w'S 2'4+5
POLICY RESEARCH WORKING PAPER 2645
Inequality Convergence Is income inequalit tending
to fall in countries with high
inequality and to rise in those
Martin Ravallion where inequality is low? Is
there a process of
convergence toward
medium-level inequality?
The World Bank
Development Research Group
Povert,vy
July 2001
| POLICY RESEARCH WORKING PAPER 2645
Summary findings
Comparing changes in inequality with initial levels, using However, the convergence process is neither rapid nor
new data, Ravallion finds that within-country inequality certain, and more observations over time are needed to
in income or per capita consumption is converging be confident of the pattern. Ravallion offers an approach
toward medium levels-a Gini index around 40 percent. to modeling the determinants of inequality that may be a
The finding is robust to allow for serially independent starting point for estimating richer models.
measurement error in inequality data and for short-run
dynamics around longer-term trends.
This paper-a product of Poverty, Development Research Group-is part of a larger effort in the group to better understand
what is happening to income inequality within developing countries. Copies of the paper are available free from the World
Bank, 1818 H Street NW, Washington, DC 20433. Please contact Patricia Sader, room MC3-556, telephone 202-473-
3902, fax 202-522-1153, email address psaderCa@worldbank.org. Policy Research Working Papers are also posted on the
Web at http://econ.worldbank.org. The author may be contacted at mravallionCa worldbank.org. July 2001. (23 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas aboot
development issuies. An objective of the series is to get the fiidings oit quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
Inequality Convergence
Martin Ravallion1
World Bank, 1818 H Street NW, Washington DC 20433, USA
Addresses for correspondence mravallion(diworldbank.org. This paper was written while the
author was visiting the Universite des Sciences Sociales, Toulouse. These are not necessarily the views
of the World Bank or any affiliated organization. For their helpful comments on an earlier version of
this paper, the author is grateful to Roland Benabou, Francois Bourguignon, Shaohua Chen, Angus
Deaton, Bill Easterly, Jyotsna Jalan, Stephen Jenkins, Aart Kraay, Branko Milanovic, Giovanna
Prennushi, Dominique van de Walle and Michael Walton.
1. Introduction
Past tests of the empirical implications of the neoclassical growth model have largely
focused on its implications for convergence in average incomes. However, the neoclassical
model can also yield convergence of the whole distribution, not just its first moment; as Benabou
(1996, p.51) puts it:
"Once augmented with idiosyncratic shocks, most versions of the neoclassical growth
model imply convergence in distribution: countries with the same fundamentals should
tend towards the same invariant distribution of wealth and pretax income."
The simplest test for inequality convergence borrows from growth empirics and looks at
the correlation across countries between changes in measured inequality and its initial levels,
analogous to standard tests for mean income convergence. This is the method used in what
appears to be the first attempt to test for inequality convergence in the literature, namely by
B6nabou (1996), who found evidence of convergence in various data sets.
This paper revisits Benabou's findings using new and better data sets. While the data
used here appear to be the best compilations currently available for this purpose, the data are far
from ideal. There are limitations in coverage across countries and over time. For example, in the
83 developing and transitional countries included in the Chen and Ravallion (2000) distributional
data set, only 21 have four or more surveys over time. There are also serious concerns about
measurement error in inequality data. There are the usual concerns about sampling and non-
sampling errors in estimates from a single survey; consumption and (even more so) income
underreporting is thought to be a common problem in surveys and its is unlikely to be
distribution-neutral. There are also concerns about survey comparability over time, given that
even seemingly modest changes in survey design (such as recall periods) and processing (such as
2
valuation methods for income-in-kind) can change measured inequality.2 These problems may
well have considerable bearing on the results of convergence tests. Under (over) estimating the
initial level of inequality would lead to over (under) estimation of the subsequent trend - a
source of bias commonly known as "Galton's fallacy". The magnitude of the bias is unclear a
priori. While there is only so much that can be done to address such concerns, the paper offers a
test for convergence that is at least robust to serially independent measurement error in inequality
data.
After reviewing the literature in the next section, the tests for inequality convergence are
described in section 3. Section 4 implements the tests on two data sets. Signs of convergence
toward medium levels of inequality are found for both the Gini index and various points on the
Lorenz curve, and for samples with and without Eastern Europe and Central Asia. Convergence
is less strong in the test allowing for measurement error, but it is still evident. The concluding
section points to implications for current policy debates and for further research.
2. Antecedents in the literature
Tests for convergence in average incomes have been used to better understand the
evolution of inequality between countries.3 We know less about what has been happening to
income inequality within countries. There have been numerous investigations of how inequality
has been changed in specific countries and there have been compilations of estimates of
inequality measures across countries and over time. Analysis of one such compilation produced
by Deininger and Squire (1996) has been used to argue that very few countries outside Eastern
Europe and Central Asia have experienced a significant trend increase or decrease in inequality
See for example Ravallion and Chen (1999) on the problems in measuring inequality in China.
On the theory and evidence on income convergence see Durlauf and Quah (1999).
3
over the last two decades or so (Bruno, Ravallion and Squire, 1997; Li Squire and Zou, 1998).4
Thus Li et al. (1998, p.26) argued that "income inequality is relatively stable within countries".
Dollar and Kraay's (2000) results also suggest approximate distribution-neutrality in the process
of economic growth; on average growth-promoting policy reforms appear to be as good at
(proportionately) raising the incomes of the poor as for anyone else.
These findings are suggestive of convergence; if inequality is in fact generated by a
stationary process without trend than initial disparities between countries in their levels of
inequality will persist, in expectation. However, that conclusion may be premature, given that
none of the work summarized above has actually tested for inequality convergence. Limitations
in data and methods cloud our current knowledge on this issue. The household surveys on which
inequality is measured are far less frequent than the National Accounts. And they tend also to be
unevenly spaced over time. Surveys tend also to be less standardized than National Accounts. So
there are comparability problems between countries and over time, and measurement errors in
existing data compilations.
Distinguishing trends from fluctuations is problematic with the available data. Yet
conclusions are often drawn about inequality trends based on data compilations and statistical
methods that ignore some or all of these problems. For example, trends are often tested using
static regressions in which measured inequality is regressed on time (as in Bruno et al., 1997, and
Li et al., 1998). This is an understandable simplification given the data available, but it is
hazardous too. From time series econometrics we know how important it is to take proper
account of the dynamic structure of any variable (such as whether it is positively or negatively
4 The countries Eastern Europe and the former Soviet Union have experienced unusually sharp
increases in inequality, starting from low levels (Milanovic, 1998).
4
serially dependent) when trying to detect a trend. If a variable is serially dependent then tests for
a significant trend that ignore this fact can be deceptive (for discussion and references see
Davidson and MacKinnon, 1993, Chapter 19). Li et al. (1998) appear to implicitly acknowledge
the problem when they note that they do not allow for dynamics in testing for trends in
inequality, because they have too few observations over time.5
Benabou (1996) appears to have been the first paper to test for inequality convergence.
He regressed the change in the Gini index between the first and last observation on the Gini
index for the first observation. B6nabou finds evidence of significant negative coefficients on the
initial inequality index in various data sets and time periods, though not all.6 In addition to
testing for convergence on a new data set, I will offer tests that are more robust to likely
measurement error.
3. Testing for inequality convergence
Borrowing from the literature on testing for convergence in mean income, the simplest
test for inequality convergence is to regress the observed changes over time in a measure of
inequality on the measure's initial values across countries, analogous to standard tests for
convergence in average incomes. This is the test for inequality convergence used by Benabou
(1996). Let Git denote the observed Gini index (or some other measure of inequality) in country
i at dates t=O,1,.., T. A test equation for inequality convergence is then:
5 Li et al. (1998) perform standard Durbin-Watson tests on their regressions for explaining
inequality in a cross-country panel, and they also give estimates with a standard correction for first-order
serial correlation in the error term. This would probably help avoid bias due to miss-specification of the
dynamics in a time-series model. However, the D-W test and standard AR(l) correction are not valid in
panel data. (One can change the results by shuffling the order of countries.)
Using the same method as Benabou, Banerjee and Duflo (1999) also not (in passing) that their
data suggest a negative linear relationship between changes in inequality and past inequality.
5
GiT - Gio = a + bGio + ei (i=1,...,N) (1)
where a and b are parameters to be estimated and e is a zero mean error term. If the
"convergence parameter" b is negative (positive) then there is inequality convergence
(divergence). For non-zero b, steady-state inequality converges to an expected value of - a / b.
One objection to this test is that measurement error in the observed inequality data will
bias such a test in the direction of suggesting convergence, as discussed in the introduction.
Another concern is that data are thrown away between the initial and final surveys. This also
raises the question as to whether the changes between the first and last dates are independent of
the path taken.
To address these concerns, let the true value of the Gini index be G,*,. (These are date
specific, since the fundamental determinants of inequality can change.) Each country is assumed
to have an underlying trend, R1, in inequality, such that the change in the true level of inequality
between date 1 and any date t is:
G, - G, = Ri(t -1) +vi (i=l,...,N; ,2,..,T) (2)
where vi, is a zero-mean innovation error term. (Measured inequality at date 0 is now retained
for use as an instrumental variable.) The observed measure of inequality is:
Git = G, , + 6it (3)
where eft is a zero-mean and serially independent measurement error.
The hypothesis to be tested is that this trend in steady-state inequality depends on its
initial level. I assume a linear relationship of the form:
Ri= a + 6G* + ,i (4)
where a and /? are parameters to be estimated and ,ui is a zero-mean innovation error term.
6
Combining equations (2)-(4), the estimable test equation can be written in the form:
Git - Gil = (a + f8Gil )(t -1) + eit (i=l,...,N; P2,.., (5)
where the composite (heteroskedastic) error term is:
eit = Vit + sit - 6ii + (t - l)(Ui -figEi) . (6)
Notice that 6il jointly influences Gil and eit. So it cannot be assumed that cov(Giot, eit) = 0.
However, Gio is a valid instrument for Gil. The key assumption for this to hold is that the errors
in measuring inequality are serially independent. That assumption can be questioned; the same
factors that lead to miss-measurement of inequality in one survey for a given country may well
carry over to the next survey. In principle one could allow for some serial dependence in
measurement errors, such as a first-order moving average process, justifying use of a second lag.
However, with so few observations over time, it is not feasible to relax the serial independence
assumption for measurement errors in the inequality data.
The above test can be generalized to allow for short-term dynamics, such that the
observed inequality index at any date is only partially adjusted to its long-run value. This
complicates the estimation procedure somewhat, given the uneven spacing of the underlying
survey data.
Given that it is not feasible to estimate country-specific autoregression coefficients with
such short series, I impose the restriction that the coefficient is the same across the whole
sample. This is the key identifying assumption used to make up for the shortage of time series
observations for individual countries. In particular, equation (3) is replaced by:
Gi,= q5 Git-I + (1 - s)G1t + git (7)
7
where q is the common first-order autoregression coefficient (-1 < b < 1). Thus measured
inequality will increase (decrease) in expectation whenever it is below (above) the true steady-
state level. Notice that there is no constant term in (7); if the expected change in inequality is
zero then inequality must be at its steady state value. (This can be taken as a defining
characteristic of the steady state.)
With this change, it is now relevant that the data are not evenly spaced over time since
surveys have diverse frequencies. Let rt denote the number of years since the last survey. On
repeatedly using equation (7) to eliminate the Gini index for years in which there was no survey,
one can re-write equation (7) in the following form (dropping the subscripts on rz, to simplify the
notation):
GJi ='Git-, + (I - 2QIoG.' -j + Vu (8)
where
vit- Cj g(9)
j=1
is the (heteroskedastic) error term. Substituting (2) into (7) and re-arranging we have:
Git =r Gil-, + G%OAit + Ti[Aitt Bit + vit0)
where
r-l
Alt-(1 ~-X 0E -o it or (l1l)
j=O
Bit-~(1-_ 4) E j0j = 0(1 4S) _TS (12)
on evaluating the two sums of arithmetic progressions in equations (8) and (9).
On taking the differences over time between surveys, and noting that:
8
Gl.oA4.t + TiAg,tt= (I - r)G;* (13)
it is instructive to re-write (8) in the form:
ArGi*t= - Gi,) - TBit + vi, (14)
This shows how the observed change in inequality can be decomposed into three components.
The first term on the right hand side of (14) is the effect of the deviation between the current
survey's measured Gini index and the underlying steady-state value for that date. The second
term arises from the uneven spacing, given the possible existence of a trend; notice that this term
drops out if rit =1 for all i and t. Finally, there is a component due to the error term.
Equation (10) is a non-linear panel data model in which the parameters include the error-
free steady-state Gini index (G%*,) at the common start date and the subsequent country-specific
trend (2T), allowing for (common) serial dependence and measurement errors. If survey spacing
was even, with the same frequency for all countries (ri, =1 for all i, t), then (10) would simply be
a linear regression of the measure of inequality on its own lagged value, country-specific
intercepts (giving (1 - O)G ), and a time trend with country-specific coefficients (giving
(1 - b)T1 ). The uneven spacing makes the regression intrinsically nonlinear in parameters.
4. Results
The convergence tests were done on two data sets. For the first, I chose all countries with
four or more surveys in the Chen and Ravallion (2000) data set.7 This gave 86 "spells" for 21
countries. The welfare indicators used in measuring inequality are a mixture of consumption
7 For the latest version of the data set see http://www.worldbank.org/research/povmonitor/.
This paper used the data set available mnid-2000; see the Appendix for details.
9
expenditures and incomes surveys, though all are per capita distributions and are household-size
weighted. About 80% of the surveys are in the 1990s. All Gini indices have been estimated from
the primary data (micro data or consistent tabulations of points on the distribution) by consistent
methods; in contrast to all other compilations I know of, no secondary sources have been used.
The Appendix gives summary data on the time periods and number of surveys for each country.
The second data set is that used by Li et al., (1998), drawing on Deininger and Squire (1996).
I found no evidence of short-run dynamics. Nonlinear least squares estimates of the
augmented test equation based on (10) (after using equation (4) to eliminate the trends) gave
estimates of 0 that were not significantly different from zero. For the (linear) Gini index the
estimate was 0.026 with a standard error of 0.251; for the log Gini index, the estimate was
-0.010 with a standard error of 0.021. While the shortage of time series observations casts
obvious doubt on how well the dynamics can be identified with these data and they are surely
biased, it appears to be reasonable to assume that 0 = 0 in the rest of the analysis.
Table 1 gives both OLS and IVE estimates of equation (5). These are regressions of the
change in the Gini index between each date and the second survey year on the Gini index for the
latter. (Results are also given for the log of the Gini index.) Notice that 21 observations have to
be dropped to form the instrument. For comparison purposes, the OLS estimate is for the same
sample as the IVE estimate. I tried adding two dummy variables to the regressions, one for when
the survey switched from income to expenditure (relative to the initial survey) and one when it
switched from expenditure to income. However, there were only a few cases of such switches,
and the extra dummy variables made negligible difference to the convergence results
(coefficients and standard errors), so I dropped them.
10
There is a strong indication of convergence for both the linear and log specifications, and
this is robust to allowing for measurement error, using initial inequality as the instrument for the
second observation in the series. (The first stage regressions were significant at better than the
0.1% levels.) Indeed, the IVE and OLS estimates are very close, suggesting only a small bias
due to measurement error.
The intercepts are low enough to generate convergence toward medium inequality.
Consider two countries, one with a Gini index of 30%, one 60%. Taking the instrumental
variables estimates for the (linear) Gini index to be preferred, the expected trend will be 0.31 per
year in the first case and -0.57 in the second. In 15 years, the two countries would expect to
reach Gini indices of 35% and 51%. The log specification gives a broadly similar result. The
implied steady-state level of the Gini index is in the range 40-41% in all specifications.
Since there is little sign of bias in the OLS estimates in Table 1, and by not instrumenting
for the first inequality observation one gains 21 observations, I now switch to OLS on the larger
samples. Table 2 gives results for various sample choices. The results are quite similar if one
excludes the countries in Eastern Europe and the former Soviet Union. The table also gives the
results of the convergence test if one uses the full sample in the Chen-Ravallion data set, i.e.,
including countries with fewer than four surveys (but at least two). This increases the sample size
considerably, with 155 observations for 66 countries. Again the convergence parameter is
negative and very significant. This is again robust to dropping Eastern Europe.
Figure 1(a) plots the annualized change in the log Gini index against the initial value.
Thus the vertical axis in Figure 1 can be interpreted as the proportionate change in the Gini index
per year. Panel (b) of Figure 1 gives the corresponding results for the sample of 66 countries.
11
Convergence is also evident throughout the Lorenz curve. Table 3 gives the test results
by fractile for the full sample, and excluding Eastern Europe. The Lorenz curve is converging to
one in which the poorest quintile hold 5.8% of income (2.4% for the poorest decile), while the
richest decile hold 33.7%. Figure 2 gives the analogous recursion diagram to Figure 1 for the
shares of the poorest and richest deciles. The four countries whose initial shares are closest to
those of the Lorenz curve that the countries as a whole are tending to converge toward are (in
ascending order of the sum of squared deviations): Jamaica, Tunisia, Philippines and Ecuador.
Figure 3(a) plots the trend against the predicted initial level (in logs) for the 21 country
sample. The country-specific trends were obtained by estimating the model without substituting
out the trends (section 3), thus allowing estimation of country-specific initial steady-state values
and trends. (While it is clearly more efficient to estimate (5) directly, it is of interest to see what
the country-specific trends look like.)
I also tested for inequality convergence in the Deininger and Squire (1996) data set which
also includes OECD countries.8 This data set also goes back further in time allowing an average
of 12 surveys per country, though with expected costs in terms of data quality, particularly for
developing countries. Li et al. (1998) report the trend coefficients and intercepts for 49 countries
of a static regression of the Gini index on time estimated on the Deininger and Squire data set (Li
et al., 1998, Table 4). I chose the reference year to be 1965, the median of the country-specific
start dates reported in Li et al. (1998, Table 2). On performing my convergence test on these
data, the OLS estimate of ,B was -0.0113 with a White standard error of 0.0028; the estimate of
8 The data sets overlap slightly. An earlier version of the Chen-Ravallion data set is one of the
sources of the Deininger-Squire (1996) data set, though the latter data set uses many other sources as
well. The main difference between the two data sets is that by going back to the raw data (or special-
purpose tabulations constructed from that data), Chen and Ravallion are able to eliminate inconsistencies
in the methods used by secondary sources.
12
a was 0.4242 with a standard error of 0.1065 (and R2=0.267). Figure 3(b) plots the trends
against the estimated 1965 level.
5. Conclusions
It has been argued in recent literature that (with few exceptions) within-country inequality
is stable over time. The above results cast doubt on this claim. Evidence is found of inequality
convergence, with a tendency for within-country inequality to fall (rise) in countries with
initially high (low) inequality. There is a reasonably strong negative correlation between the
initial Gini index and the subsequent change in the index, though this undoubtedly contaminated
by measurement error. The effect is not as strong when one allows for measurement error by
comparing estimated trends with predicted initial levels. But the correlation is still there and the
speed of convergence is very similar.
The process of convergence toward medium inequality implied by these results is clearly
not rapid, and (as always when generalizing from cross-country comparisons) it should not be
forgotten that there are deviations from these trends, both over time and across countries. The
shortage of comparable survey observations over time for many countries raises doubts about
how well the trends have been estimated. This issue should be revisited when more (and
probably better quality) data come on stream. This would permit more precise identification of
any trends and weaker identification assumptions, notably by allowing for serial dependence in
measurement errors. However, inequality convergence does appear to be a feature of the best
data currently available. It seems that countries are tending to become more equally unequal,
heading toward a Gini index of around 40%.
There are two clear directions for further work. The first is to better understand why we
are seeing inequality convergence. The phenomenon is hardly surprising if one believes modem
13
versions of the neoclassical growth model and one assumes that growth fundamentals do not
differ in important ways; then the whole levels distribution should converge, not just its first
moment. This is not a very satisfying explanation, given that fundamentals do seem to differ in
important ways. However, what we may well be seeing is the interaction of an underlying
neoclassical growth process with a process (albeit uncertain and slow) of convergence in
fundamentals. Possibly convergence arises from the interaction of economic policy convergence
with pre-reform differences between countries in the extent of inequality. Widespread transition
to a more market-oriented economy may well attenuate extremes in within-country inequality,
but reach bounds related to differences between countries in underlying asset distributions. This
could well put a break on the (unconditional) convergence process we are seeing, although the
emerging emphasis in policy discussions on achieving more pro-poor distributions of human and
physical (including land) assets may well foster continuing convergence in fundamentals.
A deeper analysis of the sources of inequality convergence could well have implications
for other explanatory variables relevant to understanding the evolution of inequality. That points
to a second direction for further work, namely to test richer causal models. The present paper has
offered an approach to modeling the determinants of inequality. Only a simple specification has
been estimated here, as required to test for (unconditional) convergence. However, the approach
appears to offer a starting point for estimating richer models.
14
References
Banerjee, Abhijit and Esther Duflo (1999), "Inequality and Growth: What Can the Data Say?"
mimeo, Department of Economics, MIT.
Benabou, Roland (1996), "Inequality and Growth", in Ben Bemanke and Julio Rotemberg (eds)
National Bureau of Economic Research Macroeconomics Annual, Cambridge: MIT Press,
pp. 1 1-74.
Bruno, Michael, Martin Ravallion and Lyn Squire (1998), "Equity and growth in developing
countries: Old and new perspectives on the policy issues," in Income Distribution and
High-Quality Growth (edited by Vito Tanzi and Ke-young Chu), Cambridge, Mass: MIT
Press.
Chen, Shaohua and Martin Ravallion (2000), "How did the world's poorest fare in the
1 990s?" Policy Research Working Paper, World Bank, Washington DC.
Davidson, Russell and James G. MacKinnon (1993), Estimation and Inference in
Econometrics, New York: Oxford University Press.
Deininger, Klaus and Lyn Squire (1996), "A new data set measuring income inequality",
World Bank Economic Review 10: 565-592.
Dollar, David and Aart Kraay (2000), "Growth is good for the poor", mimeo, Development
Research Group, World Bank, Washington DC.
Durlauf, Steven N., and Danny T. Quah (1999), "The new empirics of economic growth",
Handbook of Macroeconomics, Amsterdam: North-Holland.
Kraay, Aart and Martin Ravallion (2001), "Distributional impacts of aggregate growth when
individual incomes are measured with error," mimeo, Development Research Group,
World Bank.
15
Li, Hongyi, Lyn Squire and Heng-fu Zou, 1998, "Explaining international and intertemporal
variations in income inequality", Economic Journal 108: 26-43.
Milanovic, Branko, (1998), Income, Inequality and Poverty during the Transition from
Planned to Market Economy, Washington DC: World Bank.
, (2001), "True world income distribution: 1988 and 1993: First calculations
based on household surveys alone," Economic Journal, forthcoming.
Ravallion, Martin, (2001), "Growth, Poverty and Inequality: Looking beyond Averages,"
World Development, forthcoming.
Ravallion, Martin and Shaohua Chen, 1997, "What Can New Survey Data Tell Us about
Recent Changes in Distribution and Poverty?," World Bank Economic Review,
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_ and ,1999, "When Economic Reform is Faster than Statistical
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World Bank, 2000, World Development Indicators, Washington DC: World Bank.
16
Table 1: Tests for Inequality Convergence
Intercept (a) Slope (,) N R'
Gini index OLS 1.1527 -0.0284 65 0.1571
(0.2852) (0.0070)
lVE 1.1791 -0.0291 65 0.1570
(0.3552) (0.0089)
Log Gini index OLS 0.1012 -0.0274 65 0.1647
(0.0372) (0.0094)
IVE 0.1076 -0.0290 65 0.1391
(0.0383) (0.0103)
Note: Standard errors in parentheses; the heteroskedasticity-consistent covariance matrix estimator is used
(HC 1). IVE columns use the initial value as the instrument for the inequality measure in the second
survey.
17
Table 2: Tests for Convergence on Various Samples
Intercept Slope N R2
Coefficient s.e. Coefficient s.e.
Gini
21 country sample 1.1458 0.2246 -0.0329 0.0054 86 0.3449
Minus Eastern Europe 1.3392 0.2349 -0.0304 0.0054 74 0.3042
66 country sample 2.0843 0.2511 -0.0460 0.0058 155 0.2827
Minus Eastem Europe 1.3907 0.2312 -0.0311 0.0054 117 0.1715
Log Gini
21 country sample 0.1446 0.0209 -0.0382 0.0056 86 0.3963
Minus Eastem Europe 0.1234 0.0204 -0.0326 0.0054 74 0.3339
66 country sample 0.2090 0.0238 -0.0551 0.0064 155 0.3505
Minus Eastem Europe 0.1245 0.0185 -0.0329 0.0049 117 0.1800
Note: The dependent variable is the change in the Gini index relative to the first survey (log Gini index in the lower panel). The
heteroskedasticity-consistent covariance matrix estimator is used (HC 1).
Table 3: Tests for Lorenz Curve Convergence
Intercept Slope N R2
Coefficient s.e. Coefficient s.e.
Share of poorest decile 0.1288 0.0169 -0.0538 0.0072 155 0.2941
Minus Eastem Europe 0.0766 0.0152 -0.0240 0.0056 117 0.0956
Share of decile 2 0.1720 0.0208 -0.0505 0.0061 155 0.3228
Minus Eastem Europe 0.1115 0.0186 -0.0282 0.0049 117 0.1477
Share of niddle (3-8) 2.8299 0.3290 -0.0627 0.0070 155 0.3830
Minus Eastem Europe 2.8137 0.3932 -0.0624 0.0086 117 0.3423
Share of decile 9 0.8544 0.1557 -0.0559 0.0101 155 0.2140
Minus Eastern Europe 0.7164 0.2033 -0.0475 0.0130 117 0.1613
Share of richest decile 2.1507 0.2303 -0.0638 0.0071 155 0.3902
Minus Eastem Europe 2.0204 0.2963 -0.0605 0.0088 117 0.3217
Note: The dependent variable is the change in the Lorenz share relative to the first survey. The heteroskedasticity-consistent
covariance matrix estimator is used (HC1).
Figure 1: Inequality convergence
(a) 21 countries
0.10
0
0
C 0
> 0.05
= 0.0 °c A _
a)
0~~~~~~~~~~~~~~~~
* -0.05
0) ~~~~~~~~~0
0~~~~~~~~~~~~~~~~~
mO
-0.10 I I I
3.0 3.2 3.4 3.6 3.8 4.0 4.2
Log Gini index from first survey
(b) 66 countries
0.2 -
m~~~~~~~~~~
1._
> 0.1 - 0
a) 0 0 0
0. 0
x
*0~~~~~~~~~~~~~~~
~~ 0.0 0 cO 00 ~~~0 0
-0.1 -
2.5 3.0 3.5 4.0 4
Log Gini index from first survey
-0.2.
2.5 3.0 3.5 4.0 4.5
Log Gini index from first survey
Figure 2: Lorenz share convergence for the poor and the rich
(a) Poorest decile
1.0 ,
8 0.5-
(0 ~~~~~~~0
ID 0,0_ 0
0~~~~
00 o
0.
4-
0 0.0 2 3
20
-0.5
0)~~~~~~~~~~~~~~~~~~
1.0~~~~~~~~
0 0~0
Initial share of the poorest decile(%
(b) Richest decile
4-
v 0~~~~0
0 0 0
0~~~~~~
(U 0~~~~~~~~
(0~~~~~~~~~~~~
0)~~~~~~~~~~~~
0 -6
0 ~~~~~~0
0~~~~~~~~~~~~~~~~~~~
20~~~~~~~~~~~
Figure 3: Steady state convergence tests
(a) 21 countries (Chen-Ravallion)
0.10
0E)
0
'a 0.05
Cu
UX
a) 0.00
Cc
co )
-o o
Cu
-0.05
2.5 3.0 3.5 4.0 4.5
Predicted log Gini index 1987
(b) 47 countries (Deininger-Squire)
1.0
0~~~~
x
Cu
0.0
0)~~~~~~~~
Cm -0.5-
*0~~~~~~~~~~~~
c
-1.0- 2
10 20 3 6 50 60 70
Predicted Gini index 1965
21
Appendix: Countries with more than one survey in the Chen-Ravallion data set
Region Country Survey dates Welfare indicator
(per person)
East Asia China 1985, 1990, 1992-98 Income
Indonesia 1984, 1987, 1990, 1993, 1996, 1999 Expenditure
Korea 1988, 1993 Income
Malaysia 1984, 1987, 1992, 1995 Income
Philippines 1985, 1988, 1991, 1994, 1997 Expenditure
Thailand 1981, 1988 Income
1988, 1992, 1996, 1998 Expenditure
Eastern Belarus 1988, 1993, 1995, 1998 Income
Europe and Bulgaria 1989, 1992, 1994,1995 Expenditure
Central Asia Czech Republic 1988, 1993 Income
Estonia 1988, 1993, 1995 Income
Hungary 1989, 1993 Income
Kazakhstan 1988, 1993 Income
1993, 1996 Expenditure
Kyrgyz Republic 1988, 1993 Income
1993, 1997 Expenditure
Latvia 1988, 1993, 1995, 1998 Income
Lithuania 1988, 1993, 1994, 1996 Income
Moldova 1988, 1992 Income
Poland 1985, 1987, 1989, 1993 Income
1990, 1992, 1993-96 Expenditure
Romania 1989, 1992, 1994 Income
Russian Federation 1988, 1993 Income
1993, 1996, 1998 Expenditure
Slovak Republic 1988, 1992 Income
Slovenia 1987, 1993 Income
Turkey 1987, 1994 Expenditure
Turkmenistan 1988, 1993 Income
Ukraine 1988, 1992 Income
1995, 1996 Expenditure
Uzbekistan 1988, 1993 Income
Latin America Brazil 1985, 1988-89, 1993, 1995-96 Income
& Caribbean Chile 1987, 1990, 1992, 1994 Income
Colombia 1988, 1991, 1995-96 Income
Costa Rica 1986, 1990, 1993, 1996 Income
Dominican Rep. 1989, 1996 Income
Ecuador 1988, 1994-95 Expenditure
El Salvador 1989, 1995-96 Income
Guatemala 1987, 1989 Income
22
Honduras 1989-90, 1992, 1994, 1996 Income
Jamaica 1988-90, 1993, 1996 Expenditure
Mexico 1984, 1992 Expenditure
1989, 1995 Income
Panama 1989, 1991, 1995-97 Income
Paraguay 1990, 1995 Income
Peru 1985, 1994, 1996 Expenditure
1994, 1996 Income
Trinidad & Tobago 1988, 1992 Income
Venezuela 1981, 1987, 1989, 1993, 1995-96 hicome
Middle East Algeria 1988, 1995 Expenditure
and North Egypt 1991, 1995 Expenditure
Africa Jordan 1987, 1992, 1997 Expenditure
Morocco 1985, 1990 Expenditure
Tunisia 1985, 1990 Expenditure
Yemen 1992, 1998 Expenditure
South Asia Bangladesh 1984-85, 1988, 1992, 1996 Expenditure
India 1983, 1986-90, 1992, 1994-97 Expenditure
Nepal 1985, 1995 Expenditure
Pakistan 1986/7, 1990/1, 1992/3, 1996/7 Expenditure
Sri Lanka 1985, 1990, 1995 Expenditure
Sub-Saharan Cote d'Ivoire 1985-88, 1993, 1995 Expenditure
Africa Ethiopia 1981, 1995 Expenditure
Ghana 1987, 1989 Expenditure
Kenya 1992, 1994 Expenditure
Lesotho 1986, 1993 Expenditure
Madagascar 1980, 1993, 1997 Expenditure
Mali 1989, 1994 Expenditure
Mauritania 1988, 1993, 1995 Expenditure
Niger 1992, 1995 Expenditure
Nigeria 1985, 1992, 1997 Expenditure
Senegal 1991, 1994 Expenditure
Uganda 1988, 1992 Expenditure
Zambia 1991, 1993, 1996 Expenditure
Note: This only includes countries with more than one survey; for full details see Chen and
Ravallion (2000).
23
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A"'