WPS3592
Which Inequality Matters?
Growth Evidence Based on Small Area Welfare Estimates
in Uganda
Youdi Schipper and Johannes G. Hoogeveen*
Abstract
Existing empirical studies on the relation between inequality and growth have been criticized
for their focus on income inequality and their use of cross-country data sets. This paper uses
two sets of small area welfare estimates often referred to as poverty maps to estimate a
model of rural per capita expenditure growth for Uganda between 1992 and 1999. We
estimate the growth effects of expenditure and education inequality while controlling for
other factors such as initial levels of expenditure and human capital, family characteristics
and unobserved spatial heterogeneity. We correct standard errors to ref lect the uncertainty due
to the fact that we use estimates rather than observations. We find that per capita expenditure
growth in rural Uganda is affected positively by the level of education as well as by the
degree of education inequality. Expenditure inequality does not have a significant impact on
growth.
World Bank Policy Research Working Paper 3592,May 2005
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage
the exchange of ideas about developm ent issues. An objective of the series is to get the findings out
quickly, even if the presentations are less than fully polished. The papers carry the names of the
authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in
this paper are entirely those of the authors. They do not necessarily represent the view of the World
Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are
available online at http://econ.worldbank.org .
*Schipper is with the Vrije Universiteit Amsterdam and consultant to the World Bank. Hoogeveen is
with the World Bank. Please send correspondence to both yschipper@feweb.vu.nland
jhoogeveen@worldbank.org. We are grateful to the Uganda Bureau of Statistics, Entebbe, for their
help with the provision of the survey and census data. For useful comments and other forms of help we
would like to thank Chris Elbers and seminar participants at the Vrije Universiteit.
1
1. Introduction
Poverty reduction is fully determined by the rate of growth of mean per capita
expenditure and (changes in) the distribution of expenditure (Bourguignon, 2004;
Ravallion, 1997). This puts the empirical relation between inequality and growth at
the heart of poverty reduction strategies. Despite decades of theoretical and empirical
research on this relation, the aggregate evidence on the effect of inequality on growth
is inconclusive on the sign and robustness of the effect. Recent debate has focused on
(1) the nature of the inequality measure (income versus physical and human capital
inequality, e.g. Castello and Domenech, 2002; Elbers and Gunning, 2004) and (2)
problems of measurement and inference in macro data sets (Atkinson and Brandolini,
2001; Banerjee and Duflo, 2003). A further, remarkable feature of the literature in this
area is an apparent geographical mismatch: although the effect of inequality on
growth has important implications for poverty and African levels of poverty incidence
remain persistently high, empirical evidence on the inequality-growth relation is
virtually absent for Africa.1
Taking into account points (1) and (2), this paper provides empirical evidence for
Uganda. Regarding (1), recent studies have questioned the focus on income inequality
as a determinant of growth. A number of theoretical papers show that inequality in
human capital determines both income inequality and income growth (Benabou,
1996; Galor and Tsiddon, 1997; Elbers and Gunning, 2004). On the empirical side,
1A number of recent cross-country growth studies focus on sub-Sahara African countries
(Block, 2001; Bloom and Sachs, 1998). There are also growth studies for Africa using household level
data (Deininger and Okido, 2003, for Uganda and Dercon, 2001, for Ethiopia). However, these
analyses do not consider the effect of inequality on growth. Mbabazi et al. (2002) estimate a cross-
country inequality growth regression for a set of developing countries, a quarter of which are in Sub-
Sahara Africa.
2
Deininger and Squire (1998) find that the coefficient on income inequality in growth
regressions is not robust to the inclusion of regional dummies. Birdsall and Londono
(1997) show that once land and human capital inequality are entered in a cross-
country growth regression, income inequality no longer has a significant effect on
growth. Similarly, Castello and Domenech (2002) find a negative and robust growth
effect of human capital inequality, but no robust income inequality effect. We
construct a human capital Gini coefficient using census data and estimate the growth
effect of inequality in human capital too. Our results indicate that it is human capital
inequality rather than income inequality that affects growth; however, the effect we
find for Uganda is positive.
On point (2), we present a study based on micro data for Uganda, which allows us to
avoid data comparability problems that affect cross-country studies. While there is a
small number of inequality-growth studies that use micro (meso) data, we believe this
is the first such study for a relatively small country and the first for an African
country. Our analysis has been made possible by recent advances in the field of small
area welfare estimation (Hentschel et al., 2000). The data set thus consists partly of
imputed variables or so-called small area welfare estimates. These are obtained by
deriving expenditure estimates for a complete population, combining information
from a census and a survey (Elbers et al., 2003).
The paper is organized as follows. Section 2 briefly reviews data problems
encountered in empirical inequality-growth studies and introduces small area welfare
estimates as an alternative data source. In Section 3 we present our growth model and
descriptive statistics. Section 4 presents a discussion of econometric issues that need
3
to be addressed; in particular, we discuss a variance correction that is required
because we use imputed data. We present results in Section 5 and conclude in Section
6.
2. Data: macro, micro and small area welfare estimates
The effect of income inequality on economic growth is the subject of a large
literature. Aghion et al. (1999) and Thorbecke and Charumilind (2002) review this
literature and show that theory does not provide firm predictions of the sign of the
effect.2 Empirical studies in the 1990s have been ".. impressively unambiguous .."
(Aghion et al., 1999, p1617) in concluding that the growth effect of inequality is
negative, but more recently some authors have obtained contrasting results (e.g.
Forbes, 2000; Banerjee and Duflo, 2003). The most common denominator in these
studies is the nature of the data used: the empirical inequality-growth literature is
largely based on cross-country data.
Cross-country inequality-growth studies, while providing the bulk of existing
empirical evidence, have been criticized for a number of reasons. First and foremost,
the quality and internal consistency of datasets, in particular inequality series, have
been questioned. Deininger and Squire (1996) challenge the quality of inequality data
in growth regressions and offer an improved `high quality' dataset. However, the
consistency of inequality data in this set has been challenged by Atkinson and
2Positive inequality-growth effects can be attributed to a positive effect on savings, to the existence of
investment indivisibilities or to positive incentive effects of inequality. A negative inequality-growth
effect can be explained by political tension, instability and demands for redistribution due to inequality,
by reduced investment opportunities for the poor, worsened borrowers' incentives and by higher
macro-economic volatility. A `unified' model that aims to reconcile these conflicting effects is
presented in Galor (2000): this paper predicts that the effect of inequality on growth is non -linear, with
a positive effect at an `early stage of economic development' and a negative effect at a `later stage'.
4
Brandolini (2001), who show that national statistical agencies differ in their income
measures so that cross-country comparability of income inequality is questionable.
Moreover, changes in definitions or ruptures within country series may suggest
structural shifts in inequality without real significance. Banerjee and Duflo (2003)
argue that this type of measurement error may seriously distort causal inference in
inequality-growth models. Brock and Durlauf (2001) reject causal interpretations in
cross-country studies except under quite exceptional conditions. Their main argument
is that causal interpretation requires that estimated parameters can be assumed
constant, which is not plausible given the importance of country-specific unobserved
information (e.g. regarding policy). Deininger and Okidi (2003) also argue that data
used in cross-country studies are national aggregates that are likely to lose valuable
region or gender specific information; as a result, they question the relevance of cross-
country evidence for national policy formation even in case of perfect data.
A related, but often ignored, measurement issue affecting growth and inequality
regressions is related to the way the dependent variable is defined. Consider growth
over a period t for a country or region i, usually specified as
gri = yi - yi
,t ,0 (1)
t
where y is a measure of income or expenditure. This measure is often specified as the
logarithm of the mean of per capita expenditure over households h for country/region
i, i.e.
H
ln M (yi ) = ln
h=1yh,i (2)
H
5
where M(.) denotes an average. Ravallion (1998) points out that the use of the
logarithm of mean expenditure introduces a measure of the cha nge in inequality in the
error term of a regression with income growth as the dependent variable. The
argument is that if I is general measure of inequality
I(yi ) = ln M(yi )- M(ln yi )
then we find after rearranging terms:
ln M (yi) = M (ln yi) + I( yi) (3)
The LHS of (3) is the same as (2), and implicitly comprises a measure of inequality.
Therefore, rather than the log of household income we should use
N
yi = n=1log(yn)
(4)
,t N
which is the first term on the RHS of (3). We have addressed this point by calculating
growth using (4). Comparing two separate growth regressions, one of which has (3) as
dependent variable, we find a clear difference between the estimates (results
available, not reported). The (absolute) inequality coefficient in the model that uses
definition (3) is much larger and more significant than the alternative that uses (4).
This points to a possible spurious effect due to the definition of the variable.
6
Considering the various data issues, there appear to be two ways forward: higher
quality cross-country datasets (Bourguignon 2004) or country specific micro data
(Banerjee and Duflo 2003). A problem with the latter is that only surveys for very
large countries provide sufficient data points to meaningfully include inequality
indicators in a regression while census data typically do not provide the income or
wealth variables and covariates needed in a growth regression. As a result, there is
only a very small number of inequality-growth studies that use micro or regional data.
Ravallion (1998) estimates a household level growth model with local externalities
and finds a significant negative effect of asset inequality for rural China. Balisacan
and Fuwa (2003) find a positive effect of land inequality on provincial level growth
for the Philippines. An important advantage of regional or household data, apart from
the usually large number of observations, is that comparability problems are much
less severe than in cross-country datasets: the definitions of variables or phrasing of
survey questions are generally uniform across regions for a given dataset.
The unavailability of inequality data has long precluded the study of the inequality-
growth relation for smaller countries. However, application of techniques of welfare
estimation for small area target populations (see Elbers et al., 2003) has recently
provided expenditure estimates for all households in Uganda for 1992 and 1999
(Hoogeveen et al., 2003). It is the availability of these estimates that allows us to
estimate the effect of income inequality on growth for a smaller country such as
Uganda.
Estimates of expenditure and inequality are available for 719 rural sub-counties.
Based on comparable household expenditure data, they represent one of the first data
7
sets for Africa with comparable inequality estimates for a substantial number of
observations; see Emwanu et al. (2004), for details. A summary of the welfare
estimates used in this paper is presented in Table 1. The table confirms that on
average poverty fell over the 1990s but that the decrease in poverty was not
distributed uniformly. The decline in poverty was lowest in the North as was the
growth rate. Initial expenditure inequality was highest in the West region, whereas
initial inequality in the three other regions is almost the same.
Table 1
Region Expenditure Expenditure Poverty ratio Poverty change
Growth 92-99 Inequality 92 92 99 92-99
Central 0.057 0.302 0.543 0.245 -0.297
East 0.058 0.299 0.661 0.362 -0.299
North 0.019 0.300 0.768 0.678 -0.091
West 0.040 0.327 0.557 0.326 -0.230
National 0.043 0.308 0.633 0.403 -0.229
Note: column entries are (unweighted) region means of sub-county estimates.
3. An empirical inequality growth model
We estimate, at the sub-county level, yearly per capita expenditure growth over the
period 1992 1999 as a function of 1992 per capita expenditure, expenditure
inequality, human capital inequality, male and female human capital and household
demographics. The model can be represented as
°gi (5)
,d (%yi - yi )/7 = yi 1+ I i 2+ Iedu3+ Xi ?+d +ui
% % %exp
,99 ,92 ,92 ,92 i,92 ,92
8
All variables, except for the inequality measures and dummies, are averages by sub-
county i: g is the annual expenditure growth rate between 1992 and 1999; y is the
logarithm of per capita expenditure; Iexp is the Gini coefficient for per capita
household expenditure; Iedu is the Gini coefficient for the number of years of formal
education of the household head. X is a matrix of other covariates consisting of
human capital (number of years of formal education entered separately for household
heads and for spouses), household head age, gender of the household head, adult
equivalent household size, and the fraction of own children in the household. Given
our approach, we are limited in our choice of covariates in X to what the census has to
offer. We use district fixed effects, represented by d, to control for unobserved
spatial heterogeneity; ui is an error term. The specification includes most variables
that are common in (cross-country) inequality-growth studies. We add demographics
to account for differences in production technology and fertility, as many theoretical
models require. We do not have a measure of `market distortions', but do not expect
the value of this variable to vary much between sub-counties.
A non-standard econometric issue lies in the fact that some of our variables are not
observed but imputed as described in the previous section. The imputed variables,
expenditure, growth and expenditure inequality, are denoted using tildes. See Table 2
for definitions and summary statistics and Section 4 for a discussion of the estimation
issues involved.
9
Table2
Variable Definition* Mean Standard Minimum Maximum
error
Annual growth of log per capita
gr exp, 92-99: 0.04 0.04 -0.15 0.15
Ln(pcx99) Ln(pcx92)/7
y Log expenditure pc 92: Ln(pcx92) 9.46 0.23 8.74 10.20
Expenditure Inequality: Gini
gini coefficient wrt pcx 0.31 0.03 0.20 0.50
Education Inequality: Gini
gi_hyredu coefficient wrt household head 0.58 0.09 0.34 0.99
education years
Household head's education,
n_hyredu number of years 3.59 1.00 0.04 8.41
n_spyredu Spouse's education, number of 1.36 0.54 0.00 3.67
years
hage Age of household head 42.17 2.18 30.89 47.75
Gender, equals 1 if household
hfem head female 0.28 0.08 0.11 0.75
aesize Adult equivalent household size 3.90 0.55 2.16 8.09
pchild Percentage of children in
household 0.44 0.06 0.12 0.60
*Note: all observations are sub-county means of the household values of the variables mentioned, with the
exception of the Inequality measures. No. of observations: 719
4. Estimation
The properties of estimators obtained from downstream3 regressions using imputed
values for welfare indicators are investigated in Elbers et al. (2005). Their main
proposition is that coefficients from regressions involving imputed welfare indicators
which have been derived with small area estimation techniques, either on the LHS or
on the RHS, do not differ systematically from regressions with `real data'. The
10
intuition for this consistency result is that imputed variables can be regarded a special
kind of instrumental variables and may therefore be safely used in estimation. We
briefly explore the issues involved in estimation for the general case with imputed
values on both the LHS and the RHS of a regression equation.
We consider a simple version of our downstream regression model (omitting
inequality measures)
gi = yi + xi ?+ ui (6)
The dependent g and the independent y are obtained from upstream imputation; in
what follows, imputed variables have tildes in order to distinguish them from `true'
values or observations. Writing imputed values as the difference between true values
and an error term, g% g - and y% y - , we obtain
g%i = y%i +(i -i ) + xi?+ ui (7)
The coefficient can be consistently estimated provided that (a) the imputed values
g% and y% are consistent estimators of the conditional expectation of the true welfare
measures and (b) the error terms and are uncorrelated with the regressors y% and
x.
Elbers et al. (2005) show that when small area welfare estimates are used (a) is
satisfied and (b) is likely to be satisfied. To see the latter, first note that y% is imputed
per capita expenditure (pcx) or a non-linear measure calculated from pcx, e.g.
3It is convenient to refer to our inequality-growth regression as a `downstream' model so as to
distinguish it from the `upstream' expenditure model which has been used to generate the imputed
values.
11
inequality. 4 Both and are prediction errors and are thus orthogonal to the
predicted values y% and g% , respectively. Moreover, since y% and g% are based on the
same prediction model, the prediction errors should be orthogonal with respect to both
y% and g% .5 The prediction errors should also be uncorrelated with regressors in x:
since the upstream modelling process makes use of as many available instruments as
possible, these regressors will have been considered as instruments in the upstream
pcx prediction model, ruling out the presence of any remaining correlation.
However, a correction of the estimated standard errors of the coefficients is necessary
because the (upstream) imputation process creates correlation between the welfare
estimates. Following Elbers et al. (2005), the prediction error of imputed variables,
e.g. expenditure, can be decomposed as
y - y = [y - E(y)]+[ E( y)- y%]
% (8)
where E(y) is the conditional expectation of expenditure. The first term on the RHS of
(8) is termed the idiosyncratic error, which is due to unobserved factors that determine
expenditure, and the second part is the model error, which reflects uncertainty about
the upstream model's parameters. Applying this error decomposition to both g and y
(7) can be written as
g%i =[y% i+ xi?]+[(E(yi) - y%i) - (E(gi) - gi )] °
(9)
+[(yi -E(yi)) -(gi -E(gi)) +ui]
The RHS of the equation consists of three parts, each in square brackets. First we
have a structural part consisting of imputed and non-imputed regressors and their
4Other variables could in principle be imputed or predicted as well; however, we consider pcx
imputations.
5This holds a fortiori when either y or z is a non-linear transformation of pcx or its distribution, such as
a poverty or inequality measure.
12
respective coefficients. The second part represents the model error, the third part the
sum of upstream idiosyncratic error and downstream error.
We simplify notation by rewriting these three parts as g%i = z*i ? +i +ei where z* =
( y% ,x) represents all regressors, both observed and imputed, and = (,);
represents the `model part' of the error and e the idiosyncratic part. Assuming that the
idiosyncratic part of the error is i.i.d., the variance matrix of the OLS coefficient
estimates of (9) is
V ? = e Z'Z
( ) 2 ( )-1 +(Z'Z)-1 Z'V()Z Z'Z
( )-1 (10)
where the model part variance is
V() = 2V (E(y)- y%)+V(E(g)- g°)- 2Cov[(E( y) -y%),(E(g) - g°)] (11)
Equation (10) shows that, compared to OLS variance estimates, variance has to be
adjusted upwards. As (11) shows, this adjustment depends on the variance in the
model error. The more imputed variables are used the more terms will have to be
added: with n imputed variables, the number of terms on the RHS of (11) equals n
variance terms plus n(n-1)/2 covariance terms. For example, if one imputed variable is
used on the RHS only, the adjustment is limited to the first term. In our regression
model (equation (5)), two imputed variables are used on the RHS, one on the LHS.
Two additional econometric problems affect our growth model. First, Caselli et al.
(1996) show that estimating a cross-section growth model using a fixed effects
estimator will lead to substantial bias when the number of periods is small, especially
on the coefficient for initial expenditure (y92). The empirical growth literature
13
suggests a number of solutions to this problem, most notably the Arrelano-Bond
estimator. Such estimators, however, need at least three periods to estimate the model,
using the first period to instrument for the initial conditions of the second period
which explain growth between period two and three. Since we have only two periods,
we cannot follow this approach. However, although the bias on the `convergence
coefficient' may be significant, Monte Carlo experiments indicate that the bias on the
other RHS coefficients tends to be small (Forbes, 2000).
The second problem is endogeneity. Even though our model does not contain `flow'
variables but only beginning-of-period `stocks', initial expenditure y(92) has been
used to construct the growth variable and is thus correlated with the error term. Initial
inequality may also be an endogenous variable, as the literature suggests that growth
affects inequality (e.g. Aghion et al., 1999; Lundberg and Squire, 2003). One would
expect this to be more problematic for changes in inequality (which we do not use)
rather than for initial inequality. Put to scrutiny, a Hausman test rejects exogeneity of
expenditure inequality, but cannot reject exogeneity of education. Consequently we
deal with the endoge neity of initial expenditure and expenditure inequality.
Since we do not have lagged values, e.g. y(t-1), to use as instruments, we have to find
instruments amongst the (few) available sub-county census means. We have chosen as
instruments for income a variable that measures the `education deficit' (the number of
school years missed) of children below the age of 13. The (initial) education deficit
for children in this age group is strongly negatively correlated with initial income, but,
arguably, does not affect growth in the period analysed. The instruments for
expenditure inequality are the maximum education deficit for children below 13 and
14
`ethnic fractionalization', which is the probability that any two citizens randomly
chosen from a sub-county population are from different ethnic groups. The latter
variable has itself been used to explain growth (Easterly and Levine, 1997) and is thus
possibly a less suited instrument. We tested its validity by including ethnic
fractionalization in the model. It does not alter the other coefficient estimates in any
significant way; moreover, an overidentifying restrictions test rejects endogeneity.
Finally, we note that the instrumentation also affects the calculation of the model's
variance: imputed endogenous variables have to be instrumented first and then
instrumented values are used in the calculation of the variance-covariance matrix
V ( ).
5. Results
The estimated standard errors in all our regressions are adjusted to account for
prediction errors following the approach outlined in the previous section. The
adjustments illustrated for the baseline equation in Table 3 result in an increase in
estimated standard errors for all coefficients. The last column of Table 3 gives the
ratio of the adjusted standard error estimate to the standard 2SLS estimate. The
increase varies over coefficients between a factor 1.2 and 1.7. This is the typical
trade-off when analysing small area welfare estimates: the gain in the number of
`observa tions' obtained by using imputed variables is partly offset by the loss in
precision due to (downstream) model prediction errors.
The results in Table 3, which includes both inequality variables and their squares,
illustrates the general decrease in significance when taking into account the fact that
estimates or predictions, not data, are used. In the case of education inequality the
15
adjustment even `destroys' a significant result, that is, causes the significance level to
increase to over ten percent.
Table3 Variance adjustments
Dependent: growth coef t-val(adj) t(2SLS) incr(se)
y -0.1723 -6.6374 -8.7981 1.3255
gini -1.1909 -0.7139 -1.0176 1.4254
gini2_ 1.8082 0.7405 1.0748 1.4515
gi_hyredu 0.2377 1.3318 2.2749 1.7081
gi_hyredu2 -0.1151 -0.9057 -1.5812 1.7458
n_hyredu 0.0086 1.7077 2.6470 1.5500
n_spyredu 0.0175 4.1999 4.9129 1.1698
hage -0.0008 -1.0305 -1.6072 1.5597
hfem 0.0487 2.7689 3.7914 1.3693
aesize -0.0065 -3.1557 -4.5537 1.4430
pchild -0.0463 -1.9806 -2.5756 1.3004
_cons 1.7947 3.9631 5.5353 1.3967
Our main findings are presented in Table 4 in a series of six regressions. Conditional
convergence is pronounced in all specifications: the coefficient on initial income is
negative, highly significant and has a value of around 0.17 in all specifications.
Apparently, sub-counties with lower mean per capita expenditure in 1992 have grown
faster over the 1990s, ceteris paribus. However, note that the coefficient estimate is
biased so we should not attach significance to its exact value. The main variable of
interest, inequality, has been entered using expenditure inequality and education
inequality; these variables have been entered in linear and quadratic form in
alternative specifications. The results show that expenditure inequality (gini) does not
have a significant effect on growth in any of the specifications. In contrast, education
inequality (gi_hyredu) has a significant positive effect on growth in all specifications
we tried. This effect is robust to the inclusion of expenditure inequality (columns 4
and 5). When only education inequality is entered without expenditure inequality,
columns 5 and 6 the effect is significant at the one percent level (note again that this
16
Table 4 Regression results
(1) (2) (3) (4) (5) (6)
gr gr Gr gr gr gr
y -0.172 -0.161 -0.171 -0.171 -0.186 -0.175
(6.64)*** (5.78)*** (5.23)*** (6.02)*** (7.46)*** (7.64)***
gini -1.191 0.126 -2.048 0.096
(0.71) (1.13) (1.17) (0.84)
gini2 1.808 3.094
(0.74) (1.22)
gi_hyredu 0.238 0.089 0.099 0.349
(1.33) (2.46)** (2.90)*** (3.24)***
gi_hyredu2 -0.115 -0.192
(0.91) (2.53)**
n_hyredu 0.009 0.001 0.003 0.008 0.011 0.010
(1.71)* (0.21) (0.61) (1.51) (2.54)** (2.38)**
n_spyredu 0.018 0.016 0.015 0.017 0.015 0.018
(4.20)*** (3.91)*** (3.31)*** (4.01)*** (3.94)*** (4.56)***
hage -0.001 -0.000 -0.001 -0.000 -0.001 -0.001
(1.03) (0.52) (0.88) (0.64) (1.71)* (1.87)*
hfem 0.049 0.057 0.055 0.046 0.047 0.053
(2.77)*** (3.45)*** (2.73)*** (2.90)*** (2.97)*** (3.37)***
aesize -0.006 -0.005 -0.006 -0.006 -0.007 -0.007
(3.16)*** (2.60)*** (2.42)** (3.03)*** (3.35)*** (3.49)***
pchild -0.046 -0.042 -0.035 -0.044 -0.056 -0.063
(1.98)** (1.91)* (1.48) (2.02)** (2.39)** (2.70)***
Constant 1.795 1.550 2.034 1.593 1.785 1.604
(3.96)*** (5.08)*** (3.96)*** (5.20)*** (7.13)*** (7.03)***
Observations 719 719 719 719 719 719
R-squared 0.92 0.90 0.91 0.91 0.91 0.92
p(Hausman Chi-sq) 0.07 0.00 0.01 0.00 0.15 0.44
p(Sargan Chi-sq) 0.10 0.06 0.16 0.05 0.04 0.20
Notes: Coefficient estimates on district dummies omitted. Absolute value of t statistics in parentheses.
* significant at 10%; ** significant at 5%; *** significant at 1%
is after variance correction related to the imputation of the growth and expenditure
variables). The last specification (column 6) includes education inequality squared:
the coefficient has a negative sign and is significant at the five percent level. We
conclude that education inequality should be entered in both linear and quadratic
form. Although growth thus appears to be an inverted U-shaped function of education
inequality, ceteris paribus, we should not overstate the non-monotonicity: the
maximum of the parabola is found where gi_hyredu equals 0.91. In our data, more
than 95 percent of sub-counties has lower education inequality. In other words, only
for extremely high values of education inequality is the effect on growth negative.
17
All other variables in our growth regressions except age of the household head (hage)
are significant at the five percent level or better in the last specification (column 6).
Also, most of them are reasonably insensitive to variations in specification. Only the
coefficient on household head's education level becomes large and significant when
inequality (squared) with respect to this variable is added. Most other coefficients
have expected signs. The effect of human capital levels measured by the years of
education completed by the household head and spouse is positive: investments in
human capital levels of household members pay-off in higher growth. Interestingly,
the effect of an additional year of education for spouses is nearly twice as large as for
household heads. Although on average 28 percent of Ugandan households has a
female head in 1992, the effect of spouse human capital is striking, both in relative
size and significance. Moreover, sub-counties with larger shares of households that
are headed by females (hfem) grow faster. The latter effect is significant at the one
percent level in all specifications.6
The effect of the age of household head is small, negative and marginally significant
(ten percent level). Adult equivalent household size and the percentage of own
children in the household both have a negative effect on growth. Inother words, given
age structure, sub-counties with larger households experience lower per capita
growth. Moreover, sub-counties with households with a larger number of own
children relative to total household size grow more slowly than others, ceteris paribus.
6We note that some of our findings contrast with evidence presented in Deininger and Okidi (2003):
these authors finda non-linear, U-shaped growth effect of education levels and a negative effect of the
female household head dummy. One possible explanation for this difference is that we consider rural
households only.
18
Discussion
The two most important findings of this study are (1) income inequality does not have
a statistically significant effect on growth and (2) education (human capital)
inequality has a positive effect on growth. The first of these findings is in line with
cross-country evidence in Birdsall and Londono (1997) and Castello and Domenech
(2002), while the second finding contrasts with findings in these papers.
This second finding may appear somewhat counter intuitive at first sight: growth is
enhanced when human capital (or access to it) of the household head is more
unequally distributed. The key to understanding what is going on is the fact that we
control for mean level of education: this means that our conclusion is that at a given
mean level of human capital, a more unequal distribution of this capital is good for
growth. As noted before, a number of authors have addressed this point theoretically.
In particular, Elbers and Gunning (2004) show that our result is to be expected in a
Ramsey growth model: under the condition that the production function is convex in
human capital, a mean-preserving spread in human capital results in higher long-run
output growth. For instance suppose we were to redistribute one year of education
from someone with low educational attainment to someone who is reasonably well
educated. This would make the distribution of human capital more unequal while
keeping the mean constant. But if the increase in output by the well-educated person
exceeds the decline for the less well educated person, then the increased spread in
education has a positive effect on growth as long as the mean level of education is
kept constant.
19
Mean preserving spreads in human capital are not possible within a given population;
they only exist in thought experiments or in the long run, that is, over generations. In
reality, mean level of education and inequality change simultaneously. In Uganda, for
instance, education inequality as measured by the Gini coefficient is highly
(positively) correlated with the percentage of households whose head has never
attended school. The average years of head education is also highly (negatively)
correlated with the percentage of heads who have never attended school.
Consequently there is a strong negative correlation between education inequality and
the average level of education (see Figure 1): both are largely determined by the
number of household heads who never attended school. The implication of such a
correlation is that while raising the general level of education through policies like
universal primary education will be good for growth its positive effects will be partly
offset by the associated decline in the education inequality. This effect is substantial.
A 10% increase in education is associated with a 3% decline in the Gini which, in
turn, offsets about ? of the growth impact of an increase in the level of education. Put
differently: if the additional education years had been distributed unequally, e.g., in
such a way that the Gini would have remained constant, the growth effect would have
been larger.
20
Figure 1
8
6
education
of
4
years
Head
2
0
.2 .4 .6 .8 1
Gini head years of education
6. Conclusion
We estimated the effect of income and education inequality on growth, using imputed
data on expenditure inequality and growth for small administrative units in Uganda
(sub-counties), along with census data for education inequality. Analysing this
relation for a specific country has important benefits: first, it avoids data
comparability problems that typically affect cross-country growth regressions.
Moreover, by identifying the effects of inequality on growth for a given country,
country specificity is taken into account. This enhances the relevance of our results
for local policy makers.
In the empirical section we adjusted the standard errors of variable coefficients for the
fact that some regressors are imputedin our case initial expenditure levels and
expenditure inequality, and therefore associated with a standard error. The
21
adjustments are considerable; the y typically increase standard errors by a factor 1.2 to
1.7.
Our results show that higher levels of education enhance growth. Controlling for the
level of educational attainment, larger variation in education is good for growth. Our
results also indicate that income inequality does not affect growth.
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