Journal of Economic Growth, 7, 25±41, 2002
# 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
Income Inequality and Economic Growth: Evidence
from American Data
UGO PANIZZA
Research Department, Inter-American Development Bank, Stop W-0436, 1300 New York Avenue, NW,
Washington DC 20577, USA
While most cross-country studies ®nd a negative relationship between income inequality and economic growth,
studies that use panel data suggest the presence of a positive relationship between inequality and growth. This
paper uses a cross-state panel for the United States to assess the relationship between inequality and growth.
Using both standard ®xed effects and GMM estimations, this paper does not ®nd evidence of a positive
relationship between inequality and growth but ®nds some evidence in support of a negative relationship between
inequality and growth. The paper, however, shows that the relationship between inequality and growth is not
robust and that small differences in the method used to measure inequality can result in large differences in the
estimated relationship between inequality and growth.
Keywords: inequality, endogenous growth, political economy
JEL classi®cation: D31, E62, P16, O41, I22
1.
Introduction
The purpose of this paper is to study the relationship between inequality and growth using
a panel of income distribution data that covers the 48 states of the continental US for the
1940±1980 period. This is an interesting experiment because while cross-country studies
found a negative relationship between inequality and growth (Perotti, 1996), more recent
work showed that panel estimations yield a positive relationship between inequality and
growth (Li and Zou, 1998; Forbes, 2000). At the same time, existing work that used US
cross-state data found a negative relationship between inequality and growth when
inequality is measured with the income share of the third quintile and a positive
relationship between inequality and growth when inequality is measured with the Gini
index (Partridge, 1997).
This paper shows that panel estimations based on US data yield no support for the
presence of a positive relationship between changes in inequality and changes in growth
and concludes that, at the US cross-state level, there is no clear, robust relationship
between inequality and growth and that small differences in the method used to measure
inequality and in the econometric speci®cation yield substantial differences in the
estimated relationship between inequality and growth. In particular, the paper shows that,
while there is a class of ®xed effects speci®cations that yields a negative (or at least nonpositive) relationship between changes in inequality and changes in growth, the results are
not extremely robust and are likely to be plagued by several econometric problems.
26
UGO PANIZZA
While Kaldor (1957) suggested that there was a trade-off between equity and growth,
the recent theoretical literature often predicts a negative link between inequality and
growth (Galor and Zeira, 1993; Alesina and Rodrik, 1994; Persson and Tabellini,
1994).1 On the empirical side, most cross-country studies ®nd support for a negative
relationship between inequality and growth (Alesina and Rodrik, 1994; Persson and
Tabellini, 1994; Perotti, 1996; Easterly, 2001). However, Forbes (2000) suggests that
country-speci®c, omitted variables are the cause of a signi®cant negative bias in the
estimations of the effects of inequality on growth and concludes that ®xed effects
estimations yield the consistent result of a positive short-term correlation between
inequality and growth. Barro (2000) using a larger sample and three stages least
squares, ®nds a positive relationship between inequality and growth in developed
countries and a negative relationship between inequality and growth in developing
countries. Banerjee and Du¯o (1999), however, argue that the relationship between
inequality and growth is non-linear and that changes in inequality are associated with
lower subsequent growth.
The main problem affecting cross-country studies of the relationship between income
distribution and growth is the quality and comparability of the inequality data. Even
though the data set assembled by Deininger and Squire (1996) greatly improved the
quality of the available data on income inequality, this data set is far from being problem
free. In particular, Atkinson and Brandolini (1999) and SzeÂkely and Hilgert (1999) show
that, in the cases of OECD and Latin American countries, even the ``high quality'' data set
of Deininger and Squire is plagued by serious problems of data comparability and quality.
SzeÂkely and Hilgert also show that Forbes's (2000) results could be dependent on the
method used to compute inequality.
A possible solution to these problems consists of using regional data. As the experience
of the American states represents a very important source of data for studying the
determinants of long-run growth (Barro and Sala-i-Martin, 1991), this paper tackles the
data quality issue by building a cross-state panel of income distribution and using this data
set to explore the links between inequality and growth.
While this paper does not ®nd evidence for a positive relationship between inequality
and growth, Partridge (1997), who uses data for American states similar to the ones used in
this paper, ®nds a positive correlation between the income share of the middle class and
economic growth and a positive correlation between the Gini index and growth. One of the
main messages of Partridge's work is that different measures of inequality can convey very
different messages. There are two main differences between this paper and Partridge's.
First, while this paper uses tax data for the 1940±1980 period, Partridge uses Census data
for the 1960±1980 period.2 Second, while this paper concentrates on ®xed effects and
GMM estimations, Partridge focuses on pooled OLS. This paper shows that both the data
and the econometric methodology play a role in explaining the differences between the
results of this paper and Partridge's.
The paper is organized as follows: Section 2 illustrates the costs and bene®ts of using
regional data, discusses the methods used in deriving the income distribution data set, and
describes the variability of the cross-state data set; Section 3 presents the results of the
reduced form estimates of an equation that links income distribution to economic growth
and tests the robustness of these estimates; Section 4 concludes.
27
INCOME INEQUALITY AND ECONOMIC GROWTH
2.
The Data
The measures of income distribution used in this paper were built using adjusted gross
income data from the annual reports, Statistics of Income (SOI), published by the Internal
Revenue Service. The SOI data were used to compute Gini indices and break up the
population into quintiles for 1940, 1950, 1960, 1969, and 1980.3 The SOI data are based on
pre-tax adjusted gross income. They include capital gains but exclude interest on state and
local bonds and most transfer income. This is a good source of data for at least three
reasons: (i) since tax evasion is not a substantial problem in the US, data on taxation are
likely to be more accurate than the data of other surveys (such as the Census and the CPS),
(ii) some theoretical models link economic growth to pre-tax and transfer income
distribution, and (iii) pre-tax data show more variability than after-tax data. The biggest
problem with this data set is that it does not capture the income of the people who are not
required to ®ll out a tax return.4
As the SOI data are grouped in income classes, it was necessary to use approximation
techniques both to divide the population into quintiles and to estimate the Gini indices. To
compute the quintiles, I used the split histogram method suggested by Cowell (1995).
Technical details on the derivation of the quintiles are provided in the Appendix. The Gini
index was instead computed by using a simple linear approximation to the Lorenz curve. It
is well known that this method systematically understates inequality. However, Gastwirth
(1972) shows that if the number of groups is large enough, the error is small.
One key issue with cross-state data is their limited variability. To compare the variability
of the cross-state data set used in this paper with the cross-country variability, I concentrate
on the coef®cients of variation of the Gini index and income share of the third quintile (Q3)
(Table 1 contains the summary statistics of the data set used by Perotti, 1996, and Table 2
the summary statistics for the data set used in this paper). As expected, cross-country data
have larger variability, but the difference between the variability of the two data sets is not
as dramatic as one would think. In fact, the coef®cients of variation for the cross-state data
set are often greater than one-third of the cross-country coef®cient of variation.
As this paper focuses on ®xed effects estimations, within-state variability is more
important than cross-state variability. Rather than looking at the behavior of inequality in
one state at a time, I study the degree of within-state variability by regressing the
inequality indices on a set of state and decade dummies and check what proportion of the
total variance of the inequality index is explained by this set of dummies. A high R2 would
indicate that there is limited within-state and within-decade variability which, in turn,
would lead to unstable ®xed effects estimations.5 This experiment indicates that, while
Table 1. Cross-country data. Income distribution and income per capita.
Min.
Max.
Av.
C.V.
Gini
Third Quintile
Third and Fourth Quintiles
Income Per Capita
0.62
0.448
0.18
0.07 Gabon
0.18 Denmark
0.13
0.19
0.225 Kenya
0.42 Denmark
0.342
0.156
208 Tanzania
7380 USA
2190
0.85
Note: All the variables are measured around 1960. Income per capita is at 1980 prices.
28
UGO PANIZZA
Table 2. Cross-state data.
Income Share of the Third Quintile
1940
Min.
Max.
Av.
C.V.
0.105
0.182
0.163
0.07
1950
DE
ND
0.126
0.179
0.161
0.05
1960
DE
WA
0.097
0.212
0.164
0.11
1970
CA
NV
0.148
0.192
0.163
0.06
1980
1940±1980
FL
WY
0.118
0.174
0.153
0.05
TX
CT
0.097
0.212
0.161
0.08
ME
NM
0.399
0.524
0.471
0.04
CT
SD
0.305
0.676
0.429
0.11
Gini Index
Min
Max
Av.
C.V.
0.32
0.584
0.365
0.11
ID
DE
0.305
0.535
0.411
0.06
GA
DE
0.404
0.673
0.441
0.09
UT
MT
0.420
0.494
0.459
0.04
Note: CA, California; CT, Connecticut; DE, Delaware; FL, Florida; GA, Georgia; ID, Idaho; MT, Montana;
ND, North Dakota; NM, New Mexico; NV, Nevada; SD, South Dakota; TX, Texas; WA, Washington; WY,
Wyoming.
data variability is not a serious problem for Q3 …R2 ˆ 0:38†, it could be a problem for the
Gini index …R2 ˆ 0:76†.
Another possible criticism to the use of cross-state data is thatÐas most redistributive
and tax policies are administered by the federal governmentÐcross-state data may be
unable to capture the presence of a ®scal policy channel. There are, however, signi®cant
cross-state differences in the level of tax progressivity, income taxation, property taxation,
and social expenditure. Such differences have been used by Partridge (1997) to study the
links between inequality and growth and by Rodriguez (1999) to study the links between
inequality and redistribution.
3.
Estimations
Even though the aim of this paper is to fully exploit the panel structure of the data
illustrated in Section 2, the paper starts by presenting the results of simple cross-sectional
and pooled OLS estimations. Next, the paper moves on to standard ®xed effects and GMM
estimations and checks the robustness of the results.
3.1.
Basic Estimations
This section presents cross-sectional, pooled OLS, ®xed effects, and GMM estimations of
the relationship between inequality and growth. The section starts by estimating, for each
period, simple cross-sectional regressions of the form:
GROWTHi ˆ a ‡ byi ‡ gDISTRi ‡ yXi ‡ oRi ‡ ei ;
…1†
where GROWTHi is state i's annual growth rate of income per capita, yi is state i's log of
income per capita, DISTRi is a variable capturing income distribution (measured using the
29
INCOME INEQUALITY AND ECONOMIC GROWTH
income share of the third quintile or the Gini index), Xi is a matrix of controls, and Ri is a
matrix of regional dummies controlling for the possibility of different growth patterns in
different regions of the US (South, Mid-West, and West). All the explanatory variables are
measured at the beginning of the growth period.
The matrix Xi includes a set of controls that are likely to be correlated with both income
distribution and growth. In particular, I follow Perotti (1996) and control for the stock of
human capital (High and Coll measure the percentage of adults with high school and
college degrees), the degree of urbanization (Urb measures the fraction of the population
that lives in urban areas), and age structure (Old measures the percentage of the population
above 65 years of age).
I start by estimating equation (1) for all ten and twenty-year periods going from 1940 to
1990. Table 3 shows that the coef®cients of the cross-sectional estimates are often positive
when inequality is measured with Q3 and negative when inequality is measured with the
Gini index. However, these coef®cients are never statistically signi®cant (the table
summarizes the results of 18 regressions and reports only the coef®cient and t statistics
attached to the inequality variables).
Pooled OLS estimations of equation (1) suggest that there is a negative and signi®cant
relationship between inequality and growth when growth is measured over a ten-year
period, and no signi®cant relationship between inequality and growth when growth is
measured over a twenty-year period (Table 4; the constant and regional dummies are
omitted from the table).
Next, the paper uses a ®xed effects model that allows controlling for unobserved timeinvariant state characteristics. The basic model to be estimated is the following:
GROWTH…t;t ‡ n†;i ˆ byt;i ‡ gDISTRt;i ‡ yXt;i ‡ ai ‡ Zt ‡ et;i ;
…2†
where GROWTH…t;t ‡ n† is the annual growth rate of income per capita from period t to
period t ‡ n, ai is a state-speci®c intercept, and Zt is a period-speci®c intercept (all other
Table 3. Cross-sectional regressions: ten and twenty-year growth episodes.
Length of Growth Episode
10 years
Starting Year
Q3
1940
0.92
(0.07)
5.36
(0.58)
0.19
(0.06)
4.8
(0.62)
12.01
(0.91)
1950
1960
1970
1980
Note: t statistics in parentheses.
20 years
Gini
(
(
(
(
1.83
(0.58)
1.96
0.77)
1.35
0.84)
7.16
1.52)
5.79
1.26)
Q3
Gini
2.01
(0.38)
5.14
(0.89)
0.38
(0.16)
3.62
( 1.23)
0.47
(0.36)
2.8
( 1.81)
1.21
( 1.12)
0.09
(0.04)
30
UGO PANIZZA
Table 4. Pooled OLS: Ten and twenty-year growth episodes.
Length of Growth Episode
10 years
Q3
Y
Q3
Gini
High
Coll
Urb
Old
R2
N.obs.
(
20 years
Gini
4.19***
12.96)
11.86**
(2.12)
3.59**
(2.18)
15.85***
(5.73)
1.11**
(2.21)
3.14
(1.52)
0.59
239
4.04***
11.59)
(
(
3.92*
1.88)
4.46***
(2.69)
15.06***
(5.49)
1.15**
(2.32)
3.23
(1.56)
0.59
240
Q3
(
(
1.10***
5.16)
3.77
(1.03)
1.67
1.59)
8.40***
(3.60)
0.09
(0.41)
2.25
(1.16)
0.65
95
Gini
(
0.99***
4.73)
0.60
0.40)
1.43
( 1.39)
7.95***
(3.44)
0.15
(0.70)
2.33
(1.16)
0.64
96
(
variables are de®ned as in equation (1)).6 It is worth noting that the coef®cient g of
equation (2) has a different interpretation from the coef®cient g of equation (1). While the
latter measures the relationship between inequality and growth across states, the former
should be interpreted as a measure of the correlation between changes in inequality and
changes in growth within a given state (Forbes, 2000).
When I restrict Z to be equal to zero, I ®nd a positive and statistically signi®cant
correlation between changes in the income share of the third quintile and changes in
growth, and no signi®cant correlation between changes in the Gini index and changes in
growth (columns 1±6 of Table 5). The last three columns of Table 5, however, show that
the correlation between inequality and growth changes when the regression is augmented
with decade dummies. In particular, both the coef®cient and t statistic attached to Q3
decrease substantially and the coef®cient attached to the Gini index becomes statistically
signi®cant. Contrary to what was found by Partridge (1997), I never ®nd that both Q3 and
the Gini index are positively and signi®cantly correlated with growth.
Interestingly, both sets of regressions of Table 5 (with and without time dummies)
suggest the presence of a negative relationship between inequality and growth. However,
when one does not control for decade-®xed effects, the relevant variable seems to be the
income share of the third quintile, and when one controls for decade-®xed effects, the
relevant variable seems to be the Gini index. On the one hand, the inclusion of time
dummies exacerbates the multicollinearity problem of the ®xed effects estimations; on the
other hand, their exclusion is likely to be the cause of omitted variable bias. As the time
dummies are highly signi®cant and an F-test shows that it is impossible to reject the null
31
INCOME INEQUALITY AND ECONOMIC GROWTH
Table 5. Basic ®xed effects regressions: Ten-year growth episodes.
No Controls
Y
2.02***
(
10.64)
Q3
Controls
1.93***
(
5.76)
2.07***
(
6.06)
5.12***
(
12.63)
5.07***
(
11.21)
11.32)
6.57***
(
14.42)
16.45**
13.22**
13.09*
5.17
(2.06)
(1.92)
(2.02)
(1.73)
(1.24)
(
2.39
0.58
0.75)
(0.17)
2.81
(
High
1.03)
6.73***
Coll
Urb
Old
0.43
N.obs.
5.11***
(
15.83**
Gini
R2
Controls and Decade Dummies
239
0.42
240
0.43
239
6.42***
(
14.90)
6.95
6.03***
0.04)
7.69***
(
6.76***
(3.41)
(3.86)
(3.28)
18.21***
17.11***
18.18***
(5.86)
(5.41)
(5.67)
14.82)
(
0.12
(
6.53***
(
3.72)
1.34)
7.75***
(
3.73)
1.37
1.89
1.97
(1.06)
(1.51)
(1.56)
3.47
3.05
3.42
(1.32)
(1.20)
(1.34)
0.10
1.16*
1.00
(1.45)
(1.69)
(1.44)
4.05*
4.19*
4.19*
1.16
1.28
1.35
(1.70)
(1.71)
(1.69)
(0.77)
(0.88)
(0.93)
0.65
239
0.65
240
1.02**
(
0.65
2.36)
0.94**
(
0.78
239
2.28)
0.95**
(
0.77
239
2.29)
0.79
240
239
Notes: t statistics in parentheses. * Denotes a parameter which is statistically signi®cant at 10%; ** at 5%,
and *** at 1%.
that they are jointly equal to zero, I tend to prefer the estimations with time dummies.
However, I report both sets of estimations because some readers may think that the cost of
including the time dummies outweighs the bene®ts of their inclusion.
When I estimate equation (2) using twenty-year growth episodes, I ®nd that the model
with time dummies yields no signi®cant correlation between changes in inequality and
Table 6. Basic ®xed effects regressions: Twenty-year growth episodes.
No Controls
Y
0.43***
(
Q3
3.76)
Controls
0.58**
(
2.01)
1.05***
(
3.87)
1.13***
(
3.83)
3.98)
1.53***
(
4.56)
21.47***
12.90***
17.49***
(3.49)
(4.90)
(2.88)
(3.68)
1.86
(0.70)
6.11**
1.35
(2.45)
(
Coll
0.57
0.20
0.29)
(0.10)
8.56**
(2.15)
Urb
Old
0.34
95
0.37
96
0.09
95
(
8.40**
3.35***
(
6.67
2.44*
0.20
0.06
(0.71)
(0.23)
0.33
1.80
0.27
(0.12)
(0.59)
0.51
0.25
(
0.10)
0.56
95
1.54)
0.52)
0.09
0.17)
(0.045)
0.74
0.68
96
1.70)
5.94**
(2.03)
0.10
(
0.35
95
2.45*
(
(1.78)
0.13
(
1.97
(1.61)
5.07*
(1.99)
0.66)
0.40
(0.25)
2.18
(
5.81**
(
8.06)
(1.01)
(1.69)
0.11
3.09***
(
(1.24)
0.47)
(2.24)
9.16)
4.04
0.88
8.51**
(2.03)
96
7.97)
(2.21)
(0.42)
95
3.05***
(
5.07**
(0.57)
High
N.obs.
1.49***
(
16.58***
Gini
R2
Controls and Decade Dummies
0.14
(
0.67)
0.54
(
0.26)
0.75
95
Notes: t statistics in parentheses. * Denotes a parameter which is statistically signi®cant at 10%, ** at 5%,
and *** at 1%.
32
UGO PANIZZA
changes in growth (Table 6) and that the model without time dummies yields a signi®cant
correlation between Q3 and growth (the Gini index is positive and signi®cant when both
measures of income inequality are included in the same regression). Although the
difference between the results of the regressions for ten and twenty-year growth episodes
may be due to the fact that the short-run relationship between changes in inequality and
changes in growth is different from the respective long-run relationship, they could also be
driven by the limited degrees of freedom in the regressions of Table 6.7
The ®xed effects estimations of Tables 5 and 6 may be biased by the fact that equation
(2) contains a lag of the endogenous variable (Caselli et al. 1996; Judson and Owen, 1999).
To address this issue, I re-run the regressions of Table 5 using the two robust GMM
estimators developed by Arellano and Bond (1991).8 As GMM estimations in differences
require one extra period, the estimations of Tables 7 and 8 are for 1950±1990 rather than
1940±1990 (the ®xed effects estimations reported under the FE columns refer to this subperiod). It should also be noted that the coef®cient
attached to the lagged dependent
~ ˆ b ‡1 .
variable should be interpreted as b
10
GMM estimations with time dummies suggest a positive but not statistically signi®cant
relationship between changes in Q3 and changes in growth (the coef®cient is marginally
signi®cant when GMM2 is used) and a negative and signi®cant correlation between
changes in growth and changes in the Gini index (this is true for both GMM1 and GMM2).
The last two columns of Table 7 also indicate that, contrary to the ®xed-effects
Table 7. GMM estimations. Regressions with decade dummies.
FE
GMM1
GMM2
FE
GMM1
GMM2
FE
GMM1
GMM2
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Y
0.43***
0.26**
(6.96)
Q3
0.44***
(2.39)
0.43***
(5.03)
1.3
3.55
4.6*
(0.35)
(1.06)
(1.73)
1.7
(
High
Coll
Urb
0.43***
(5.05)
0.28***
(6.99)
1.06)
3.5**
(
2.26)
(
0.30)
(
1.04)
42.8***
(
2.83)
0.43***
(2.89)
(5.27)
1.5
(
0.37)
(
2.68)
2.7
1.2
(0.35)
3.8**
3.7***
(
2.68)
2.5**
1.8*
1.8*
2.6**
2.1**
2.2**
2.6**
2.1**
2.0**
(2.42)
(1.77)
(1.85)
(2.53)
(2.09)
(2.19)
(2.54)
(1.98)
(1.96)
2.9
2.9*
4.1**
2.9
2.3
3.3**
2.9
3.0
4.3**
(1.41)
(1.66)
(2.35)
(1.39)
(1.30)
(1.93)
(1.40)
(1.70)
(2.50)
0.4
(
0.43***
(2.73)
1.7
Gini
Old
0.28***
(7.06)
1.01)
0.6**
(
2.28)
1.2
1.3**
(0.96)
(2.25)
1.0***
(
3.84)
1.8***
(3.20)
0.4
(
0.98)
0.6***
(
2.28)
1.2
1.3**
(1.03)
(1.96)
1.0***
(
3.53)
1.8***
(2.82)
0.4
(
0.96)
0.7**
(
2.39)
1.3
1.4**
(1.03)
(2.32)
1.0***
(
3.67)
1.9***
(3.21)
Test for 1st
order serial
1.84
correlation
p ˆ 0.07
2.67
p ˆ 0.007
2.26
p ˆ 0.02
2.92
p ˆ 0.004
2.31
P ˆ 0.02
2.87
p ˆ 0.004
Test for 2nd
order serial
1.09
0.20
0.92
0.11
0.98
0.32
correlation
p ˆ 0.28
p ˆ 0.84
p ˆ 0.36
P ˆ 0.91
P ˆ 0.33
p ˆ 0.75
Notes: t statistics in parentheses. * Denotes a parameter which is statistically signi®cant at 10%, ** at 5%,
and *** at 1%. The standard errors were computed using Arellano and Bond (1991) robust estimators that
allow for heteroskedastic residuals.
33
INCOME INEQUALITY AND ECONOMIC GROWTH
Table 8. GMM estimations. Regressions without decade dummies.
FE
(1)
Y
Q3
Gini
High
Coll
Urb
Old
Test for 1st
order serial
correlation
Test for 2nd
order serial
correlation
0.79***
(16.67)
10.6*
(1.85)
6.7***
(4.23)
2.3
(0.81)
1.9***
(3.16)
3.6*
(1.81)
GMM1
(2)
GMM2
(3)
FE
(4)
GMM1
(5)
GMM2
(6)
FE
(7)
GMM1
(8)
GMM2
(9)
0.41
(1.42)
14.3*
(1.86)
0.39
0.75***
0.72
0.41
0.75***
0.67
0.51
(1.37) (15.26)
(1.41)
(0.86) (15.87)
(1.41)
(1.18)
13.6**
20.2***
9.8
11.7
(2.03)
(3.19)
(1.18)
(1.44)
4.9*
9.8
3.04
9.4***
7.20
4.9
(1.85)
( 1.12) ( 0.46) (3.20)
( 0.94)
(0.81)
0.9
0.9*
6.4***
2.0
3.4
5.2***
1.5
2.2
(0.43)
(0.41) (4.03)
(0.78)
(1.43) (3.28)
(0.54)
(0.91)
5.7
5.6
2.4
4.4
3.5
3.5
5.6
5.1
(1.56)
(1.57) (0.84)
(0.97)
(0.79) (1.25)
(1.26)
(1.16)
0.02
0.1
1.9***
0.2
0.1
1.5**
0.2
0.3
(0.02) ( 0.16) (3.19)
( 0.14)
(0.06) (2.54)
( 0.86) ( 0.23)
2.8**
2.8** 3.2*
3.8*
3.6*
3.1*
3.7**
3.4**
(2.38)
(2.35) (1.64)
(1.90)
(1.79) (1.60)
(2.11)
(1.99)
2.24
2.30
p ˆ 0.03 p ˆ 0.02
2.05
1.49
p ˆ 0.04 p ˆ 0.13
2.10
1.80
p ˆ 0.04 P ˆ 0.07
0.29
0.20
p ˆ 0.77 p ˆ 0.84
0.63
0.12
p ˆ 0.53 p ˆ 0.91
0.60
0.16
p ˆ 0.55 P ˆ 0.87
Notes: t statistics in parentheses. * Denotes a parameter which is statistically signi®cant at 10%, ** at 5%,
and *** at 1%. The standard errors were computed using Arellano and Bond (1991) robust estimators that
allow for heteroskedastic residuals.
estimations, the negative correlation between the Gini index and growth is robust to the
inclusion of Q3 in the regression. As in the ®xed effects estimations of Table 5, GMM
estimations without time dummies yield a positive and signi®cant correlation between
changes in Q3 and changes in growth and a negative but not signi®cant relationship
between changes in growth and change in the Gini index.
The last rows of Tables 7 and 8 show that I cannot reject the null of ®rst order correlation
in the differenced residuals but that I can reject the null of second order autocorrelation
(only the latter is a necessary condition for consistent estimates). One serious caveat with
the estimates of Tables 7 and 8 is that the Sargan test applied to the homoskedastic
estimators (the test is not de®ned for the robust estimators reported in Tables 7 and 8)
always rejects the null that the over-identifying restrictions are valid. While this could be
due to the presence of heteroskedasticity (with heteroskedasticity, the Sargan test tends to
over-reject the null), it could also signal that there are problems with the instruments used
in the estimation.
The fact that the estimated relationship between inequality and growth changes when I
use different inequality measures (the Gini index versus Q3) is rather puzzling. One
possible interpretation is that these two indices allow discriminating between the
theoretical models that emphasize the role of the median voter (and hence Q3) and the
models that focus on a more comprehensive inequality measure (and hence the Gini
34
UGO PANIZZA
index). However, I do not think that the results of this paper are strong enough to justify the
claim that the paper ®nds empirical support for some speci®c channel linking inequality to
growth.
The economic impact of inequality is lower than the one found in cross-country studies.
While Forbes (2000) found that a one-standard deviation increase in the Gini index is
correlated with a 1.3 percent increase in annual average growth over the next ®ve years,
the estimations of Table 7 (columns 5 and 6) indicate that a one-standard deviation
decrease in the Gini index is associated with a 0.2 percentage points increase in average
annual growth over the next ten years. To obtain an idea of the economic impact of
inequality on growth, I will use the example of the state of Mississippi (the poorest state in
the sample). During the 1960±1970 period, Mississippi had an average annual growth rate
of 4.8 percent and a Gini index of 0.45. In the 1970±1980 period, the growth rate had
decreased to 3.1 percent, and the Gini index had increased to 0.48. The estimations of
Table 7 (column 5) suggest that this increase in inequality is associated to a change in
growth of 0.1 percentage points … 3.52*0.03†, less than 6 percent of the total change in
growth between the two periods.
The ®nding that the economic impact of inequality on growth is smaller than in the case
of cross country studies is not surprising. In particular, higher factor mobility (both labor
and capital) and the role of the federal government are important reasons for expecting
income distribution to have a much smaller impact on growth in the cross-state sample as
opposed to the cross-country sample.
3.2.
Sensitivity Analysis
This section checks whether the results of the previous section are robust to outliers, tests
for the presence of serial correlation, structural breaks in the panel, and explores why the
results of this paper differ from the results in Partridge (1997).
To check for the role of outliers, I start by running the regressions of Tables 7 and 8 by
dropping one state at a time and observe that the results are basically unchanged. Next, I
drop one period at a time and observe that this substantially changes the results. In the
GMM regressions, dropping 1960 or 1980 weakens the correlation between changes in
inequality and changes in growth (all the coef®cients are not statistically signi®cant) and
dropping 1970 strengthens the correlation between changes in inequality and changes in
growth.9
A possible concern with the estimations of the previous section is the presence of serial
correlation. In the GMM estimations of Tables 7 and 8, the tests developed by Arellano
and Bond (1991) reject the null of no ®rst order serial correlation in the differenced
residuals but do not reject the null of no second order serial correlation. A rough way to
check whether serial correlation is a serious problem in the ®xed effects regressions is to
lag the independent variables and observe if the results change signi®cantly.10 When I reestimate the full model (including time dummies) and lag inequality by ten years, the
coef®cients attached to Q3 and the Gini index drop substantially (however, the Gini index
remains statistically signi®cant) suggesting that serial correlation could be an issue.
INCOME INEQUALITY AND ECONOMIC GROWTH
35
As panel estimations require a stable relationship between the dependent and
explanatory variables, they are not appropriate if there are structural breaks in the
sample. Table 3 shows that, although never statistically signi®cant, the coef®cients
attached to the inequality indices change noticeably over time. It is, therefore, important to
formally test the hypothesis of no structural breaks. To this purpose, I divide the sample in
two different ways (1940±1960 versus 1960±1990, and 1940±1970 versus 1970±1990) and
perform Chow tests to verify equality of slopes in the two sub-periods. The results of the
Chow tests to verify equality of slopes in the two sub-periods. The results of the Chow
tests are mixed. When I only test for differences in the inequality coef®cients, I strongly
reject the null of a constant slope. However, when I test the equality of all parameters, I
cannot reject the null of no structural breaks.11
One ®nal issue is the possibility of non-linearities in the relationship between inequality
and growth (Banerjee and Du¯o, 1999). While non-parametric estimations are beyond the
scope of this paper, it is interesting to test for non-linearities by augmenting the regressions
of Table 7 with quadratic and cubic terms of the inequality index. While I do not ®nd any
evidence for a signi®cant quadratic or cubic relationship between changes in Q3 and
changes in growth, I do ®nd evidence for a signi®cant quadratic relationship between
changes in the Gini index and changes in growth. However, the coef®cients ( 3.49 for
the linear term and 319 of the quadratic term) indicate that the correlation between
changes in growth and changes of the Gini index becomes positive when the changes of
the Gini index is greater than 0.11. As this is an extremely high value (close to 3 standard
deviations of the within-state change of the Gini index over the 1940±1980 period), it is
fair to conclude that, for any reasonable change of the Gini index, the relationship between
changes in inequality and change in growth is non-negative.
Using pooled OLS for the 1960±1990 period, Partridge (1997) ®nds a positive
relationship between Q3 and growth and between the Gini index and growth. There are
four major differences between this paper and Partridge's paper: (i) the estimations
technique ( pooled OLS versus ®xed effects) partly compensated by the fact that Partridge
uses a larger set of controls; (ii) the period under analysis (1960±1980 versus 1940±1980);
(iii) the source of the data (Census data versus IRS data); and (iv) the use of the level rather
than the log of initial income per capita as control. Table 9 compares the results obtained
with different estimation techniques using both this paper's and Partridge's data.
The ®rst three columns of part A of Table 9 reproduce Partridge's (1997) result of a
strong positive relationship both between the Gini index and growth and Q3 and growth.
The last three columns of part A of Table 9 show that, while ®xed-effects estimations
strengthen the correlation between growth and the Gini index, the positive correlation
between Q3 and growth is not robust to the use of ®xed-effects estimation. Furthermore,
the last three columns of parts B and C of Table 9 show that, when one uses ®xed effects
estimations and controls for the log of initial income, the two data sets yield the consistent
result of a negative and signi®cant correlation between changes in the Gini index and
changes in growth.12
The ®nding that replacing the level of income per capita with the log of income per
capita completely reverses the results for the Gini index is puzzling because the correlation
between the level and log income variables is very high (the correlation coef®cient is
0.987). Interestingly, this does not seem to be a problem for the data used in this paper
36
UGO PANIZZA
Table 9. OLS and ®xed-effects regressions. Ten-year growth episodes 1960±1990.
OLS
Fixed Effects
A. Using Partridge's data and yt 1
Q3
13.53
(1.09)
Gini
6.47**
(2.54)
B. Using Partridge's data and log…yt
Q3
11.72
(0.98)
Gini
4.35
(1.64)
C. Using this paper's data and log…yt
Q3
0.53
(0.14)
Gini
3.61**
( 2.01)
D. Using this paper's data and yt 1
Q3
1.68
(0.45)
Gini
4.36**
( 2.44)
44.87***
(3.16)
11.74***
(3.95)
1†
38.37**
(2.58)
9.63***
(2.91)
1†
(
(
(
(
5.45
1.19)
4.96**
2.29)
4.84
1.09)
5.53**
2.57)
47.36
(1.58)
(
19.76***
(4.79)
4.95
0.20)
(
(
39.19
(1.49)
19.36***
(4.71)
2.32
0.43)
(
2.40
(0.58)
(
10.13**
2.13)
3.51
1.31)
2.97
1.50)
16.21
0.65)
10.79**
( 2.21)
(
(
(
(
(
8.23
1.30)
5.42*
1.76)
1.48
0.30)
3.28
1.37)
Notes: All regressions include time dummies. t statistics in parentheses. * Denotes a parameter which is
statistically signi®cant at 10%, ** at 5%, and *** at 1%.
( parts C and D of Table 9 show that the coef®cients are rather stable across speci®cations).
An exploration of the data shows that, while the overall data variability is not a key issue,
the Partridge data set has a much higher within-state correlation. In the case of Partridge's
data set, the state and decade dummies explain 86 percent of the variance of the Gini
index, but in the data set used in this paper, the state and decade dummies explain less than
55 percent of the variance of the Gini index (this ®gure is different from the one reported in
Section 2, because here I only consider the 1960±1980 period). It is probably this high
within-state correlation that leads to the unstable results of Table 9.13
Although, Table 9 indicates that ®xed-effects estimations that control the log of initial
income yield the consistent result of a negative correlation between inequality and growth,
it is fair to conclude that small differences either in the data used to measure inequality or
in the methodology (and speci®cation) used to estimate the relationship between
inequality and growth could yield very different results. While I deem the ®xed-effects
estimation to be superior to the pooled OLS, it is not clear whether tax data are superior to
survey data. The main problem with tax-based inequality measures is the incomplete
coverage of households with income below the tax threshold (this may cause the
measurement error to be non-random and correlated with income levels). The main
INCOME INEQUALITY AND ECONOMIC GROWTH
37
problems with survey data include a less accurate measurement of income and the
sampling error.14
4.
Conclusions
This paper reassesses the relationship between inequality and growth using a US crossstate data set similar to the one used by Partridge (1997) and panel data techniques similar
to the ones used by Forbes (2000). Contrary to the ®ndings of Forbes, this paper does not
®nd any evidence of a positive relationship between changes in inequality and changes in
growth, and contrary to the ®ndings of Partridge (1997), this paper does not ®nd that both
the Gini index and the income share of the third quintile are positively correlated with
growth. In fact, while the paper ®nds some evidence in support of a negative relationship
between inequality and growth, the paper suggests that the cross-state relationship
between inequality and growth is not robust to small changes in the data or econometric
speci®cation.
In particular, the paper shows that the negative correlation between the Gini index and
growth is not robust across all sub-periods and is highly dependent on the speci®cation
used (with or without time dummies). Furthermore, the Sargan test suggests that there may
be problems with the identifying restriction imposed in the GMM estimations. Even with
the above caveats, the paper never ®nds a signi®cant positive relationship between
inequality and growth.
Given the differences in data quality and coverage, it is not dif®cult to justify the
differences between the results of this paper and Forbes' paper. However, the ®ndings of
this paper are harder to reconcile with Partridge's (1997) work. The latter, using a similar
sample of cross-state data, ®nds a positive and statistically signi®cant relationship between
the income share of the third quintile and growth and a positive and statistically signi®cant
relationship between the Gini index and growth. Section 3.2 shows that the differences
between the results of this paper and Partridge's are partly due to differences in the
estimation technique, but it also shows that small differences in the source of the data used
to measure inequality can make a big difference in the observed relationship between
inequality and growth.
Appendix
A.
Description of the Split Histogram Method
This split histogram method suggested by Cowell (1995) was used to divide the population
into quintiles. De®ne F…y† as the proportion of population with income less than or equal
to y. Let F…y† be the proportion of total income received by those who have an income less
than or equal to y. Let ai be the lower limit of income class i, ai ‡ 1 its upper limit, and mi the
average income. Interpolation on the Lorenz curve may be performed as follows: between
the observation i and i ‡ 1 the interpolated values of F…y† and F…y† are.
38
UGO PANIZZA
Z
F…y† ˆ Fi ‡
y
fi …x†dx;
ai
1
F…y† ˆ Fi ‡
y
Z
y
ai
…3†
xfi …x†dx;
and the split histogram density function is:
( f …a ‡ 1 m †
i i
i
;
for ai x5mi
:
f…y† ˆ …ai ‡ 1 fi …maii†…mai i † ai †
a †…a
m † ; for mi x5ai ‡ 1
…a
i‡1
i
i‡1
…4†
…5†
i
B.
Data Sources
1.
Data on income and growth. The data on per capita personal income are from the
Bureau of Economic Analysis and from the Survey of Current Business.
2.
Data on inequality. The Gini index and Q3 are computed using data on tax returns
published by the Internal Revenue Service. The data are from the annual report
Statistics of Income, Individual Income Tax Return (the data are not available for the
period 1982±1986).
3.
Data on school attainment, age structure of the population and urban
concentration. These data are from the Census and are available online from the
library of the University of Virginia at: http://®sher.lib.virginia.edu/census/.
Acknowledgments
I would like to thank Laurence Ball, Michelle Barnes, Nada Choueiri, Momi Dahan, Luisa
Ferreira, Oded Galor, Alejandro Gaviria, Mandana Hajj, Louis Maccini, Carmen PagesSerra, Miguel SzeÂkely, three anonymous referees, participants to the Hopkins macro
lunch, and participants to the 7th Summer School in Economic Theory at the Hebrew
University of Jerusalem for helpful comments. I would also like to thank Ann Owen for
providing a user-friendly version of the DPD Gauss program and Mark Partridge for useful
comments and sharing his data with me. The usual caveats apply. The opinions expressed
in this paper are my own and do not necessarily re¯ect the views of the Inter-American
Development Bank.
INCOME INEQUALITY AND ECONOMIC GROWTH
39
Notes
1. Galor and Moav (1999) argue that inequality is bene®cial for growth in early stages of development when
physical capital is the prime engine of growth and harmful in more advanced stages when human capital is
the prime engine of growth. Saint-Paul and Verdier (1993) and Galor and Tsiddon (1997), instead, predict a
positive relationship between inequality and growth.
2. While Deininger and Squire (1996) dismiss tax records as non-representative, Atkinson and Brandolini
(1999) suggest that income tax records should constitute an important source of primary data for the
calculation of inequality indices.
3. A previous version of this paper also used data for 1920 and 1930. The observations for these two decades
were dropped because of the very small percentage of people who ®lled out a tax report. Data for 1969 were
used instead of 1970 data because of a change in the reporting procedure that greatly reduced the number of
reporting individuals in 1970.
4. The censoring at the lower end of the distribution may explain the low correlation between the inequality
indices computed with tax data and the inequality indices computed with Census data. While, at 0.44, the
correlation between Gini indices computed with tax data and Gini indices computed with Census data may
seem extremely small, this ®gure is not very different from the correlation (0.48) between the Gini indices in
the Deininger and Squire data set and the Gini indices computed for a set of OECD countries by Gottschalk
and Smeeding (1997). This last result is even more puzzling, because for most countries, Deininger and
Squire, and Gottschalk and Smeeding computed the Gini indices using the same primary source (the LIS data
set).
5. Formally, assume that we are interested in estimating a model of the kind: GR…t;t‡n† ; i ˆ
gDISTRt;i ‡ ai ‡ Zt ‡ et;i , where DISTRt;i is an inequality index and ai and Zt are vectors of state and
time dummies. De®ne R2D as the R2 in the regression of DISTR on ai and Zt . Then, it is easy to show that:
var…g† ˆ
…1
R2D †
s2
P
…DISTRt;i
DISTR†
:
Therefore,
lim var…g† ˆ ?.
R2D ?1
6. To compare my results with Partridge's (1997), I also introduce both the Gini index and Q3 in the same
regression.
7. Unfortunately, my data set does not include inequality data at a higher frequency and therefore precludes the
possibility of studying the correlation between inequality and growth episodes over 5 and 15 years.
8. While the two estimators are asymptotically equivalent, the one-step estimator (GMM1) requires some
assumption on the weighting matrix. The two-step estimator (GMM2) instead builds the weighting matrix
using the residuals of the one-step estimator. Although the two-step estimator seems less ad hoc than the onestep estimator, the former tends to produce low-power t statistics (Arellano and Bond, 1991).
9. When 1960 is dropped from the panel the coef®cient attached to the Gini index increases to 2.4 (with a t
statistic of 1.6), when 1970 is dropped from the panel the coef®cient goes to 8.1 ( 3.4 t statistics), and
when 1980 is dropped from the panel the coef®cient goes to 7.4 ( 1.1 t statistics). Similar results are
found for the income share of the third quintile.
10. I am grateful to a referee for suggesting this method. To estimate the model with lagged inequality over the
1940±1990 period, I had to use 1930 inequality data. Similar changes in the inequality coef®cients are found
by estimating the model over the 1950±1990 period.
11. In the tests of inequality of coef®cients, the statistics are F(2,182) ˆ 8.07 for the 1940±1960 versus 1960±
1990 sub-periods and F(2,182) ˆ 6.40 for the 1940±1970 versus 1970±1990 sub-periods (all above the 5 and
1 percent critical values of 3.00 and 4.72). In the test of inequality of all parameters, the statistics are
F(56,72) ˆ 1.46 for the 1940±1960 versus 1960±1990 sub-periods and F(56,72) ˆ 1.04 for the 1940±1970
versus 1970±1990 sub-periods (below the 5 percent critical value of 1.5). All the tests are performed using a
40
UGO PANIZZA
®xed-effects model that includes time dummies. GMM estimations could not be performed because the subperiods are too short.
12. In the growth literature, it is standard to control for the log of initial income. However, Partridge (1997) uses
the level of income per capita to make his results comparable with the ones of Persson and Tabellini (1994).
13. Pooled OLS estimations are unlikely to be a quick ®x for this problem because formal tests reject the
restriction that ai ˆ 0 and, by suggesting that E…ai ; Xi †=0, indicate that the pooled OLS model will yield
biased estimations. However, in Partridge's (1997) speci®cation, the omitted variable bias is attenuated by
the inclusion of a large set of control variables. It should also be pointed out that the presence of low withinstate variability exacerbates the measurement error of ®xed effects estimations.
14. Sampling error should not be a serious issue for the Census data used by Partridge (1997).
References
Aghion, P., E. Caroli, and C. Garcia-PenÄalosa. (1999). ``Inequality and Economic Growth: The Perspective of the
New Growth Theories,'' Journal of Economic Literature 37, 1615±1660.
Alesina, A., and D. Rodrik. (1994). ``Redistributive Politics and Economic Growth,'' Quarterly Journal of
Economics 436, 465±490.
Arellano, M., and S. Bond. (1991). ``Some Tests of Speci®cation for Panel Data: Monte Carlo Evidence and
Application to Employment Equations,'' Review of Economic Studies 58, 277±297.
Atkinson, A., and A. Brandolini. (1999). ``Promise and Pitfalls in the Use of Secondary Data-Sets: A Case Study
of OECD Income Inequality.'' Mimeo, Oxford University.
Banerjee, A., and E. Du¯o. (1999). ``Inequality and Growth: What Can the Data Say?'' Mimeo, MIT.
Barro, R. (2000). ``Inequality, Growth in a Panel of Countries,'' Journal of Economic Growth 5, 5±32.
Barro, R., and X. Sala-i-Martin. (1991). ``Convergence Across States and Regions,'' Brookings Papers on
Economic Activity 1, 107±182.
Caselli, F., G. Esquivel, and F. Lefort. (1996). ``Reopening the Convergence Debate: A New Look at Crosscountry Empirics,'' Journal of Economic Growth 1, 363±389.
Cowell, F. (1995). Measuring Inequality, 2nd edn, London: Prentice Hall.
Deininger, K., and L. Squire. (1996). ``Measuring Income Inequality: A New Database,'' World Bank Economic
Review 10, 565±591.
Easterly, W. (2001). ``The Middle Class Consensus and Economic Development,'' Journal of Economic Growth
6, 317±335.
Flora, P. (1987). State, Economy and Society in Western Europe, 1815±1975, Vol. II. Frankfurt: Campus Verlag.
Forbes, K. (2000). ``A Reassessment of the Relationship Between Inequality and Growth,'' The American
Economic Review 90, 869±887.
Galor, O., and O. Moav. (1999). ``From Physical to Human Capital Accumulation: Inequality in the Process of
Development.'' CEPR discussion paper N. 2307.
Galor, O., and D. Tsiddon. (1997). ``Technological Progress, Mobility and Economic Growth,'' The American
Economic Review 87, 363±382.
Galor, O., and J. Zeira. (1993). ``Income Distribution and Macroeconomics,'' The Review of Economic Studies
60, 33±52.
Gastwirth, J. (1972). ``The Estimation of the Lorenz Curve and Gini Index,'' Review of Economics and Statistics
54, 306±316.
Gottschalk, P., and T. Smeeding (1997). ``Cross-National Comparisons of Earning and Income Inequality,''
Journal of Economic Literature 35, 633±687.
Judson, R., and A. Owen. (1999). ``Estimating Dynamic Panel Data Models: A Guide for Macroeconomists,''
Economic Letters 65, 9±15.
Kaldor, N. (1957). ``A Model of Economic Growth,'' Economic Journal 57, 591±624.
Li, H., and H. Zou. (1998). ``Income Inequality is Not Harmful for Growth: Theory and Evidence,'' Review of
Development Economics 2, 318±334.
Partridge, M. (1997). ``Is Inequality Harmful for Growth? Comment,'' The American Economic Review 87, 1019±
1032.
INCOME INEQUALITY AND ECONOMIC GROWTH
41
Perotti, R. (1996). ``Growth, Income Distribution, and Democracy: What the Data Say,'' Journal of Economic
Growth 1, 149±187.
Persson, T., and G. Tabellini. (1994). ``Is Inequality Harmful for Growth?'' The American Economic Review 84,
600±621.
Rodriguez, F. (1999). ``Does Inequality Lead to Redistribution? Evidence from the United States,'' Economics
and Politics 11, 171±199.
Saint-Paul, G., and T. Verdier. (1993). ``Education Democracy and Growth,'' Journal of Development Economics
42, 399±407.
SzeÂkely, M., and M. Hilgert. (1999). ``What's Behind the Inequality We Measure?'' Inter-American
Development Bank, Research Department Working Paper 409.