
growth, we can provide
a forecast of the very long-run income distribution. Table 2
follows the approach
of Quah (1993a,b) based on Markov transition analysis. As in
Table 1, we sort
countries into intervals based on their 1960 levels of income
relative to the world's
leading economy, the United States during recent decades.13
Then, using annual
data from 1960 to 1988 for the 121-country sample, we
calculate the probabilities
that countries will move from one interval to another. Finally,
using these sample
probabilities, we compute an estimate of the long-run
distribution of incomes.14
The sense in which this computation is different from the
forecasts of the
income distribution in previous sections of the paper is worth
emphasizing. Previ-
ously, we computed the steady state toward which each
economy seems to be
headed and examined the distribution of the steady states based
on current policy
regimes. Here, the exercise recognizes that all countries may be
subject to policy
changes that shift their steady state positions. Therefore, the
computation empha-
sizes a longer-term view of the income distribution. Moreover,
instead of focusing

on any particular country, we focus on the shape of the
distribution as a whole. It
turns out that in the long-run distributions computed using this
approach, there is
a positive probability of any country spending some time in any
interval. This is
because there is some probability that a country, no matter how
rich or poor, will
experience a large policy disaster or policy reform.
13I use the United States as the world's leading economy for the
entire 1960-1988 period despite the
fact that a number of oil-producing economies had higher GDP
per worker in the late 1970s.
14Mathematically, the computation is easily illustrated. First,
we estimate the transition probabilities of
a Markov transition matrix using sample data. Multiplying this
matrix by a vector that corresponds to
the current distribution yields an estimate of the distribution
during the next period. Doing this many
times yields an estimate of the long-run distribution.
Table 2 shows the distribution of countries across the income
intervals in 1960
and 1988 as well as estimates of the future distributions. The
basic changes from
1960 to 1988 have already been documented. There has been
some "convergence"
toward U.S. income at the top of the income distribution, and
this phenomenon is
evident in the table. The long-run distribution, according to the
Markov results,

strongly suggests that this convergence will play a dominant
role in the continuing
evolution of the income distribution. For example, in 1960 only
3 percent of coun-
tries had more than 80 percent of U.S. income, and only 20
percent had more than
40 percent of U.S. income. In the long run, according to the
results, 19 percent of
countries will have relative incomes of more than 80 percent of
the world's leading
economy and 49 percent will have relative incomes of more than
40 percent. Similar
changes are seen at the bottom of the distribution: in 1988, 17
percent of countries
had less than 5 percent of U.S. income; in the long run, only 8
percent of countries
are predicted to be in this category. This latter result is of
interest in light of the
finding reported in Table 1 that large upward and downward
movements occur
with roughly the same frequency at the bottom of the
distribution. The long-run
results here suggest that there is no development trap into which
the poorest coun-
tries will be permanently condemned. The columns in the table
labeled "2010"
and "2050" provide some indication of how long it takes before
this long-run dis-
tribution is reached.
The world income distribution has been evolving for centuries.
Why doesn't
the long-run distribution look roughly like the current
distribution? This is a broad
and important question. The fact that the data say that the long-
run distribution is

different from the current distribution indicates that something
in the world con-
tinues to evolve: the frequency of growth miracles in the last 30
years must have
been higher than in the past, and there must have been fewer
growth disasters.
One possible explanation of this result is that society is
gradually discovering
the kind of institutions and policies that are conducive to
successful economic
performance, and these discoveries are gradually diffusing
around the world. To
take one example, Adam Smith's An Inquiry into the Nature and
Causes of the Wealth
of Nations was not published until 1776. The continued
evolution of the world in-
come distribution could reflect the slow diffusion of capitalism
during the last 200
years. Consistent with this reasoning, the world's experiments
with communism
seem to be coming to an end only in the 1990s. Perhaps it is the
diffusion of wealth-
promoting institutions and infrastructure that accounts for the
continued evolution
of the world income distribution. Moreover, there is no reason
to think that the
institutions in place today are the best possible institutions.
Institutions themselves
are simply ideas, and it is quite likely that better ideas are out
there waiting to be
found. Over the broad course of history, better institutions have
been discovered
and implemented. The continuation of this process at the rates
observed during
the last 30 years would lead to large improvements in the world

income distribution.
Using the Markov methods, we can conduct some other
experiments that
are informative. For example, we can calculate the likelihood of
large move-
ments within the income distribution. Consider first the
frequency of growth
miracles. T h e "Korean e x p e r i e n c e " is not all that
unlikely. A country in the
10 percent bin will move to an income level in the 40 percent
bin or higher with
a 10 percent probability after 37 years. The same is true of the
"Japanese ex-
perience:" a country in the 20 percent bin will move to the
richest category with
a 10 percent probability after 50 years. Given that there are a
large number of
countries in these initial categories, one would expect to see
several growth
miracles at any point in time.
One can also speculate on the frequency of large movements in
the opposite
direction. A famous historical example of such a move occurred
in China. At least
in terms of inventions and technologies, China was one of the
most advanced coun-
tries in the world around the fourteenth century but today has a
GDP per worker
of something like 10 percent of that of the United States. What

is the likelihood of
a similar change today, based on the Markov results? Taking a
country in the richest
bin, only after more than 125 years is there a 10 percent
probability that the country
will fall to a relative income of less than 10 percent.
Conclusion
The post-World War II period has seen substantial changes in
the distribution
of GDP per worker around the world. A number of countries
have exhibited large
increases in income relative to the richest countries. A
significant but smaller num-
ber of countries have seen incomes fall relative to the richest
countries. The net
result of these changes is a movement in the shape of the world
income distribution
from something that looks like a normal distribution in 1960 to
a bimodal "twin-
peaks" distribution in 1988.
One of the key facts that stands out from this analysis is that
fast growth has
been more common than slow growth in the last 30 years. That
is, countries have
shown a tendency to move up in the income distribution. If such
dynamics con-
tinue, the world income distribution across countries is likely to
be more compact
in the future, as a result of the general movement up in the
distribution by poor
countries. In terms of the distributions plotted in Figure 1, one
might expect the
mass to continue to shift from the bottom part of the

distribution toward the top.
Viewed in terms of population instead of countries, the recent
rapid growth in
China and India reinforces this conclusion, as roughly 40
percent of the world's
population lives in these two countries.
Of course, these changes are by no means automatic, and the
fact that we
have not already reached the long-run distribution indicates that
the forces cur-
rently shaping the income distribution are a somewhat recent
phenomenon.
Understanding exactly what these forces are continues to be the
subject of active
research. Whatever, they are, however, the experience of the
last 30 years pro-
vides some reason to be optimistic about the future of the world
income
distribution.
• I would like to thank Brad De Long, Pete Klenow, Alan
Krueger, Lant Pritchett, Andrés
Rodríguez-Clare, Danny Quah and Timothy Taylor for helpful
comments. This research was
partially supported by a grant from the National Science
Foundation (SBR-9510916).
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http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.12.4.51On the
Evolution of the World Income DistributionFactsThe
Assumption of Similar Long-Term Growth RatesThe Future of
the Global Income DistributionProjecting from Current
Investment LevelsTransition Dynamics and Steady State
IncomesThe Very Long-Run Income
DistributionConclusionReferences
American Economic Association
Divergence, Big Time
Author(s): Lant Pritchett
Source: The Journal of Economic Perspectives, Vol. 11, No. 3
(Summer, 1997), pp. 3-17
Published by: American Economic Association
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Journal of Economic Perspectives-Volume 11, Number 3-
Summer 1997-Pages 3-17
Lant Pritchett
ivergence in relative productivity levels and living standards is
the domi-
nant feature of modern economic history. In the last century,
incomes in
the "less developed" (or euphemistically, the "developing")
countries

have fallen far behind those in the "developed" countries, both
proportionately
and absolutely. I estimate that from 1870 to 1990 the ratio of
per capita incomes
between the richest and the poorest countries increased by
roughly a factor of five
and that the difference in income between the richest country
and all others has
increased by an order of magnitude.' This divergence is the
result of the very dif-
ferent patterns in the long-run economic performance of two
sets of countries.
One set of countries-call them the "developed" or the "advanced
capi-
talist" (Maddison, 1995) or the "high income OECD" (World
Bank, 1995) -is
easily, if awkwardly, identified as European countries and their
offshoots plus
Japan. Since 1870, the long-run growth rates of these countries
have been rapid
(by previous historical standards), their growth rates have been
remarkably sim-
ilar, and the poorer members of the group grew sufficiently
faster to produce
considerable convergence in absolute income levels. The other
set of countries,
called the "developing" or "less developed" or
"nonindustrialized," can be
easily, if still awkwardly, defined only as "the other set of
countries," as they
have nothing else in common. The growth rates of this set of
countries have
been, on average, slower than the richer countries, producing
divergence in

' To put it another way, the standard deviation of (natural log)
GDP per capita across all countries has
increased between 60 percent and 100 percent since 1870, in
spite of the convergence amongst the
richest.
* Lant Pritchett is Senior Economist, World Bank, Washington,
D.C.
relative incomes. But amongst this set of countries there have
been strikingly
different patterns of growth: both across countries, with some
converging rapidly
on the leaders while others stagnate; and over time, with a
mixed record of
takeoffs, stalls and nose dives.
The next section of this paper documents the pattern of income
growth and
convergence within the set of developed economies. This
discussion is greatly aided
by the existence of data, whose lack makes the discussion in the
next section of the
growth rates for the developing countries tricky, but as I argue,
not impossible.
Finally, I offer some implications for historical growth rates in
developing countries
and some thoughts on the process of convergence.
Convergence in Growth Rates of Developed Countries

Some aspects of modern historical growth apply principally, if
not exclusively,
to the "advanced capitalist" countries. By "modern," I mean the
period since 1870.
To be honest, the date is chosen primarily because there are
nearly complete na-
tional income accounts data for all of the now-developed
economies since 1870.
Maddison (1983, 1991, 1995) has assembled estimates from
various national and
academic sources and has pieced them together into time series
that are compa-
rable across countries. An argument can be made that 1870
marks a plausible date
for a modern economic period in any case, as it is near an
important transition in
several countries: for example, the end of the U.S. Civil War in
1865; the Franco-
Prussian War in 1870-71, immediately followed by the
unification of Germany; and
Japan's Meiji Restoration in 1868. Perhaps not coincidentally,
Rostow (1990) dates
the beginning of the "drive to technological maturity" of the
United States, France
and Germany to around that date, although he argues that this
stage began earlier
in Great Britain.2
Table 1 displays the historical data for 17 presently high-
income industrialized
countries, which Maddison (1995) defines as the "advanced
capitalist" countries.
The first column of Table 1 shows the per capita level of
income for each country
in 1870, expressed in 1985 dollars. The last three columns of
Table 1 show the

average per annum growth rate of real per capita income in
these countries over
three time periods: 1870-1960, 1960-1980 and 1980-1994.
These dates are not
meant to date any explicit shifts in growth rates, but they do
capture the fact that
there was a golden period of growth that began some time after
World War II and
ended sometime before the 1980s.
Three facts jump out from Table 1. First, there is strong
convergence in per
capita incomes within this set of countries. For example, the
poorest six countries
in 1870 had five of the six fastest national growth rates for the
time period 1870-
2 For an alternative view, Maddison (1991) argues the period
1820-1870 was similar economically to the
1870-1913 period.
Lant Pritchett 5
Table 1
Average Per Annum Growth Rates of GDP Per Capita in the
Presently High-
Income Industrialized Countries, 1870-1989
Per annum growth rates
Level in 1870
Country (1985 P$) 1870-1960 1960-80 1980-94
Average 1757 1.54 3.19 1.51

Std dev. of growth rates .33 1.1 .51
Australia 3192 .90 2.43 1.22
Great Britain 2740 1.08 2.02 1.31
New Zealand 2615 1.24 1.39 1.28
Belgium 2216 1.05 3.70 1.52
Netherlands 2216 1.25 2.90 1.29
USA 2063 1.70 2.48 1.52
Switzerland 1823 1.94 2.07 .84
Denmark 1618 1.66 2.77 1.99
Germany 1606 1.66 3.03 1.56
Austria 1574 1.40 3.81 1.58
France 1560 1.56 3.53 1.31
Sweden 1397 1.85 2.74 .81
Canada 1360 1.85 3.32 .86
Italy 1231 1.54 4.16 1.62
Norway 1094 1.81 3.78 2.08
Finland 929 1.91 3.77 1.09
Japan 622 1.86 6.28 2.87
Source: Maddison, 1995.
Notes: Data is adjusted from 1990 to 1985 P$ by the U.S. GDP
deflator, by a method described later in
this article. Per annum growth rates are calculated using
endpoints.
1960; conversely, the richest five countries in 1870 recorded the
five slowest growth
rates from 1870 to 1960.3 As is well known, this convergence
has not happened at
a uniform rate. There is as much convergence in the 34 years
between 1960 and
1994 as in the 90 years from 1870 to 1960. Even within thi s
earlier period, there
are periods of stronger convergence pre-1914 and weaker
convergence from 1914

to 1950.
Second, even though the poorer countries grew faster than the
richer countries
did, the narrow range of the growth rates over the 1870-1960
period is striking. The
United States, the richest country in 1960, had grown at 1.7
percent per annum
since 1870, while the overall average was 1.54. Only one
country, Australia, grew
either a half a percentage point higher or lower than the
average, and the standard
deviation of the growth rates was only .33. Evans (1994)
formally tests the hypothesis
'The typical measure of income dispersion, the standard
deviation of (natural log) incomes, fell from
.41 in 1870 to .27 in 1960 to only .11 in 1994.
that growth rates among 13 European and offshoot countries
(not Japan) were
equal, and he is unable to reject it at standard levels of
statistical significance.
Third, while the long run hides substantial variations, at least
since 1870 there
has been no obvious acceleration of overall growth rates over
time. As CharlesJones
(1995) has pointed out, there is remarkable stability in the
growth rates in the
United States. For instance, if I predict per capita income in the
United States in

1994 based only on a simple time trend regression of (natural
log) GDP per capita
estimated with data from 1870 to 1929, this prediction made for
65 years ahead is
off by only 10 percent.4 Although this predictive accuracy is
not true for every
country, it is true that the average growth rate of these 17
countries in the most
recent period between 1980 and 1994 is almost exactly the same
as that of the 1870-
1960 period. However, this long-run stability does mask modest
swings in the growth
rates over time, as growth was considerably more rapid in the
period between 1950
to 1980, especially outside the United States, than either in
earlier periods or since
1980.
These three facts are true of the sample of countries that
Maddison defines as
the "advanced capitalist" countries. However, the discussion of
convergence and
long-run growth has always been plagued by the fact that the
sample of countries
for which historical economic data exists (and has been
assembled into convenient
and comparable format) is severely nonrepresentative. Among a
sample of now
"advanced capitalist" countries something like convergence (or
at least nondiver-
gence) is almost tautological, a point made early on by De Long
(1988). Defining
the set of countries as those that are the richest now almost
guarantees the finding
of historical convergence, as either countries are rich now and
were rich historically,

in which case they all have had roughly the same growth rate
(like nearly all of
Europe) or countries are rich now and were poor historically
(likejapan) and hence
grew faster and show convergence. However, examples of
divergence, like countries
that grew much more slowly and went from relative riches to
poverty (like Argen-
tina) or countries that were poor and grew so slowly as to
become relatively poorer
(like India), are not included in the samples of "now developed"
countries that
tend to find convergence.
Calculating a Lower Bound For Per Capita GDP
This selectivity problem raises a difficult issue in trying to
estimate the possible
magnitude of convergence or divergence of the incomes since
1870. There is no
'Jones (1995) uses this basic fact of the constancy of growth to
good effect in creating a compelling
argument that the steadiness of U.S. growth implies that
endogenous growth models that make growth
a function of nonstationary variables, such as the level of R&D
spending or the level of education of the
labor force, are likely incorrect as they imply an accelerating
growth rate (unless several variablesworking
in opposite directions just happen to offset each other). These
issues are also discussed in his paper in
this issue.
Divergence, Big Time 7

historical data for many of the less developed economies, and
what data does exist
has enormous problems with comparability and reliability. One
alternative to
searching for historical data is simply to place a reasonable
lower bound on what
GDP per capita could have been in 1870 in any country. Using
this lower bound
and estimates of recent incomes, one can draw reliable
conclusions about the his-
torical growth rates and divergence in cross-national
distribution of income levels.
There is little doubt life was nasty, brutish and short in many
countries in 1870.
But even deprivation has its limit, and some per capita incomes
must imply stan-
dards of living that are unsustainably and implausibly low.
After making conservative
use of a wide variety of different methods and approaches, I
conclude that $250
(expressed in 1985 purchasing power equivalents) is the lowest
GDP per capita
could have been in 1870. This figure can be defended on three
grounds: first, no
one has ever observed consistently lower living standards at any
time or place in
history; second, this level is well below extreme poverty lines
actually set in impov-
erished countries and is inconsistent with plausible levels of
nutritional intake; and
third, at a lower standard of living the population would be too
unhealthy to
expand.

Before delving into these comparisons and calculations, it is
important to stress
that using the purchasing power adjustments for exchange rates
has an especially
important effect in poor countries. While tradable goods will
have generally the
same prices across countries because of arbitrage, nontradable
goods are typically
much cheaper in poorer countries because of their lower income
levels. If one
applies market exchange rates to convert incomes in these
economies to U.S. dol-
lars, one is typically far understating the "true" income level,
because nontradable
goods can be bought much more cheaply than market exchange
rates will imply.
There have been several large projects, especially the UN
International Compari-
sons Project and the Penn World Tables, that through the
collection of data on the
prices of comparable baskets of goods in all countries attempt
to express different
countries' GDP in terms of a currency that represents an
equivalent purchasing
power over a basket of goods. Since this adjustment is so large
and of such quan-
titative significance, I will denote figures that have been
adjusted in this way by 1$.
By my own rough estimates, a country with a per capita GDP
level of $70 in U.S.
dollars, measured in market exchange rates, will have a per
capita GDP of J$250.
The first criteria for a reasonable lower bound on GDP per
capita is that it be
a lower bound on measured GDP per capita, either of the

poorest countries in the
recent past or of any country in the distant past. The lowest
five-year average level
of per capita GDP reported for any country in the Penn World
Tables (Mark 5) is
J$275 for Ethiopia in 1961-65; the next lowest is J$278 for
Uganda in 1978-1982.
The countries with the lowest level of GDP per capita ever
observed, even for a
single year, are J$260 for Tanzania in 1961, J$299 for Burundi
in 1965 and J$220
Uganda in 1981 (in the middle of a civil war). Maddison (1991)
gives estimates of
GDP per capita of some less developed countries as early as
1820: J$531 for India,
J$523 for China and J$614 for Indonesia. His earliest estimates
for Africa begin in
1913: J$508 for Egypt and J$648 for Ghana. Maddison also
offers increasingly
speculative estimates for western European countries going
back much further in
time; for example, he estimates that per capita GDPs in the
Netherlands and the
United Kingdom in 1700 were P$1515 and P$992, respectively,
and ventures to
guess that the average per capita GNP in western Europe was
P$400 in 1400. Kuz-
nets's (1971) guess of the trough of the average per capita GDP
of European coun-
tries in 900 is around P$400.' On this score, P$250 is a pretty
safe bet.

A complementary set of calculations to justify a lower bound
are based on
"subsistence" income. While "subsistence" as a concept is out of
favor, and right-
fully so for many purposes, it is sufficiently robust for the task
at hand. There are
three related calculations: poverty lines, average caloric intakes
and the cost of
subsistence. Ravallion, Datt and van de Walle (1991) argue that
the lowest defen-
sible poverty line based on achieving minimally adequate
consumption expendi-
tures is P$252 per person per year. If we assume that personal
consumption expen-
ditures are 75 percent of GDP (the average for countries with
GDP per capita less
than P$400) and that mean income is 1.3 times the median, then
even to achieve
median income at the lowest possible poverty line requires a per
capita income of
$437.6
As an alternative way of considering subsistence GDP per
capita, begin with
the finding that estimated average intake per person per day
consistent with work-
ing productively is between 2,000 to 2,400 calories.7 Now,
consider two calculations.
The first is that, based on a cross-sectional regression using
data on incomes from
the Penn World Tables and average caloric intake data from the
FAO, the predicted
caloric consumption at P$250 is around 1,600.8 The five lowest
levels of

5 More specifically, Kuznets estimated that the level was about
$160, if measured in 1985 U.S. dollars.
However, remember from the earlier discussion that a
conversion at market exchange rates-which is
what Kuznets was using-is far less than an estimate based on
purchasing power parity exchange rates.
If we use a multiple of 2.5, which is a conservative estimate of
the difference between the two, Kuznets's
estimate in purchasing power equivalent terms would be equal
to a per capita GDP of $400 in 1985 U.S.
dollars, converted at the purchasing power equivalent rate.
" High poverty rates, meaning that many people live below
these poverty lines, are not inconsistent with
thinking of these poverty lines as not far above our lower
bound, because many individuals can be in
poverty, but not very far below the line. For instance, in South
Asia in 1990, where 33 percent of the
population was living in "extreme absolute poverty," only about
10 percent of the population would be
living at less than $172 (my estimates from extrapolations of
cumulative distributions reported in Chen,
Datt and Ravallion, 1993).
7The two figures are based on different assumptions about the
weight of adult men and women, the
mean temperature and the demographic structure. The low
figure is about as low as one can go because
it is based on a very young population, 39 percent under 15 (the
young need fewer calories), a physically
small population (men's average weight of only 110 pounds and
women of 88), and a temperature of
250 C (FAO, 1957). The baseline figure, although based on
demographic structure, usually works out to
be closer to 2,400 (FA0, 1974).
8 The regression is a simple log-log of caloric intake and
income in 1960 (the log-log is for simplicity
even though this might not be the best predictor of the level).

The regression is
ln(average caloric intake) = 6.37 + .183*ln(GDP per capita),
(59.3) (12.56).
Lant Pritchett 9
caloric availability ever recorded in the FAO data for various
countries-
1,610 calories/person during a famine in Somalia in 1975; 1,550
calories/person
during a famine in Ethiopia in 1985; 1,443 calories/person in
Chad in 1984; 1,586
calories/person in China in 1961 during the famines and
disruption associated with
the Cultural Revolution; and 1,584 calories/person in
Mozambique in 1987-reveal
that nearly all of the episodes of average daily caloric
consumption below 1,600 are
associated with nasty episodes of natural and/or man-made
catastrophe. A second
use of caloric requirements is to calculate the subsistence
income as the cost of
meeting caloric requirements. Bairoch (1993) reports the results
of the physiolog-
ical minimum food intake at $291 (at market exchange rates) in
1985 prices. These
calculations based on subsistence intake of food again suggest
J$250 is a safe lower
bound.
That life expectancy is lower and infant mortality higher in
poorer countries
is well documented, and this relation can also help establish a

lower bound on
income (Pritchett and Summers, 1996). According to
demographers, an under-five
infant mortality rate of less than 600 per 1000 is necessary for a
stable population
(Hill, 1995). Using a regression based on Maddison's (1991)
historical per capita
income estimates and infant mortality data from historical
sources for 22 countries,
I predict that infant mortality in 1870 for a country with income
of J$250 would
have been 765 per 10O.9 Although the rate of natural increase
of population back
in 1870 is subject to great uncertainty, it is typically estimated
to be between .25
and 1 percent annually in that period, which is again
inconsistent with income levels
as low as J$250.1o
If you accept: a) the current estimates of relative incomes
across nations;
b) the estimates of the historical growth rates of the now-rich
nations; and c) that
even in the poorest economies incomes were not below J$250 at
any point-then
you cannot escape the conclusion that the last 150 years have
seen divergence, big
time. The logic is straightforward and is well illustrated by
Figure 1. If there had
been no divergence, then we could extrapolate backward from
present income of
the poorer countries to past income assuming they grew at least
as fast as the United

'The regression is estimated with country fixed effects:
ln(IMR) = -.59 ln(GDP per capita) _ .013*Trend _
.002*Trend*(l if >1960)
(23.7) (32.4) (14.23)
N = 1994 and t-statistics are in parenthesis. The prediction used
the average country constant of 9.91.
"' Livi-Basci (1992) reports estimates of population growth in
Africa between 1850 and 1900 to be
.87 percent, and .93 percent between 1900 and 1950, while
growth for Asia is estimated to be .27 1850
to 1900, and .61 1900 to 1950. Clark (1977) estimates the
population growth rates between 1850 and
1900 to be .43 percent in Africa and India and lower, .33
percent, in China.
Figure 1
Simulation of Divergence of Per Capita GDP, 1870-1985
(showing only selected countries)
1870 1960 1990
Richest / poorest 8.7 38.5 45.2
std. dev.: 0.64 0.88 1.06
o | l
j~~~~~~~~~~~~~~P$18054
USA USA
- - -Ethiopia

<
<5
..... Chad
90 - -- MirlimumI
ct 00
W P$20631 1
~~~~~~~~~~~Actual
l
X _ l ~~~~~~~~Imputed ll
= _ l *-- | l ~~~~~~~~~~Chad
P$250
(assumed lower bound) I l
t ,,,, I,,,,,,,,,~~~~~~~~~ ~~~~ I, , I, , I, ,1,,, I .
1850 1870 1890 1910 1930 1950 1970 1990 2010
States. However, this would imply that many poor countries
must have had incomes
below J$100 in 1870. Since this cannot be true, there must have
been divergence.
Or equivalently, per capita income in the United States, the
world's richest indus-
trial country, grew about four-fold from 1870 to 1960. Thus,
any country whose
income was not fourfold higher in 1960 than it was in 1870
grew more slowly than
the United States. Since 42 of the 125 countries in the Penn
World Tables with data
for 1960 have levels of per capita incomes below $1,000 (that
is, less than four times

$250), there must have been substantial divergence between the
top and bottom.
The figure of J$250 is not meant to be precise or literal and the
conclusion of
massive divergence is robust to any plausible assumption about
a lower bound.
Consider some illustrative calculations of the divergence in per
capita incomes
in Table 2. I scale incomes back from 1960 such that the poorest
country in 1960
just reaches the lower bound by 1870, the leader in 1960 (the
United States) reaches
its actual 1870 value, and all relative rankings between the
poorest country and the
United States are preserved." The first row shows the actual
path of the U.S. econ-
" The growth rate of the poorest country was imposed to reach
F$250 at exactly 1870, and the rate of
the United States was used for the growth at the top. Then each
country's growth rate was assumed to
be a weighted average of those two rates, where the weights
depended on the scaled distance from the
bottom country in the beginning period of the imputation, 1960.
This technique "smushes" the distri-
Table 2
Estimates of the Divergence of Per Capita Incomes Since 1870
1870 1960 1990

USA (F$) 2063 9895 18054
Poorest (F$) 250 257 399
(assumption) (Ethiopia) (Chad)
Ratio of GDP per capita of richest to poorest country 8.7 38.5
45.2
Average of seventeen "advanced capitalist" countries 1757 6689
14845
from Maddison (1995)
Average LDCs from PWT5.6 for 1960, 1990 (imputed for 740
1579 3296
1870)
Average "advanced capitalist" to average of all other 2.4 4.2 4.5
countries
Standard deviation of natural log of per capita incomes .51 .88
1.06
Standard deviation of per capita incomes F$459 F$2,112
F$3,988
Average absolute income deficit from the leader F$1286 F$7650
F$12,662
Notes: The estimates in the columns for 1870 are based on
backcasting GDP per capita for each country
using the methods described in the text assuming a minimum of
P$250. If instead of that method,
incomes in 1870 are backcast with truncation at P$250, the 1870
standard deviation is .64 (as reported
in Figure 1).
omy. The second row gives the level of the poorest economy in
1870, which is J$250
by assumption, and then the poorest economies in 1960 and
1990 taken from the

Penn World Tables. By division, the third row then shows that
the ratio of the top
to the bottom income countries has increased from 8.7 in 1870
to 38 by 1960 and
to 45 by 1990. If instead one takes the 17 richest countries
(those shown in Table
1) and applies the same procedure, their average per capita
income is shown in
the fourth row. The average for all less developed economies
appearing in the Penn
World Tables for 1960 and 1990 is given in the fifth row; the
figure for 1870 is
calculated by the "backcasting" imputation process for
historical incomes de-
scribed above. By division, the sixth row shows that the ratio of
income of the richest
to all other countries has almost doubled from 2.4 in 1870 to 4.6
by 1990.
bution back into the smaller range between the top and bottom
while maintaining all cross country
rankings. The formula for estimating the log of GDP per capita
(GDPPC) in the ith country in 1870 was
GDPPCi 870' = GDPPCi 96"* *(1/w,)
where the scaling weight wi was
wi = (1 - ai)*min(GDPPC'96()/F$250 +
ai*GDPPCusA/GDPPCusA,
and where ai is defined by
ai = (GDPPC19N - min (S DPPC'9"))/(GDPPCL9? -
min(CDPPC'96"()).

The magnitude of the change in the absolute gaps in per capita
incomes
between rich and poor is staggering. From 1870 to 1990, the
average absolute gap
in incomes of all countries from the leader had grown by an
order of magnitude,
from $1,286 to $12,662, as shown in the last row of Table 2.12
While the growth experience of all countries is equally
interesting, some are
more equally interesting than others. China and India account
for more than a
third of the world's population. For the conclusion of
divergence presented here,
however, a focus on India and China does not change the
historical story. One can
estimate their growth rates either by assuming that they were at
$250 in 1870 and
then calculating their growth rate in per capita GDP to reach the
levels given by
the Penn World Tables in 1960 (India, $766; China, $567), or
by using Maddison's
historical estimates, which are shown in Table 3, India's growth
rate is a fifth and
China's a third of the average for developed economies. Either
way, India's and
China's incomes diverged significantly relative to the leaders
between 1870 and
1960.
The idea that there is some lower bound to GDP per capita and
that the lower

bound has implications for long-run growth rates (and hence
divergence) will not
come as news either to economic historians or to recent thinkers
in the area of
economic growth (Lucas, 1996). Kuznets (1966, 1971) pointed
out that since the
now-industrialized countries have risen from very low levels of
output to their pres-
ently high levels, and that their previously very low levels of
output were only con-
sistent with a very slow rate of growth historically, growth rates
obviously accelerated
at some point. Moreover, one suspects that many of the
estimates of income into
the far distant past cited above rely on exactly this kind of
counterfactual logic.
Considering Alternate Sources of Historical Data
Although there is not a great deal of historical evidence on GDP
estimates in
the very long-run for the less developed countries, what there is
confirms the finding
of massive divergence. Maddison (1995) reports time series data
on GDP per capita
incomes for 56 countries. These include his 17 "advanced
capitalist" countries
(presented in Table 1), five "southern" European countries,
seven eastern Euro-
pean countries and 28 countries typically classified as "less
developed" from Asia
(11), Africa (10) and Latin America (7). This data is clearly
nonrepresentative of
the poorest countries (although it does include India and China),
and the data for
Africa is very sparse until 1960. Even so, the figures in Table 3

show substantially
lower growth for the less developed countries than for the
developed countries. If
12 In terms of standard deviations, the method described in the
text implies that the standard deviation
of the national log of per capita GDP has more than doubled
from 1870 to 1990, rising from .51 in 1870
to .88 in 1960 to 1.06 by 1990. In dollar terms, the standard
deviation of per capita incomes rose from
$459 in 1870 to $2,112 in 1960 to $3,988 in 1990 (again, all
figures expressed in 1985 dollars, converted
at purchasing power equivalent exchange rates).
Lant Pritchett 13
Table 3
Mean Per Annum Growth Rates of GDP Per Capita
1870-1960 1960-1979 1980-1994
Advanced capitalist countries (17) 1.5 3.2 1.5
(.33) (1.1) (.51)
Less developed countries (28) 1.2 2.5 .34
(.88) (1.7) (3.0)
Individual countries:
India .31 1.22 3.07
China .58 2.58 6.45
Korea (1900) .71 5.9 7.7
Brazil 1.28 4.13 -.54
Argentina (1900) 1.17 1.99 .11
Egypt (1900) .56 3.73 2.21

Source: Calculations based on data from Maddison (1995).
one assumes that the ratio of incomes between the "advanced
capitalist" countries
and less developed countries was 2.4 in 1870, then the .35
percentage point differ-
ential would have produced a rich-poor gap of 3.7 in 1994,
similar to the projected
increase in the gap to 4.5 in Table 2.
Others have argued that incomes of the developing relative to
the developed
world were even higher in the past. Hanson (1988, 1991) argues
that adjustments
of comparisons from official exchange rates to purchasing
power equivalents imply
that developing countries were considerably richer historically
than previously be-
lieved. Bairoch (1993) argues that there was almost no gap
between the now-
developed countries and the developing countries as late as
1800. As a result, his
estimate of the growth rate of the "developed" world is 1.5
percent between 1870
and 1960 as opposed to .5 percent for the "developing" world,
which implies even
larger divergence in per capita incomes than the lower bound
assumptions reported
above.
Poverty Traps, Takeoffs and Convergence
The data on growth in less developed countries show a variety
of experiences,
but divergence is not a thing of the past. Some countries are

"catching up" with
very explosive but sustained bursts of growth, some countries
continue to experi-
ence slower growth than the richest countries, and others have
recently taken
nosedives.
Let's set the standard for explosive growth in per capita GDP at
a sustained
rate of 4.2 percent; this is the fastest a country could have
possibly grown from 1870
to 1960, as at this rate a country would have gone from the
lower bound in 1870
to the U.S. level in 1960. Of the 108 developing countries for
which there are
available data in the Penn World Tables, 11 grew faster than 4.2
per annum over
the 1960-1990 period. Prominent among these are east Asian
economies like Korea
(6.9 percent annual growth rate in per capita GDP from 1960-
1992), Taiwan (6.3
percent annual growth) and Indonesia (4.4 percent). These
countries are growing
at an historically unprecedented pace. However, many countries
that were poor in
1960 continued to stagnate. Sixteen developing countries had
negative growth over
the 1960-1990 period, including Mozambique (-2.2 percent per
annum) and Guy-
ana (-.7 percent per annum). Another 28 nations, more than a
quarter of the total

number of countries for which the Penn World Tables offers
data, had growth rates
of per capita GDP less than .5 percent per annum from 1960 to
1990 (for example,
Peru with .1 percent); and 40 developing nations, more than a
third of the sample,
had growth rates less than 1 percent per annum.'3
Moreover, as Ben-David and Papell (1995) emphasize, many
developing coun-
tries have seen their economies go into not just a slowdown, but
a "meltdown." If
we calculate the growth rates in the Penn World Tables and
allow the data to dictate
one break in the growth rate over the whole 1960-1990 period,
then of the 103
developing countries, 81 have seen a deceleration of growth
over the period, and
the average deceleration is over 3 percentage points. From
1980-1994, growth in
per capita GDP averaged 1.5 percent in the advanced countries
and .34 percent in
the less developed countries. There has been no acceleration of
growth in most
poor countries, either absolutely or relatively, and there is no
obvious reversal in
divergence.
These facts about growth in less developed countries highlight
its enormous vari-
ability and volatility. The range of annual growth rates in per
capita GDP across less
developed economies from 1960 to 1990 is from -2.7 percent to
positive 6.9 percent.
Taken together, these findings imply that almost nothing that is

true about the
growth rates of advanced countries is true of the developing
countries, either in-
dividually or on average. The growth rates for developed
economies show conver-
gence, but the growth rates between developed and developing
economies show
considerable divergence. The growth rates of developed
countries are bunched in
a narrow group, while the growth rates of less developed
countries are all over with
some in explosive growth and others in implosive decline.
Conclusion
For modem economists, Gerschenkron (1962) popularized the
idea of an "ad-
vantage to backwardness," which allows countries behind the
technological frontier to
13 The division into developed and developing is made here by
treating all 22 high-income members of
the OECD as "developed" and all others as "developing."
experience episodes of rapid growth driven by rapid
productivity catch-up.'4 Such rapid
gains in productivity are certainly a possibility, and there have
been episodes of indi-
vidual countries with very rapid growth. Moreover, there are
examples of convergence
in incomes amongst regions. However, the prevalence of
absolute divergence implies

that while there may be a potential advantage to backwardness,
the cases in which
backward countries, and especially the most backward of
countries, actually gain sig-
nificantly on the leader are historically rare. In poor countries
there are clearly forces
that create the potential for explosive growth, such as those
witnessed in some countries
in east Asia. But there are also strong forces for stagnation: a
quarter of the 60 countries
with initial per capita GDP of less than $1000 in 1960 have had
growth rates less than
zero, and a third have had growth rates less than .05 percent.
There are also forces for
"implosive" decline, such as that witnessed in some countries in
which the fabric of
civic society appears to have disintegrated altogether, a point
often ignored or ac-
knowledged offhand as these countries fail to gather plausible
economic statistics and
thus drop out of our samples altogether. Backwardness seems to
carry severe disadvan-
tages. For economists and social scientists, a coherent model of
how to overcome these
disadvantages is a pressing challenge.
But this challenge is almost certainly not the same as deriving a
single "growth
theory." Any theory that seeks to unify the world's experience
with economic growth
and development must address at least four distinct questions:
What accounts for con-
tinued per capita growth and technological progress of those
leading countries at the
frontier? What accounts for the few countries that are able to
initiate and sustain

periods of rapid growth in which they gain significantly on the
leaders? What accounts
for why some countries fade and lose the momentum of rapid
growth? What accounts
for why some countries remain in low growth for very long
periods?
Theorizing about economic growth and its relation to policy
needs to tackle these
four important and distinct questions. While it is conceivable
that there is an all-
purpose universal theory and set of policies that would be good
for promoting eco-
nomic growth, it seems much more plausible that the
appropriate growth policy will
differ according to the situation. Are we asking about more
rapid growth in a mature
and stable economic leader like the United States or Germany or
Japan? About a
booming rapidly industrializing economy trying to prevent
stalling on a plateau, like
Korea, Indonesia, or Chile? About a once rapidly growing and
at least semi-
industrialized country trying to initiate another episode of rapid
growth, like Brazil or
Mexico or the Philippines? About a country still trying to
escape a poverty trap into
sustained growth, like Tanzania or Myanmar or Haiti?
Discussion of the theory and
policy of economic growth seems at times remarkably
insensitive to these distinctions.
* I would like to thank William Easterly, Deon Filmer, Jonathan
Isham, Estelle James, Ross
Levine, Mead Over, Martin Rama and Martin Ravallion for
helpful discussions and comments.

'4 I say "for modern economists," since according to Rostow
(1993), David Hume more than 200 years
ago argued that the accumulated technological advances in the
leading countries would give the followers
an advantage.
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Article Contentsp. [3]p. 4p. 5p. 6p. 7p. 8p. 9p. 10p. 11p. 12p.
13p. 14p. 15p. 16p. 17Issue Table of ContentsThe Journal of
Economic Perspectives, Vol. 11, No. 3 (Summer, 1997), pp. 1-
202+i-viFront Matter [pp. 1 - 2]Symposium: Distribution of
World IncomeDivergence, Big Time [pp. 3 - 17]On the
Evolution of the World Income Distribution [pp. 19 -
36]Symposium: European UnemploymentLabor Market
Rigidities: At the Root of Unemployment in Europe [pp. 37 -
54]Unemployment and Labor Market Rigidities: Europe versus
North America [pp. 55 - 74]Symposium: Electronic Journals in
EconomicsThe Future Information Infrastructure in Economics
[pp. 75 - 94]The AEA's Electronic Publishing Plans: A
Progress Report [pp. 95 - 104]Bridging the Gap Between the
Public's and Economists' Views of the Economy [pp. 105 -
118]Restructuring, Competition and Regulatory Reform in the
U.S. Electricity Sector [pp. 119 - 138]FDICIA After Five Years
[pp. 139 - 158]A Nobel Prize for Game Theorists: The
Contributions of Harsanyi, Nash and Selten [pp. 159 -
174]Policy Watch: The Family and Medical Leave Act [pp. 175
- 186]Recommendations for Further Reading [pp. 187 -
194]Correspondence [pp. 195 - 198]Notes [pp. 199 - 202]Back
Matter [pp. i - vi]

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