Pollcy Resarch 1
WORKING PAPERS
Transition and Macro-Adjustment
Country Eeconomics Department
The World Bank
December 1992
WPS 1064
More Evidence
on Income Distribution
and Growth
George R. G. Clarke
Inequality is not a necessary condition for growth. Indeed,
inequality is associated with slower growth - perhaps because
increased inequality causes more conflict over distributional
issues, encouraging greater economic intervention and higher
taxes.
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not be attibuted todti Wod Bank, its Baud of Dimtoa, its managemndo or any of its manbercounties.
Policy Research|
Transition and Macro-Adjustment
WPS 1064
This paper - a product of the Transition and Macro-Adjustment Division, Country Economics Depart-
ment- is part of a larger effort in the department to understand the determinants of economic growth. The
study was funded by the Bank's Research Support Budget under research project "How Do National
Policies Affect Long-Run Growth?" (RPO 676-66). Copies of the paper are available free from the World
Bank, 1818 H Street NW, Washington, DC 20433. Please contact Rebecca Martin, room Ni 1-054,
extension 39065 (December 1992, 28 pages).
Inequality is often regarded as a necessary evil term between the type of regime and inequality
that has to be tolerated to allow growth, says is included in the base regression, it is insignifi-
Clarke. The view that inequality is necessary for cant at conventional significance levels.
the accumulation of wealth, and contains the
seeds of eventual increases in everyone's in- * The cross-country data on inequality follows
comc is evident in "trickle down" economic Kuznets' inverted-U shape.
theories, where societal acceptance of inequality
allows the rich to camn a greater rate of return on Care should be taken in interpreting these
their assets. results. Although inequality is negatively corre-
lated with growth, this does not necessarily
Others argue that inequality slows growth - imply that "soak-the-rich" policies will improve
because increased inequality causes more long-term growth.
conflict over distributional issues, thereby
encouraging greater economic intervention and First, theoretical work on inequality and
higher taxes. growth stresses that this negative correlation is
caused by high levels of inequality provoking
According to Clarke, the empirical evidence high levels of government economic interven-
shows that: tion. Soak-the-rich policies may be less neces-
sary where there is less inequality.
- Inequality is negatively, and robustly,
correlated with growth. This result is robust to Second, although the partial correlation is
many different assumptions about the exact form robust, the direction of causality has not been
of the cross-country growth regression. determined and the effects of specific income
distribution policies have not been tested.
* Although statistically significant, the
magnitude of the relationship between inequality Finally, if policies designed to decrease
and growth is relatively small. Decreasing inequaiity result in greater government consump-
inequality from one standard deviation above to tion and the cost of increased government
one standard deviation below the mean increases consumptions outweighs the benefits of greater
the long-term growth rate by about 1.3 percent- equality, long-term growth may be harmed.
age points a year.
But for certain: inequity is not a prerequisite
* Inequality has a similar effect in democra- for growth.
cies and non-democracies. When an interaction
The Policy Research Working Paper Series disseniinate the findings of work under way in the Bank. An objective of the series
is to get these findings out quickly, even if presentations are less than fully polished. The findings, interpretations, and
conclusions in these papers do not necessarily represent official Bank policy.
Produced by the Policy Research Dissemination Center
More Evidence on Income Distribution and Growth.
George R.G. Clarke
University of Rochester
The World Bank
I would like to thank Bill Easterly, Ross Levine, Sergio Rebelo and Sarah Zervos for advice and comments.
TABLE OF CONTENTS
I. Introduction ...................................................1
H. Properties of the Inequality Data ...................................... 2
IE. Regression Results .............................................. 9
IV. Sensitivity Analysis ............................................. 19
V. Conclusions .................................................. 23
Appendix I: Data ........................ .......................... 25
References .......................... ............................ 27
More Evidence on Income Distribution and Growth.
I. Introductin
Inequality is often regarded as a necessary evil which has to be tolerated to allow growth.
Adelman and Robinson (1989) state "it has been argued that inequality is necessary for accumulation, and
that it therefore contains the seeds of eventual increases in everyone's income".' This view is evident
in "trickle down" economic theories where societal acceptance of inequality allows the rich to earn a
greater rate of return on their assets, encouraging them to accumulate wealth faster; some of which can
be redistributed to make everyone wealthier. In the Harrod Domar model, if the rich save a greater
share of income than the poor, transfers of wealth from rich to poor reduce capital accumulation, thus
leading to slower growth.2 In contrast, Alesina and Rodrik (1991) and Persson and Tabellini (1990)
argue that inequality actually slows growth. This is because increased inequality causes greater conflict
over distributional issues, thereby encouraging greater government intervention into the economy and
higher taxes. This lowers the rate of return on private assets, restricting capital accumulation and slowing
growth. Both Alesina and Rodrik (1991) and Persson and Tabellini (1990) confirm these theoretical
predictions with cross country growth regressions.3 However, a well known property of these
regressions is that results are highly dependent upon the other variables included in the regression
(Levine and Renelt (1992)).
This paper argues that the empirical evidence supports the assertion that inequality is negatively
associated with long run growth. This result is robust to many different assumptions about the exact
form of the cross country growth regression. In addition, this observed negative correlation is not
dependent upon political regime - whether a country is a democracy or not. When an interaction term
Adolman and Robinson, p951.
a Fiolds(1989), p173.
' In addition Pwrson and TabeDini (1990) confirm teir reult with a
historic panel data set.
2
between type of regime and inequality is included in the base regression, its coefficient is insignificant.
This indicates, in contrast to Alesina and Rodrik (1991), that inequality has a similar effect on both
democracies and non democracies. The paper is set up as follows: the second section of the paper
discusses properties of the inequality data, including Kuznets' Inverted U hypothesis and simple
correlations with other variables. The third section shows preliminary results from cross country
regressions with inequality measures included. In the fourth section the robustness of the correlation
between inequality and growth is tested using a variant of extreme bounds analysis. The final section
discusses results and makes final comments.
H. Properties of the Inequality Data
In order to include "inequality" in cross country growth regressions, the abstract concept of
inequality needs to be quantified. Since there is no single universally accepted measure of inequality,
various measures are constructed to test that results are not dependent on inequality being measured in
a particular way. The measures are the coefficient of variation (COEFFVAR), Theils' index (THEIL),
and the Gini coefficient (GINI). Additionally, the ratio of the share of total income earned by the poorest
forty percent of the population to the share of total income earned by the richest twenty percent of the
population, the measure used in both Alesina and Rodrik (1991) and Persson and Tabellini (1990), is
computed.
The Gini Coefficient, probably the most common inequality measure, is derived from the Lorenz
curve, a graphical device which represents inequality in a society. The Lorenz curve plots F(z), the share
of population with income less than z, against +(z) the share of total income of people with income less
than z. It is important to note that this curve must lie below the 45 degree line. For example, suppose
F(z) = 1/h and that 4(z) > 1/z, this would imply that the poorer half of the population earned more than
half of total income, which therefore is more than the richer half could earn. The Gini coefficient is
3
LORENZ CURVE
Twice the shaded
hare of income uea iste Oh
amedby p(D Coefficient.
ersons with l
0 Fz) 1
|L - Shre of-oogulation withincome less thanz
Figure 1
twice the area between the Lorenz curve and the 45 degree line (See Figure l).
In order to describe the other two measures it is useful to suppose there are n persons in the
population with incomes Y,,Y2. ..,y3. The variance of the incomes may seem an intuitive way to judge
how spread out incomes are from the mean. However multiplying all incomes by a factor of n increases
the variance by a factor of n squared. So, for example a society where half the population earned $4 a
year and half $60 would be (four times) more unequal than if half the population earned $2 and half $30.
The coefficient of variation (COEFFVAR) corrects this problem by dividing the square root of variance
by the mean income.
In information theory the entropy of a system is defined as:
where pi is the probability of event i occurring and h(p;) is the "value" of knowing event i occurred.
It is defined as twice the area so that it is between O and 1. When yi= l/n for adl i then it is the 45 degre line and the Gini Coefficient
is zero, when one person earns all income then 4(z) = 0 fbr z < y. and O(z) = I when z = y,. Hence the Gini coefficient for this is 2*(area
between 45 degree line and x axis) - 2*(%) = 1.
4
(1) Coefficient of variation c = C_ n_
(2) ENTRaDY = E pi *h(pi) - Epi 1ogp1
Theil proposed an inequality measure whtm,e si, person i's share of total income, is substituted into the
entropy equation for pi . The "entropy" of the income distribution reaches a maximum when sj= 1/n for
all i, that is when income is evenly distributed5. Theils' index, a measure of inequality, is defined as
the "entropy" of income distribution when s;= l/n for all i, less the "entropy" of the observed data.
(3) Theils' Index= - '.*log 1) - ( - Es,*log(sd)
Properties of these indices have been discussed in the literature on inequality.6 For all measures,
the more equitably income is distributed, the lower the measure's value. It should be noted that the
measures, other than the ratio are designed to be computed on entire populations. Since this data is
unwieldy and less available than the decile income shares, these measures were calculated as if within
deciles income is distributed evenly. In general, the Gini coefficient, the coefficient of variation and
Theils' index may be preferable to the ratio measure since they utilize more information. A shift in
income shares between deciles within the broad groups of the poorest forty percent, the richest twenty
percent or the middle forty percent of the population, while not affecting the ratio, changes the other
measures.
Although these measures give different values and even different orderings for countries in the
sample, they are very highly correlated. (See Table 1). In particular the coefficient of variation and
Theils index are extremely highly correlated.
S Real that the Si's are constrained to add to one.
65 ee for example Cowell (1977). Or for properdes of the Gini coefficient, Lambert (1989).
5
As an initial exercise, table 2 shows the simple correlations between the inequality variables and
Barro regressors and other related variables7. Exc., ' for per capita GDP, which is negatively correlated
with growth, and enrollment rates in secondary, and to a lesser extent primary, education, no variables
Table 1: Simple Correlations of Inequality measures.
aini Coeffirar Theil RTP40
alai 1.00 0.97 0.97 0.91
Cooffvar 1.00 0.99 0.87
The_ 1.00 0.94
RTP4O 1.00
TABLE 2: Simple Correlations with Barro Regressors and other Variables
Variable obs Corr. w/ T stat # obs Corr w/ T stat
GINI RTP40
ASSP7085 75 -0.031 -0.26 83 -0.035 -0.31
REVC708S 75 -0.045 -0.39 83 -0.012 -0.11
8GoV7088 76 -0.061 -0.53 84 -0.050 -0.45
sLNV7088 76 -0.106 -0.92 84 0.002 0.02
C57088 8l 0.068 0.61 90 0.003 0.03
SODPPC7O 75 -0.319 -2.87 82 -0.255 -2.36
LGDPPC70 75 -0.216 -1.89 82 -0.131 -1.18
CPRIM60 82 -0.166 -1.51 89 -0.095 -0.89
CSEC60 82 -0.373 -3.59 89 -0.317 -3.11
SODPPCIY 72 -0.354 -3.16 77 -0.290 -2.63
LODPPCIY 72 -0.225 -1.94 77 -0.162 -1.42
SCONIY 72 0.083 0.69 77 0.024 0.21
SGOVIY 72 -0.208 -1.78 77 -0.170 -1.49
SNVIY 72 -0.120 -1.01 77 -0.039 -0.34
' The measures denoted xxxxxlY are measured in the same year as the inequality measures for each countfy. SCONIY is private
consumption as percent of GDP, slNvn is investment as percent of GDP, SGoVIY is government consumption as percent of GDP and
SODPPCIY is per capita GDP and LGDPPCIY is the log of per capita GDP. AU measures are from Surmmers and Heaton (1991).
6
are highly correlated with inequality. Private consumption (SCONIY) and investment (SINVIY)
measured for each country in the same year as the inequality measures are both insignificantly correlated
with inequality.
Government consumption (SGOVIY) also measured for each country in the same year as
inequality is negatively correlated with the Gini coefficient8. If slower growth in countries with greater
inequality were caused "i greater government intervention in the economy, one may hope to find a
significant relationship between greater inequality and large government.
A final aspect of the data regarding the level of development, not the growth rate, is whether the
data appears to follow Kuznets' inverted U shape. Kuznets' inverted U hypothesis asserts inequality first
increases, and then decreases, as per capita income increases. Various cross country studies have tested
this hypothesis and have generally supported it.9 It has been suggested that this result is driven by the
high negative correlation between inequality and wealth among developed countries, and that the increase
in inequality observed among the poorer of the less developed countries is largely illusionary."0 Even
if one accepts the hypothesis, questions exist about its causes. The shape may be structural, perhaps
caused by a shift from an agrarian base to an industrial base, or could be policy induced."1 The data
used in this study appears to follow the inverted U shape, but the cause of this relationship is not clear.
As is customary the hypothesis is tested using log values of GDP. In all four cases when Log GDP is
regressed on the inequality measures its coefficient is negative. However, coefficients on two of these
' However this result is very weak since the correlation is only significant at a two tailed significance level of ten percent for two of the four
measures, Thei and Giai. The other two measures are insignificantly correlated with soovIY instilling little confidence in this result.
Additionally. this result appears to be driven by one country, Suriname. When this point is excluded from the sample the correlation becomes
insignificant.
I See Lecallion et al. (1984), Chapter one, for a survey of some of these studies.However, as noted in Easterly, King, Levine and Rebelo
(1991), results from intertemporal studies have not supported the hypothesis. Since the relationship, as it was formulated is intertemporal, these
studies would seem a more appropriate way of testing the hypothesis.
'° LecaUion et al, p14-15.
"Adelman and Robinson (1989), p955-57 argue that the initial increase in inequality is caused by a shift from agriculture to industry, but
that the following decrease if it occurs is due to policy decisions.
7
measures are not significant at the five percent level (See Table 3). When squared Log GDP per capita
is added to the regression, the regressions' R-Squared term becomes significantly larger and the
coefficients on both Log GDP per capita and Squared Log GDP per Capita become highly significant"2
(See Table 4). This result agrees with previous studies which find that in cross country comparisons,
the average level of inequality is lower in both very poor and rich countries, than in moderately poor
countries." The turning point, where average inequality appears to begin to decrease with increased
wealth varies between $1433 for the coefficient of variation, and $1826 for the ratio measure in 1985
prices. This empirical regularity does not necessarily prove the existence of either an intertemporal, or
structural relationship between level of development and inequality. The data suffers from the usual
problems relating to poor quality, as well as additional problems caused by comparing income distribution
data for households and for individuals and using approximations of inequality measures. The "Inverted
U" relationship for the Gini Coefficient is shown in figure 2.
Table 3: Regression of Inequality variables on Log of ODP per Capita
Dep. Variable GENI COEFFVAR THE8L RrP40
No of Obs 72 72 72 77
Constant 0.6102 1.6801 0.7177 7.3076
l ___________________ (6.85) (6.53) (4.42) (3.24)
LODPPCIY -0.0220 4.0950 -0.0461 -0.4076
(-1.94) (-2.89) (-2.22) (-1.42)
0.05 0.11 0.07 0.03
12 Third and fourth powers of log GDP per capita are insignificant when added to the regression.
" See for example Ahluwahlia (1976).
8
Gini Coefficient
against GDP per capita
0.,
CCU
0.6 NN0 G0}
SEN JRmm5 T 0EX
e0.5 NIL M%BMOWt CQIYS CHLtQ
W0°'s~~~~60 H9enacyr
YZA rO'. .u
0.2 IND SA
0.2
lO to 1000 10000 IO000
GDP per Capita
Figure 2
Table 4: Regression of Inequality variables on Log of GDP per Capita and Squared Log of GDP per Capita
Dep. Variable olNI COEFFVAR THEIL RTP40
No of Obs 72 72 72 77
Consant -1.6683 -4.8235 -3.3680 -47.346
(-2.68) (-2.67) (-2.96) (-3.02)
LGDPPCIY 0.5780 1.6178 1.0299 13.924
.___________________ (3.54) (3.43) (3.45) (3.41)
LUDPCIY2 -0.0390 -0.1112 -0.0699 -0.927
(-3.69) (-3.64) r-3.62) (-3.52)
0.21 0.23 0.21 0.17
9
III. Regression Results
Table 5 presents the first set of cross country growth regressions. The inequality variables are
added to a "Barro type" growth regression including variables to proxy political instability levels, levels
of human capital, size of government and initial GDP per capita.
Table 5: Ordinary Least Squares Results for Barro Type Regression with Inequality Variables.
(1) (2) (3) (4) (5)
Dep. Var L0PC7088 L0PC7088 LOPC7088 L0PC7088 L0PC7088
# of Obs 81 74 74 74 81
Constant 0.0154 0.0533 *4 0.0394 ** 0.0537 ** 0.0255 *
(1.47) (3.14) (3.10) (3.53) (2.29)
SUDPPC70 -0.0023 * -0.0026 * -0.0026* -0.0Q27 * -0.0025 **
l_______________ (-1.84) (-1.79) (-1.83) (-1.89) (-2.04)
REVC7085 -0.0017 -0.0040 -0.0044 -0.0050 -0.0030
________________ (-0.18) (-0.43) (-0.47) (0.55) (0.31)
ASSP7085 -0.0385 ** -0.0511 ** -0.0527 ** 0.0531 4* -0.0405 **
l______________ (-2.03) (-2.27) (-2.37) (-2.41) (-2.20)
PP170DVN -0.0053 4 -0.0059 ** -0.0062 ** -0.0063 ** -0.0058 *
______________ (-1.95) (-2.28) (-2.42) (-2.48) (-2.18)
CPRIM60 0.0134 0 9116 0.0127 0.0121 0.0175
l__________________ (1.22) (1.05) (1.16) (1.12) (1.63)
CSEC60 0.0282 0.0193 0.0152 0.0122 0.0178
(1.57) (0.94) (0.74) (0.59) (0.98)
SGOV7088 -0.0426 -0.0595 ** -0.0606 ** -0.0604 ** -0.0479*
(-1.51) (-2.00) (-2.06) (-2.08) (-1.74)
GIN! -0.0691 **
l________________ (-2.59.)
THEIL -0.0438 **
(-2.91)
COEFFVAR -0.0298 *
(-3.15)
RTP40 -0.0022 **
(-2.26)
R-Squared 0.23 0.32 0.34 0.35 0.28
4 t datistic significant at 10% level
44 t stAtistic significant at 5% level
10
PARTIAL SCATTER OF RESIDUALS
Growth Us Gini Coefficients
0.08
1am
0.06
EGY
0.04 ON 5 04
CYP
0.02 ION T1H
r NUN IRL rl"mN EWc N
0! SWYS R
SUR Crii7 NLPL rz
-n
-0.04
-0. 06
-0.25 -0.7. -0.IS -0.1 -0.05 -1.387SE-17 0.05 0.1 0.IS 0.2
Glnl Residuds
Figure 3
The dependent variable is the least squares growth of rate of GDP per capita (where GDP is taken
from BESD, the World Bank data base). The independent variables are initial GDP per capita in constant
dollars, from Summers and Heston (1991) (SGDPPC70), primary and secondary enrollment rates lagged
ten years (CPRIM60 and CSEC60), the average number of revolutions and coups per year between 1970
and 1985 (REVC7085), the number of assassinations per million population per year between 1970 and
1985 (ASSP7085), the deviation of the price level for investment in 1970 from the sample mean
(PPI70DVN) from Summers and Heston (1991)4 and average government share of GDP between 1970
and 1988 (SGOV7088V)5.
" This is the price purchasing parity measure divided by exchange rate relative to the United States.
" Barro (1991) uses governmentshare of ODP from Summers and Heston (1988) less experditureon defenseand education. The measure
used here, from Summers and Heston (1991), is lightly different in that it does not exclude expenditure on defense and education. The measure
used in Berro is not used since it is available only over a shorter subperiod and for a smaller subseample of countries.
11
In table 5, the coefficients on all inequality measures are significantly negative. For all of the
inequality measures, as inequality increases the value of the measure increases. These negative
coefficients indicate that increased inequality is correlated with slower long run growth. A primary
concern is that one or two outliers may be driving the result. To show this is not the case, a partial
scatter of the residuals from growth and the Gini coefficient regressed on the Barro variables is presented
in figure three." This appears to confirm that the result is not driven by one or two outliers.
Another concern is heteroskedasticity. This hypotheses is tested using a Breusch-Pagan Lagrange
multiplier test with GDP per capita and a Goldfeldt Quandt test 7. In the Goldfeldt Quandt test, the
observations were ordered by GDP per capita and the ten middle observations (twelve middle
observations for RTP40) were dropped. The results which reject the null hypothesis of homoskedasticity
are presented below."8
To correct for heteroskedasticity, the following two regressions are run: OLS with Whites'
heteroskedastic consistent standard errors, and weighted least squares weighting by (I/GDP per capita)
squared. Correcting for heteroskedasticity does not change the sign or significance of the results. In both
cases the coefficients on all inequality variables remain significantly negative at conventional significance
levels. In addition, throughout the rest of the analysis, Whites' Heteroskedastic Consistent Standard
Errors are used.
6 Results are similar for the other inequality measures.
17 The variation of the Breusch - Pagan test suggested by Koenkar(1981) and Koenkar and Barrett(1982) which may be more powerful in
the absence of normally distributed errors is used.
'In the extended regression listed in table 10 the null hypothesis of homoskedasticity was also rejected. For the Goldfeldt Quandt test the
middle eight (nine for RTP40) observations were dropped, and in each case the null hypothesis of homoskedastic errors was rejected at the five
percent level. For the Breusch Pagan test on GDP per capita the null hypothesis was rejected at the five percent level for GnMI and RTP40 and
COEFFVAR, and at the ten percent level for THEIL (significance level of 0.0510).
12
Table 6: Testng for heteroskedastioity in the residuals from the Barro type regression
H0: Errors are distributed homoskedastioaly
H,: Errors are distnbuted beteroskedastically
GOLDFELDT QUANDT Test Statistic Significance Lovel
w/ included variable
GMIN F (23,23) = 8.30 0.000
THMIL F (23,23) = 8.08 0.000
COHFFVAR F (23,23) = 7.80 0.000
RTP40 F (26,26) - 4.82 0.000
BREUSCH PAGAN TEST
w/includod variable
GIN! CMI SQUARED (1) = 4.54 0.033
TH81L CMI SQUARED (1) = 4.51 0.033
COBFFVAR CHII SQUARED (1) = 4.40 0.036
RTP40 CIM SQUARED (1) = 5.49 0.019
Table 7: OrdinaLy Least Squares with Whito Heteroskodastic Consistent Standard Errors for 8aro Type Regression with Incquality Variables.
(1) (2) (3) (4) (5)
Dep. Var LOPC708S LGPC7088 LaPC70s8 LaPC7088 LaPC7088
# of Obs 81 74 74 74 81
Constant 0.0154 0.0533" 0.0394" 0.05371 0.0255*
(1.45) (3.64) (3.34) (3.98) (2.19)
SaDPPC70 -0.0023 -0.0026 * -0.0026 -0.0027 * -0.0025*5
(-2.20) (-2.01) (-2.06) (-2.10) (-2.52)
REVC7085 -0.0017 -0.0040 -0.0044 -0.0050 -0.0030
(-0.17) (-0.37) (-0.41) (-0.48) (-0.28)
ASSP708S -0.038S5 -0.0SI I' -0.0527 0.0531 " -0.0405S
(-2.27) (-2.25) (-2.31) (-2.32) (-2.43)
PP170DVN -0.0053 -0.0059 -0.0062 -0.0063 -0.0058 *
(-1.82) (-1.87) (-1.97) (-1.99) (-1.90)
CPRIM60 0.0134 0.0116 0.0127 (1.30) 0.0121 0.0175*
(1.35) (1.16) (1.25) (1.77)
CSBC60 0.0282 * 0.0193 0.0152 0.0122 0.0178
(1.91) (1.23) (0.97) (0.78) (1.27)
SOoV7088 -0.0426 -0.0595 * -0.0606 -0.0604 -0.0479
(-1.23) (-1.73) (-1.78) (-1.79) (-1.40)
amN -0.0691
a w________________ ___________________ (-3.04) _ 11
THE[L -0.0438"
( .22)
C!OMFFAR -0.0298"
___________________ ___________________ __________________ (-3.53) _______________353
RTP40 -0.0022"0
RTP40_____________ ___________________ __________________ (-2.40)
R-Squaed 0.23 0.32 0.34 0.35 0.29
13
Table 8: Weighted Lem Squae (with l/DPr2 as tho weight) for Barro Type Regresion with Inequality masures.
(1) (2) (3) (4) (5)
Dop. Var LOPC7088 LaPC7088 LaPC7088 LoPC70s8 LGPC7O88
IofOba e1 74 74 74 81
Consnt 0.0197 O 0.0466 0.0362 0.0456 0.0343 *
(I .99) (3.84) (3.59) (4.05) (3.33)
SaDPPC70 40.0014 - -0.0008 -0.0008 -0.0009 -0.0002 '
(-2.37) (-1.07) (-1.16) (-1.25) (-3.52)
RBVC7085 -0.0134 -0.0130 -0.0130 -0.0118 -0.0165 *
__________________ (-1.33) (-1.45) (-1.47) (-1.35) (-1.74)
ASSP7085 -0.0189 -0.0239 -0.025S -0.0261 -0.0261
(-0.86) (-1.07) (-1.15) (-1.19) (-1.27)
PP170DVN -0.0098 O -0.0100 * -0.0101 -0.0097' -0.0087
(-1.76) (-1.98) (-2.00) (-1.95) (-1.66)
CPRIM60 0.0059 0.0055 0.0052 0.0053 0.0073
(0.65) (0.67) (0.64) (0.65) (0.85)
CSBC60 0.0019 0.0064 0.0046 0.0045 0.0167"
(2.68) (0.73) (0.53) (0.52) (2.50)
S0oV7088 -0.0369 O -0.0447O -0.0455 -0.0458 -0.0405 *
l________________ (-1.71) (-2.17) (-2.24) (-2.28) (-2.01)
GIN -0.0589"
l _________________ (-3.43)
THEL -0.040
(-3.68)
COBFVAR -0.0250"
____________ ~(-3.85)_ _ _ _ _ _
RTP40 -0.2741*
__________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________ ___________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (-3 .34)
R-Squued 0.64 0.72 0.72 0.73 0.68
Even under ideal conditions inequality data is perceived as poor quality. In this case the problem
is exacerbated by using income distribution data from different sources, for different income receiving
unit, and for different years. Some observations are from the early seventies (and a few from the eighties
for RTP40), hence endogeneity may be a concern. To correct these problems, two stage least squares
is performed. In addition to the Barro regressors the following instruments are used: a dummy for
socialist economies (SOC from the Barro Wolf data set), a dummy for African countries, a dummy for
Latin American countries, log of initial per capita GDP and squared log of initial per capita GDP (from
Summers and Heston (1991)). Using these instruments, the coefficients are slightly more negative than
14
Table 9: Two Stage Least Squares for Barro Type regression and Inequality variables using Barro regressors, Log of per capita ODP, Squared
Log of per capita GDP, Africa dunmmy, Latin America dummy and Socialist Government dummy as instruments.
(2) (3) (4) (5)
Dep. Var LGPC7088 LOPC7088 L()PC7088 LOPC7088
# of Obs 72 72 72 79
Constant 0.08266 ** 0.0526 * 0.0721 ** 0.0350 *5
(2.96) (3.11) (3.23) (2.53)
SODPPC70 -0.0032 * -0.0032 ** -0.0033 ** -0.0030 *
_______________ (-2.00) (-2.02) (-2.14) (-2.20)
REVC7085 -0.0084 -0.0080 -0.0088 -0.0047
(-0.82) (-0.81) (-0.89) (-0.47)
ASSP7085 -0.0542 ** -0.0566 * -0.0574 *0 4.0436 **
- (-2.31) (-2.45) (-2.53) (-2.26)
PP170DVN -0.0060 * -0.0064 -0.0065 ** -0.0061 s
(-2.23) (2.42) (-2.51) (-2.20)
CPRIM60 0.0165 0.0172 0.0160 0.0220 *
(1.38) (1.46) (1.40) (1.87)
CSEC60 0.0113 0.0082 0.0059 0.0124
(0.46) (0.33) (0.24) (0.60)
SOV7088 -0.0725 * 40.0714 ** -0.0710 * -0.0556 *
(-2.27) (-2.28) (-2.32) (-1.90)
GINI -0.1265**
(-2.47)
THEEL -0.0707 *
(-2.59)
COBFPVAR -4.0454**
(-2.70)
RTP40 -0.0041 e
(-2.21)
R-Squared 0.32 0.34 0.35 0.28
15
in the OLS regressions, and all measures remain significant at the five percent level."
The regression presented in table 10 adds additional variables suggested in the empirical growth
literature to the base Barro regression. The variables added are: trade share of GDP averaged over 1970
to 1988, used as a measure of trade policy (STRD7088); money and quasimoney as share of GDP
averaged over 1970-88 (m27088) used as a measure of size and development of the financial sector;'m
the standard deviation of inflation over the period 1970 to 1988 used as a measure of overall
macroeconomic uncertainty (SDPI7088), the average of the ratio of claims on the private sector by the
central bank and deposit money banks to GDP over 1970 to 1988 (DCPT7088) (Levine and King (1992)),
a measure suggested as a proxy for development of financial markets, and the average number of war
casualties between 1970 and 1988 (Easterly, Kremer, Pritchett and Summers(1992)). Whites'
Heteroskedastic Consistent standard errors are used to correct for heteroskedasticity. As shown in table
10, adding these variables affects neither the sign nor the significance of the coefficients on the inequality
measures.
The results indicate that under a broad range of assumptions, within the context of cross country
growth regressions, initial inequality is negatively correlated with growth. Hence, improving equality
may improve future growth prospects.
9 These instruments are chosen, because with the exception of the socialist government dummy, they are highly significant in the first stage
regression and are exogenous. The R2 terms for the first stage regression ranges between .58 for the Theil index and .43 for the ratio measure.
Excluding the socialist dummy does not change the significance of the results.
20 Since money supply is a year end stock and GDP is a flow over the year, as suggested in p7 of Levine and King (1992) and Appendix
I of Ghmni (1992), money supply is the average of money supply at the end of the previous year and the end of that year.
16
Table 10: Ordinary Least Squarea with Whites' Haeroskedastic Consistent Standard Errors for Augmented Barro Type Regression.
Dep Var LGPC7088 LOPC7088 L0PC7088 L0PC7088 LOPC7088
# OF OBS 61 56 56 56 61
Constant 0.0161 0.0479 ** 0.0324 ** 0.0482 ** 0.0221 *
(1.40) (2.61) (2.27) (2.90) (1.79)
SODPPC70 -0.0017 -0.0030 * -0.0031 * -0.0031 ** -0.0025 *
(-1.38) (-1.94) (-2.00) (-2.02) (-2.08)
REVC7085 0.0127 0.0038 0.0031 0.0018 0.0082
_____________ (1.06) (0.32) (0.27) (0.15) (0.72)
ASSP7085 -0.0442* -0.0495 -0.0511 -0.0525 -0.0378
(-1.71) (-1.55) (-1.60) (-1.59) (-1.51)
PP170DVN -0.0033 -0.0009 -0.0012 -0.0015 -0.0019
(-0.33) (0.09) (-0.13) (-0.16) (-0.20)
CPRIM60 0.0193 * 0.0211 * 0.0214 ** 0.fl10 ** 0.0207 **
(2.17) (1.96) (2.03) (2.;4 (2.15)
CSEC60 0.0312** 0.0263 0.0225 0.0211 0.0269**
(2.20) (1.38) (1.20) (1.12) (2.12)
SOV7088 -0.0600 * -0.0668 * -0.0672 * -0.0672 * -0.0663 **
iL____________ !(-1.85) (-1.79) (-1.85) (-1.89) (-2.03)
CS7088 -1.02 -1.77 -1.78 -1.69 -1.54
(-0.38) (-0.68) (-0.69) (-0.66) (0.58)
M27088 -0.0022 -0.0025 ** -0.0024 + -0.0026 ** -0.0024 **
(-1.77) (-2.55) (-2.69) (-2.93) (-2.47)
SDP17088 -0.00004 0.00001 0.00002 0.00001 0.00002
(-0.55) (0.24) (0.38) (0-19) (0.25)
STRD7088 -0.0056 -0.0088 -0.0084 -0.0093 -0.0070
(-0.75) (-1.13) (-1.10) (-1.24) (-0.98)
DCPT7088 -0.0057 0.0102 0.0098 0.0081 0.0066
(-0.43) (0.64) (0.62) (0.52) (0.43)
OiNi -0.0783 *
(-2.66) .
THEIL 40.04,99**
______________ _______________ (-3.06)
COEFFVAR -0.0328 **
(-3.07)
RTP40 -0.0024 *
_______ _______ ___________ _ __ (-2.28)
R-Squared 0.37 0.45 0.47 0.47 0.42
17
A final topic is whether the observed relationship between growth and inequality differs for
democracies and non democracies. Persson and Tabellini suggest "in a society where distributional
conflict is more important, political decisions are likely to result in policies that allow less priva.s
appropriation and therefore less accumulation and growth. But the growth rate also depends on political
institutions, for it is through the political process that conflicting interests ultimately are aggregated into
public policy decisions."11
To test this hypothesis, an interaction term between regime type and inequality is added to the
base regression. This interaction term is a dummy variable equal to one if the country is a democracy
and zero if it is a non-democracy multiplied by the inequality variables. Hence if the t statistic on this
term is significant, it indicates that inequality affects democracies and non-democracies in a different
manner. Countries are classified as democracies and non-democracies using the following procedure.
If a country spent more the fifty percent of the time between 1970 and 1988 as a democracy, as classified
in ongoing work by Cukierman, Neyapti and Webb, than it is classified as a democracy. This list is
supplemented with the classifications used in Alesina and Rodrik(1991) for countries not covered in
Cukierman, Neyapti and Webb. Table 11 shows that the coefficients on the interaction terms are
insignificant; the coefficients on the inequality measures remains significantly negative. Hence the null
hypotheses, that democracies and non-democracies have a similar relationship between long term growth
and inequality, is accepted.
" Pernon d Tablini, p.1.
18
Table 11: Ordinary LeastSquareawith Whites HeterokedasticConsistentStandard Errors for Barro type regression including inequality measures
and interaction term between inequality and political system
Dep Vars (1) (2) (3) (4)
L0PC7088 LGPC7088 LOPC7088 LUPC7088
#of Obs 68 68 68 71
Conotant 0.0467*0 0.0486** 0.0330** 0.0298**
(3.05) (3.52) (2.64) (2.45)
SODPPC70 -0.0028** -0.0029** 40.0029** -0.0029**
_______________ (-2.09) (-2.26) (-2.22) (-2.85)
REVC7085 -0.0071 -0.0095 -0.0090 -0.0093
(-0.62) (-0.84) (-0.79) (-0.80)
ASSP7085 -0.0555** -0.0550** -0.0557$* 0.0387**
(-2.12) (-2.23) (-2.24) (-2.85)
PP170DVN -0.0057* 0.0061** -00059* -0.0056*
_ (-1.91) (-2.03) (-1.98) (.1.82)
CPRIM60 0.0201* 0.02070* 0.0215** 0.0198
________ __ (1.85) (2.00) (2.05) (1.88)4
CSEC60 0.0175 0.0087 0.0111 0.0211
_______ __ (1.04) (0.53) (0.67) (1.62)
SO0V7088 -0.0226 -0.0245 -0.0252 -0.0418
(-0.56) (0.63) (-0.64) (-1.11)
GNI -0.0785**
(-3.48)
GINIDEM -0.0055
(4.44) l
COBFFVAR -0.0353**
(-4.34)
CVARDEM 0.0025
(4.44)
THEn. -0.0535**
(-4.32)
THEILDEM -0.0061
(4.44) l
RTP4O -0.0032*l
__ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _3_ (3.85)
RTP40DEM -0.0012
R-Squared 0.34 0.390.38(-0.97
R-Square 0.34 0.39 0.38 10.36
19
IV. Sensitivity Analysis
A common criticism of cross country growth regressions is that both the sign and significance
of variables in cross country growth regressions are highly sensitive to the inclusion, or exclusion, of
variables found to be significant in other parts of the literature. To counter concerns about the robustness
of results to the inclusion of other plausible variables, Levine and Renelt (1992) propose a vai .ant of
Leamner's (1983) extreme bound analysis to test the robustness. A brief summary of the procedure
Levine and Renelt (1992) propose follows22.
(1) Y= ,Il + #mM + ,(ZZ + u
The first step is to divide the independent variables into three categories; the 1, or included
variables, the M variable, the variable of interest; and the Z variables. The I variables are always
included in the regression, as is the M variable which in this case is inequality. The M variables'
coefficient, OB, is observed to gauge its reaction to different combinations of the Z variables. The Z
variables are a large pool of variables, suggested in other empirical and theoretical works as potentially
important for growth, but whose importance is more controversial. The Z variables are added to the base
regression, until all combinations have been tried, noting at each step f,t and its standard error. The
highest and lowest values of the coefficient on the variable of interest, IPm. that would be accepted at a
given significance level are then computed for each combination of Z variables. After a comparison of
the highest acceptable O's from all regressions, the l,B with the highest acceptable P associated to it
becomes the upper extreme bound. Likewise the P. with lowest acceptable P associated with it becomes
the lower extreme bound. If the extreme bounds have the same sign, and are both significant, this
P For the complete description of this form of sensitivity analysis see Levine and Renelt (1992).
2 in the first part of the analysis, following Levine and Renelt (1992), up to three variables from a pool of seven Z variables are added at
any one time. This is, of course, not an exhaustive list of possible variables.
20
indicates that the relationship between the M variable and growth is not highly sensitive to the inclusion
of other variables, providing strong evidence as to the robustness of the results.
At this point, it should be noted that all that is really needed to show a relationship between the
variable of interest and growth is the sign (and significance) of the variable of interests' coefficient in the
"true" growth regression.2' A variable which is related to growth can become insignificant, or switch
signs, due to the inclusion of irrelevant Z variables, or the exclusion of relevant Z variables. On the
other hand, in an area such as cross country growth regressions, where there is little agreement on the
precise form of the growth regressions and where theory indicates a large number of possibly relevant
variables, such a procedure may increase the readers' confidence in the results presented.
Another concern is the division of plausible variables into the I and Z variables. The I variables
used in the first section are the Barro regressors from the previous sectioil. This base regression is
preferred to the base regression used in Levine and Renelt (1992), due to doubts about the exogeniety
of investment (one of the I variables in Levine and Renelt (1992)), and because many regressors in the
Barro regression are significant at the five and ten percent levels. Results are also presented using the
Levine and Renelt (1992) base regression. In a later section the Barro regressors that are insignificant
in the base regression, when inequality variables are included, are dropped one at a time untll all
regressors are significant at the ten percent level in at least one of the regressions. This further excludes
CSEC60, secondary enrollment rates, and REVC7085, the average number of revolutions and coups.
The seven Z variables are money and quasimoney as percent of GDP averaged between 1970 and
1988 (M27088), war casualties per capita averaged between 1970 and 1988 (CS7088), ratio of claims on
the private sector by the central bank to GDP averaged between 19708 and 1988 (DCPT7088), the
average inflation rate between 1970 and 1988 (PI7088), Standard Deviation of the Inflation between 1970
and 1988 (SDPI7088), trade share of GDP averaged between 1970 and 1988 (STRD7088), and the ratio
2 For a discussion of those and other problems in sensitivity analysis see McAleet, Pagan and Volcker (1985).
21
of the assets of deposit money banks to the combined assets of deposit money banks and the central bank
(BTOT7088). These variables are chosen to proxy for aspects of monetary and trade policy, as well as
macroeconomic and social stability. The base regression includes a proxy for fiscal policy (SGOV7088).
Throughout the sensitivity analysis Whites' Heteroskedastic Consistent Variances are used.
Results are presented below in table 12. The Gini Coefficient, coefficient of variation and Theils'
index remain significantly negative at the five percent level in all regres3ions. The final measure, RTP40
, is significantly negatively correlated with growth at the ten percent level. These results confirm that
in a wide variety of specifications, inequality measures are significantly and negatively correlated with
growth.25
The sensitivity analysis is next expanded to include more than three additional regressors at one
time. In addition, two regressors from the base Barro regression that are insignificant once inequality
measures are included, secondary enrollment rate in 1960, and average number of revolutions and coups
are dropped from the base regression ([ variables) and added to the pool of Z variables.3' Growth of
population, used in the base regression in Levine and Renelt (1992) is also added to the pool of Z
variables. All possible combinations of these ten variables (with up to all ten variables added at the same
23 Sensitivity Analysis is also conducted using the base regression from Levine and Renelt (1992), which contains the following variables:
initial GDP per Capita (SODPPC70), investment share of ODP averaged over 1970 to 1988 (SINV7088), growth rate of population (LGPP7088)
and secondary enrollment rates (CSEC60). The seven Z-variables used are also similar to those used in the paper by Levine and Renelt;
government share of GDP (SOV7088), trade share of GDP (STRD7088), average inflation rate (P17088), sbndard deviation of inflation
(SDP17088), and number of revolutions and coups (REVC7085). To proxy for monetary phenomenon slightly different measures from those
used in the Levine and Renelt paper were used. The measures used were ratio of claims on private sector by the central bank and deposit money
banks (DCPT7088) and ratio of money and quasi money to GDP (M27088). Once again, following Levine and Renelt, a maximum of three
variables were added at the same time. Using this specification the Gini coefficient, Theils' index and coefficient of variation remain significantly
negatively cormlated with growth at the ten percent level. RTP40 remains negatively correlated with growth, but becomes insignificant at the
convetional significance levels of five and ten percent.
26 Primary enrollment rate in 1960, although also insignificant in the base regression, is not dropped. Dropping CSEC60 and REVC7085
from the base regression makes CPRIM60 significant when RTP40 is the measure of inequality . In addition human capital variables have been
stssed throughout the literature as especially important for growth. If CPRIM60 is dropped, then in the RTP40 regression CSBC60 becomes
significant also. However,CPRIM60 is preferred since in the extended regression as shown in table 10, it is significant at least the ten percent
level with all inequality measures. Using CSEC60 instead of CPRIM60, the coefficient of variation remains sigificant at the five percent level;
Gini and Theil are sigficant at the ten percent level, and RTP40 remains negative, but is insignificant at conventional significance levels.
22
Table 12: Results from Sensitivity Analysis for Inequality Variables, using Barro type regression as Base Regression
#obs Coeff S.E T-stat Included Variables
COEFFVAR
High 67 -0.0243 0.0087 -2.81 CS7088, M27088, SDP17088
Low 61 -0.0376 0.0095 -3.95 BTlT7088, P17088, SDP17088.
THEIL
High 70 -0.0337 0.0128 -2.63 CS7088, SDP17088, STRD7088
Low 61 -0.0563 0.0147 -3.82 BTOT7088, P17088, SDP17088
GIN- _I
High 67 -0.0527 0.0237 -2.22 CS7088, M27088, SDP17088
Low 61 -0.0868 0.0258 -3.37 BTOT7088, SDP17088, P17088
RTP40
High 64 -0.0020 0.0010 -1.94 CS7088, SDP17088, DCPT7088
il Low 64 -0.0027 0.0009 -2.92 M27088, BTOT7088, STRD7088
Table 13: Extended Sensitivity Analysis
#obs Coeff S.B T-stat Included Variables
COEFFVAR
High 70 -0.0237 0.0095 -2.51 STRD7088, SDP17088, CS7088, LOPP7088,
CS_CE_
Low 57 40.0403 0.0118 -3.41 RBVC7085, P17088, BTOT7088, L0PP7088,
DCPT7088
TIM I____ _______
High 70 -0.0341 0.1532 -2.23 STRD7088, SDP17088, CS7088, LOPP7088
Low 57 -0.0591 0.0179 -3.29 REVC7085, P17088, SDP17088, M27088,
BTOT7088, LOPP7088, DCPT7088
High 70 -0.0462 0.0240 -1.93 STRD7088, SDP17088, CS7088, CSEC60,
LGPP7088
LOw 58 -0.1010 0.0280 -3.61 REVC7085, STRD7088, P17088, SDPI7088,
______________ ____________ M27088, BTOT7088
RTP40 _ __________
High 64 -0.0018 0.0011 -1.64 STRD7088, SDPI7088, CS7088,
DCPT7088,BTOT7088, LGPP7088
CSEC60
Low 63 -0.0032 0.0010 -3.26 STRD7088, REVC7085, P17088, SDPI7088,
M27088, BTOT7088
23
time) are added to the base regression (now excluding REVC7085 and CSEC60 since they are included
in the pool of doubtful variables).
The results are presented above in table 13. Two of inequality measures, the coefficient of
variation and Theils' index, remain significant at the five percent level, and the Gini coefficient is still
significant at the ten percent level. All measures of inequality remain negatively correlated with growth
in all regressions, although the ratio measure becomes insignificant at conventional significance levels.
These results confirm a robust and negative relationship between inequality and growth.
V. Conclusions
In summary, the empirical results are as follows:
1) Inequality is negatively, and robustly, correlated with growth. This result is not highly
dependent upon assumptions about either the form of the growth regression or the measure of inequality.
The analysis includes a variation of Leamer's extreme bounds analysis proposed by Levine and Renelt
(1992).
2) Although statistically significant the magnitude of the relationship between inequality and
growth is relatively small. Decreasing inequality from one standard deviation above to one standard
deviation below the mean increases the long term growth rate by approximately 1.3% per annum.Y
3) The correlation between inequality and growth is not dependent upon whether the government
is a democracy or a non-democracy. When an interaction term between the type of regime and inequality
is included in the base regression it is insignificant at conventional significance levels.
4) The cross country data on inequality follows Kuznets' inverted U shape.
Some care should be taken when interpreting these results. Although inequality is negatively
' Using Gini coefficients and coefficient from the base Barro regression, going from one standard deviation above the mean value to one
standard deviation below the mean value
24
correlated with growth, this does not necessarily imply that "soak the rich" policies will improve long
term growth. First, theoretical work on inequality and growth has stressed that this negative correlation
is caused by high levels of inequality provoking high levels of governmental economic intervention.
Hence, the reason for this correlation may be that "soak the rich" policies are less necessary where there
is less inequality. Second, although the partial correlation is robust, the direction of causality has not
been determined and the effects of specific income distribution policies have not been tested. Finally,
looking at the empirical results, once inequality variables are included in the base regression size of
government consumption is negatively, although not robustly, correlated with growth in many
specifications. Hence if policies designed to decrease inequality result in larger government consumption
and the cost of increased government consumption outweighs the benefits of greater equality, long term
growth may be harmed. These results, however, do indicate quite conclusively that inequity is not a
necessary precondition for growth.
25
Appendix I: Data
The data used in the analysis is from BESD, the World Bank database with the following
exceptions'. Per capita gross domestic product, government share of GDP, trade share of GDP, and
investment share of GDP are from Summers and Heston (1991). Assassinations per million population,
and revolutions and coups, are constructed from the raw data used in the Barro-Wolf data set. Primary
and secondary enrollment rates in 1960 are obtained from the Barro-Wolf data set, but are supplemented
with data from SOCIND, United Nations Social Indicators, which is part of the World Bank data base.
The War Casualties data is from Easterly, Kremer, Pritchett, and Summers (1992) and the two financial
variables, DCPT7088, the ratio of claims on the private sector by the central bank and deposit money
banks to GDP, and BTOT7088, the ratio of the assets of deposit money banks to the combined assets of
deposit money banks and the central bank are from raw data from King and Levine (1992). The raw
income distribution data used to construct the inequality variables comes from four basic sources. The
primary source is SOCIND. This is supplemented by Jain (1975), and "A Survey of National Sources
of Income Distribution Statistics" published by the United Nations(1981). The quintile income
distribution data, used for some points in RTP40, is from Lecallion et al (1984) and United Nations
(1985).
In addition to the general problems encountered in cross country growth regressions there are
additional problems specific to inequality measures.' A problem in cross country studies concerning
inequality is that data on inequality tends to be very sparse. To deal with this concern, as in Alesina and
Rodrik (1991) and Persson and Tabellini (1990), income distribution is measured in different years for
28 With the exception of the inequality data, the data used in the following analysis is from William Easterly and Sergio Rebelo, 'Fiscal
Policies and Economic Growth: An Empirical Investigation', part of an ongoing World Bank research project 'How Do National Policies affect
Long Term Growth?
29 See Easerly, King, Levine and Rebelo (1991) or Levine and Renelt (1992) for a discussion of common problems in growth regressions.
26
different countries. It would seem plausible that income distribution changes slowly over time, which
may indicate that this is the most appropriate way to deal with the sparseness of data. The income
distribution data used to construct COEFFVAR, GINI and THEIL are from the eighteen year period
between 1958 (Jamaica) and 1976 (Botswana, Dominican republic, Italy, Nepal and El Salvador) with
the majority of these observations coming from between 1960 and 1970. Since endogeneity is a potential
concern, data before 1970 is preferred to data from between 1970 and 1976. The final measure RTP40
includes additional observations from the early eighties for a few countries. Since these data are in
quintiles, and not deciles as used to construct the other measures, COEFFVAR, GINI and THEIL do not
include these points.
27
References
Adelman, Irma and Sherman Robinson (1989). "Income Distribution and Development. " in Chenery H.
and T.N. Srinivisan, eds. Handbook of Development Economics. New York: North Holland.
Ahluwahlia, Montek (1976). "Inequality, Poverty and Development." Journal of Development Economics
3, pp307-342.
Alesina, A and D. Rodrik (1991). "Distributive Policies and Economic Growth." Cambridge, MA:
NBER Working Paper 3668.
Barro, Robert J. "Economic Growth in a Cross Section of Countries" Ouarterly Journal of Economics
98, ppS103-S125.
Breusch, T.S. and Adrian Pagan (1979)." A Simple Test for Heteroskedasticity and Random Coefficient
Variation." Econometrica 47, (September) pp 1287-1995.
Cowell, Frank A. (1977). Measurin2 Inequality: Techniques for the Social Sciences. New York: John
Wiley and Sons.
Easterly, William; Michael Kremer; Lant Pritchett and Lawrence Summers (1992). "Good Policy or
Good Luck? Country Growth Performance and Temporary Shocks" Working Paper.
-. Robert King; Ross Levine and Sergio Rebelo (1991). "How Do National Policies Affect Long-
Run Growth? A Research Agenda". Washington DC: World Bank Working Paper, WPS 794.
Fields, Gary S. (1989) "Changes in Poverty and Inequality in Developing Countries." World Bank
Research Observer. 4,(July) ppl67-185.
Ghani, Ejaz (1992). "How Financial Markets Affect Long-Run Growth: A Cross Country Study."
Washington DC: World Bank Working Paper, WPS 843.
Greene, William E. (1990). Econometric Analysis. New York: Macmillan Publishing Company.
Jain, Shail (1975). Size Distribution of Income. Washington DC:World Bank.
King, Robert and Ross Levine "Financial Indicators and Growth in a Cross Country Section of
Countries." Washington DC: World Bank Working Paper, WPS 819.
Koenekar, R. (1981) "A Note on Studentizing a Test for Heteroskedasticity" Journal of Econometrics
17, pplO7-112.
Koenekar, R. and G. Basset (1982). "Robust Tests for Heteroskedasticity Based on Regression
Quantiles. " Econometrica 50, pp43-61
Lambert, Peter J. (1989). The Distribution and Redistribution of Income. Oxford, England: Basil
Blackwell Press.
28
Learner, Edward E. (1983). "Let's Take the Con out of Econometrics" American Economic Review
73, (March) pp3l-43.
---- (1985). " Sensitivity Analysis would Help" American Economic Review 75 (June), pp 308-313.
Lecallion, Jacques; Felix Paukert; Christian Morrison and Dimitri Germadis (1984). Income Distribution
and Economic Development: An analytical survey. Geneva: International Labour Office.
Levine, Ross and David Renelt (1992). "A Sensitivity Analysis of Cross Country Growth Regression"
American Economic Review, forthcoming.
- (1991). "Cross Country Studies of Growth and Policy: Some Methodological, Conceptual and
Statistical Problems." Washington DC: World Bank Working Paper, WPS 608.
Lindert, P. and J.G. Williamson (1984) "Growth, Equality and History." Cambridge, MA: Harvard
Institute of Economic Research Discussion Paper Series.
McAleer, Michael; Adrian Pagan and Paul A Volcker (1985). "What Will Take the Con out of
Econometrics?" American Economic Review 75 (June) pp 293-307.
Moll, Terrance (1992) "Mickey Mouse Numbers and Inequality Research in Developing Countries".
Journal of Development Studies 28, (July) pp 689-704.
Papanek, Gustav and Oldrich Kyn (1986). "The Effect on Income Distribution of Development, the
Growth Rate and Economic Strategy." Journal of Development Economics 23, pp55-65.
Persson, Torsten and Guido Tabellini (1990). "Is Inequality Harmful for Growth? Theory and Evidence."
Cambridge, MA: NBER Working Paper 3599.
Ram, Rati. (1988) "Economic Development and Income Inequality. " World Development 16, ppl371-76.
Summers, R and A. Heston (1988). "A New Set of International comparisons of Real Product and Price
Levels: Estimates for 130 Countries" Review of Income and Wealth 34, ppl -25.
Summers, R. and A. Heston (1991). "The Penn World Tables (Mark V): An Expanded Set of
International Comparisons, 1950-1988." Ouarterly Journal of Economics 106, pp327-368.
United NaEions, Statistical Office(1981). A Survey of National Sources of Income Distribution Statistics:
first report. New York: United Nations.
United Nations, Statistical Office(1985). National Accounts Statistics: Compendium of Income
Distribution Statistics. New York: United Nations.
White, H.L. (1980) "A Heteroskedastisticity-Consistent Covariance Matrix Estimator and a Direct Test
for Heteroskedasticity." Econometrica 68, pp 817-38.
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WPS1047 C6te d'lvoire: Private Sector Enrique Rueda-Sabater November 1992 P. Infants
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