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Income inequality and macroeconomic activity in Greece
K. Chrissis, S. Dimelis, A. Livada
Athens University of Economics and Business
Technical Report No 263
ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS
DEPARTMENT OF STATISTICS
MARCH 2013
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Abstract
The purpose of this technical report is to examine the relationship between income
inequality and macroeconomic activity in Greece. The relationship between income
inequality and economic growth is a central issue in the study of macroeconomics.
The macroeconomic indicators of most interest are the economic growth and the
openness of the economy. Other control variables such as financial development,
inflation and the growth of population are incorporated in the econometric model
presented here. The econometric methodology implemented is Autoregressive
Distributed Lag (ARDL) approach.
The empirical findings for the relationship of income inequality and macroeconomic
activity suggest that 1% top income share depends on growth since the real GDP per
capita has a significant negative impact on the long term. A significant impact, also,
yields the openness of economy. Trade as a percentage of GDP influences positively
top income shares. Inflation, expressed as the growth rate of CPI, has a statistical
significant negative impact on top income share. On the contrary the pattern of
financial development (domestic credit to private sector as percentage of GDP) andpopulation (growth rate of population) do not affect income inequality in the long run.
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1. Introduction
This paper presents the empirical findings of the response of aggregate income
inequality to changes in macroeconomic activity in Greece. A short review of theory
and evidence is presented in section two. Data are described in section three. In
section four, the econometric methodology implemented is presented (ARDL
approach). The empirical results are illustrated in section five. Moreover, alternative
income inequality proxies and supplementary econometric approach (VAR-approach
Johansen cointegration) are presented in section six. Finally, section seven concludes.
2. Theory and evidence
The relationship between income inequality and economic growth is a central issue in
the study of macroeconomics. According to the pioneer work of Kuznets (1955),income inequality increases until a critical income level is attained, after which
inequality begins to decrease. The graphical representation of this hypothesis is an
inverted U shaped curve. Though Kuznets hypothesis has found some empirical
support at global level [Ram (1989) and Park and Brat (1995)] the economic research
does not provide a clear perspective. Kaldor (1956), Bourguignon (1981), Li and Zou
(1998), Forbes (2000), Roine et al (2007) and Frank (2009) suggest that there is a
positive relationship between income inequality and economic growth. Andrews et al
(2009) note that they find no systematic relationship between top income shares
(proxy for income inequality) and economic growth in a panel of twelve developed
countries; after 1960, however, a statistically significant relationship seems to exist.
On the contrary, Alesina and Rodrik (1994), Perotti (1996), Benabou (1996), Persson
and Tabellini (1994) and Aghion et al. (1999) have shown that there is a negative
relationship between economic growth and income inequality. Glomm and
Kaganovich (2008) show how the relationship between economic growth and
inequality depends upon the levels of funding of two of the largest government
programs, public education and social security. Their model indicates that an increase
in government spending on social security reduces income inequality and can have a
non-monotonic effect on growth (positive when the initial level is low and negative
when the initial level is high). Empirical work by Panizza (2002) and Quah (2001) hasfound little or no stable relationship between inequality and growth; Deininger and
Squire (1996) state, also, that they do not find a systematic link between growth and
changes in aggregate inequality. Moreover, Barro (2000) has found evidence that
inequality is positively related to growth among wealthier countries and negatively
related to growth among low-income countries. Voitchovsky (2005) has found
evidence that while top-end inequality is positively associated with growth, bottom-
end inequality may be negatively related to growth. Lee (2010) provides a short
literature review for theoretical and empirical studies on the growth-inequality
relationship. Frank (2009) states that the results appear to be extremely sensitive tothe econometric specification.
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In the recent years empirical research test the relationship of income inequality and
openness in the framework of Kuznets curve. Dobson and Ramlogan (2009) suggest
that data from Latin America provide evidence for the consistency of Kuznets
hypothesis; inequality increases with trade openness until a critical level of openness
is reached after which inequality begins to fall. According to Lee (2010) empiricalfindings from Asia indicate that there is a significant turning point of globalization at
which inequality starts decreasing as further globalization proceeds. Jalil (2011) notes
that Kuznets curve fits the relationship between openness and income inequality in the
case of China. In a more broad context, Bergh and Nilsson (2010) using panel data
(from SWIID) note that freedom to trade internationally is robustly positively related
to within-country income inequality. Barro (2000), Hurrell and Woods (2000) and
Carter (2007) find that the trade openness worsens the income inequality.
Additionally, Roine et al (2007) include openness in their econometric model (GMM)
suggesting that international trade is not associated with increases in top incomes
(proxy for income inequality) on average, but is associated in Anglo-Saxon countries.
Jalil (2012) provides a short literature review for theoretical and empirical studies on
the growth-openness relationship.
The economic literature remains inconclusive about the effect of inflation on the
income inequality. Cutler and Katz (1991), Clarke et al (2006) and Ang (2010) state
that inflation improves the income inequality. On the contrary, Easterly and Fisher
(2001) and Beck et al. (2007) note that inflation has an adverse effect on the
distribution of income. However, as highlighted by Easterly and Fischer (2001), the
way inflation affects the poor may well differ between economies due to the
compilation of the tax system and therefore is an empirical issue.Several empirical studies employ other control variables in their econometric
methodology. In this paperfinancial developmentand population have been utilized
as independent variables.
3. Data description
This section outlines the data used in the econometric analysis and their sources.
Income inequality: The main proxy variable applied for the estimation of income
inequality is 1% top income share (tis). The compilation of top income shares was
made according to Piketty (2001) approach for tabulated tax data. Tax data provide
detailed information on nominal family income and its sources, as reported annually
in tax declaration forms. Family income is the sum of income received by the husband
and/or wife. This definition also includes single persons. Tax data are reported in
tabulated form. A significant issue of tabulated tax data is that the thresholds of
income classes do not coincide with the percentiles which are necessary for the
estimation of top income shares. The standard approach to tackle this issue is
assuming the top end of income distribution is well described by the Pareto
distribution. In this paper the Piketty (2001) approach for Pareto procedure is used.
Control total for population is needed since the amount of fillers of tax returns were
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low especially in the beginning of the period under investigation. The control total
used is the population over the age of 20 minus half the number of the married men
and women. To estimate income shares a control total for aggregate income is needed.
Two approaches are commonly applied. One approach starts from the income tax and
adds the income of those not covered (the so called non-fillers). The secondapproach starts from an external control total, typically derived from the national
accounts. This is a standard approach employed since Kuznets (1953) and followed
by many researchers in historical studies of income inequality. In this paper the
control total for income is derived from national accounts. For more technical details
on the compilation procedure on Greek tax data see Chrissis et al (2011). The choice
of top income shares as the main proxy of income inequality was made due to the fact
that upper shares according to Piketty (2001) approach are comparable with the
corresponding shares estimated using micro data from other data sources (Household
Expenditure Survey, European Community Household Panel (ECHP), European
Union Survey on Income and Living Conditions (EU-SILC) see Chrissis and
Livada, 2012). Moreover, other top income shares and aggregate inequality measures
will be utilized as alternative measures.
Growth: The real Gross Domestic Product (GDP) at 2005 market prices per head of
population is utilized for the approximation of growth. The real GDP per capita is
obtained from European Commission statistics.
Openness: The measure of trade openness is standard and it is defined as the sum of
exports and imports as a percentage of GDP. The data source is World Bank, WorldDevelopment Indicators.
Financial Development: The proxy variable for the description of the financial
development is private credit. Private credit is defined as the domestic credit to
private sector as a share of GDP. The data source is World Bank, World Development
Indicators.
Inflation: The growth rate of Consumer Price Index (CPI) is used as an approximation
for inflation. The data source is the Greek National Statistical Institute (ELSTAT).
Population: The proxy variable for the description of population is the growth rate of
total population from demographic statistics. Data are obtained from European
Commission statistics.
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4. Econometric methodology
The empirical model to be estimated is
(1)Where ineq is a measure (proxy) of inequality. contains all regressors (or controlvariables) which may vary across time. The parameter A contains a constant and/or
trend and is the classical error term.The empirical model is familiar to Roine et al (2007) and similar to Dobson and
Ramlogan (2009), Lee (2010), Jalil (2012) and Frank (2009) under the scope that
certain control variables are the same; nevertheless the framework differs from study
to study.
This study employs the Autoregressive Distributed Lag (ARDL) (or bounds testing)
cointegration procedure for the empirical analysis of the long-run relationships and
dynamic interacting among the variables of interest. This procedure was popularized
by Pesaran and Pesaran (1997), Pesaran and Smith (1998), Pesaran and Shin (1999)
and Pesaran et al (2001).
There are certain advantages of the ARDL approach. This technique is applicable
irrespective of whether the regressors in the model are purely I(0), purely I(1) or
mutually cointegrated (Pesaran (1997)). The error correction model (ECM) can be
derived from ARDL through a simple linear transformation (Banerjee et al (1993)).
The small sample properties of ARDL approach are superior to that of the Johansenand Juselius cointegration technique (Pesaran and Shin (1999)). Moreover, as long as
the ARDL model is free of residual correlation, endogeneity is less of a problem
(Pesaran and Shin 1999).
According to Pesaran and Pesaran (1997) we apply the following augmented
autoregressive distributed lag ARDL ( model:
Where
L is a lag operator such as , and is a sx1 vector of deterministicvariables such as the intercept term, seasonal dummies, time trends, or exogenous
variables with fixed lags. All possible values of p=0,1,2,m; =0,1,2,,m;i=1,2,,k with a total of ARDL models can be estimated by OLS.
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The long run coefficients for the response of the dependent variable to a unit change
in the regressors are estimated by
Where and , i=1,2,,k are the selected (estimated) values of p and , i=1,2,,k.
The long-run coefficients associated with the deterministic/exogenous variables with
fixed lags are estimated by
Where denotes the OLS estimate of in (2) for the selected ARDLmodel.
The corresponding unrestricted error correction model is given by
where is the correction term defined by
For more technical details see Pesaran and Pesaran (1997).
On the basis of equations (2)-(4), the unrestricted error correction model of interest
can be specified as (this is the ARDL framework for equation (1)):
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Where are the long run multipliers, is the drift, is the trend coefficient and are white noise errors.
The first step in the ARDL bounds testing approach is to estimate equation (9) by
ordinary least squares (OLS) in order to test for the existence of a long-run
relationship among the variables by conducting an F-test for the joint significance ofthe coefficients of the lagged levels of the variables. Therefore the hypothesis test has
the form
H0: (no long relationship)Against the alternative hypothesis
H1: (a long relationship exists)
The computed F-statistic value will be evaluated with the critical values tabulated by
Pesaran et al (2001). According to these authors, the lower bound critical values
assumed that the explanatory variables
are integrated of order zero, or I(0), while
the upper bound critical values assumed that variables are integrated of order one,or I(1). Therefore, if the computed F-statistic is smaller than the lower bound value,
then the null hypothesis is not rejected and we conclude that there is no long
relationship the variables of interest. On the contrary, if the computed F-statistic is
greater than the upper bound value, then a long-run relationship is assumed. Finally, if
the computed F-statistic lies between the lower and the upper bound values the results
are inconclusive.
In the second step, once cointegration is established the ARDL ( model is estimated as follows:
This step involves selecting the orders of the ARDL ( model in thevariables using Schwarz Bayesian criterion. The choice of the appropriate lags
according to Akaike information criterion has been, also, conducted. Then, as
described above the long-run coefficients are estimated.
In the third and final step, the short-run dynamic parameters have been obtained by
the estimation of an error correction model associated with the long-run estimates.
This is specified as follows:
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Here a, b, c, d, e, f, are the short-run dynamic coefficients of the models convergence
to equilibrium and is the speed of adjustment back to long run equilibrium after a
short run shock.
5. Estimation Results
Unit roots tests
A variable is stationary, or integrated of order zero, when the mean and the variance
do not depend on time. If the stochastic process that generate the time series does not
alter in time, i.e. it is stationary, then it is feasible to model this process through
regression and therefore estimate the coefficients. On the contrary, the non
stationarity of the time series could lead to issues about the robustness of the
estimated standard errors and therefore the credibility of the model will be limited.
The variables of interest will be tested for the stationarity status for the determination
of their order of integration. Since the bounds test is based on the assumption that the
variables are I(0) or I(1), the implementation of unit root tests are necessary in order
to ensure that none of the variables is integrated of order two or beyond.
Two econometric tests are applied in this study: the Augmented Dickey Fuller (ADF)
test and the Phillips-Perron (PP) test. The results for the ADF and PP tests with no
exogenous, one exogenous (intercept) and two exogenous (intercept and trend)
regressors are illustrated in the following table.
Table 1. Summary results for ADF and PP tests for stationarity
ADF (firt difference) Phillips-Perron (first difference)
No constant
No trend
constant
No trend
constant
trend
No constant
No trend
constant
No trend
constant
trendTis_01 -3.013876* -3.055774** -5.560674* -5.661297* -5.662898* -5.736735*
Rgdp_pc -3.347194* -4.249739* -4.241093* -3.356625* -4.320717* -4.312802*
Trade -5.458381* -5.535058* -5.595912* -3.711501* -3.575065* -3.442633***
Credit -4.222798* -4.733619* -4.968420* -4.402065* -4.939950* -5.077983*
Cpi_r -6.571467* -6.500329* -6.243614* -6.644670* -6.555692* -8.046719*
Population_r -4.832358* -4.784957* -4.732516* -4.550032* -4.473749* -4.393780*
Note: Reject null hypothesis of unit root at 10% (***), 5% (**) and 1% (*) significance level
The analysis indicates that no variable is integrated above order one, therefore the
ARDL approach of cointegration can be implemented.
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Bounds test for cointegration
In the first step of ARDL analysis, the presence of long-run relationships is tested
using equation (9)1. The maximum length of lags applied was two, three and four
lags. Apart from the dependent variable of income inequality the model contains asregressors, proxies for growth, openness, financial development, inflation and
population. The following tables illustrate the results from the Wald restriction as
well the critical values provided by Pesaran (2001).
Table 2. Critical values by Pesaran (2001), case III: No intercept and no trend90% 95% 97,5% 99% Mean Variance
k I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1)
5 1.81 2.93 2.14 3.34 2.44 3.71 2.82 4.21 1.02 1.84 0.34 0.67
Table 3. Critical values by Pesaran (2001), case III: Unrestricted intercept and no trend90% 95% 97,5% 99% Mean Variance
k I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1)
5 2.26 3.35 2.62 3.79 2.96 4.18 3.41 4.68 1.34 2.17 0.48 0.79
Table 4. Critical values by Pesaran (2001), case V: Unrestricted intercept and unrestricted trend90% 95% 97,5% 99% Mean Variance
k I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1) I(0) I(1)
5 2.75 3.79 3.12 4.25 3.47 4.67 3.93 5.23 1.72 2.53 0.59 0.91
Table 5. Results for Wald restrictionsVariable ARDL Exogenous F-stat (joint by Wald restrictions)
Tis_01 2 C 3.711542***
C+T3.107592
none2.433334
3 C 2.500047
C+T2.357803
none2.069196
4 C 1.476491
C+T1.304211
none1.386082
Note: * 1%, ** 5% and *** 10% significance
The estimated F-statistic with Wald restrictions is compared with the critical values
provided by Pesaran. The results suggest that the null hypothesis of no long run
relationship is rejected at 10% significance with the presence of one exogenousregressor and with two lags. The important issue is that the existence of the intercept.
Having establish the existence of a relationship in the long term the ARDL model is
estimated. The choice of the appropriate lags has been made according to Schwarz
Bayesian Criterion (SBC). The selected model is ARDL (1,1,0,0,2,0). The use of
Akaike Criterion (AC) yields similar results [ARDL (1,1,2,0,2,0)2]. The models were
selected on the basis of SBC because it is known that SBC selects the most
parsimonious model3.
1
The model changes if trend is included or the intercept is abolished2Results are available upon request
3Pesaran 1997, p. 354
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The Autoregressive Distributed Lag estimates are:
Table 6. ARDL (1,1,0,0,2,0) selected based on Schwarz Bayesian Criterion
Regressors Coefficient Standard error T-ratio [prob]
Income inequality (-1) .75384 .052755 14.2894 [.000]Real GDP per capita -.0024391 .8042E-3 -3.0330 [.004]
Real GDP per capita (-1) .0017415 .8838E-3 1.9706 [.056]
Openness .019831 .0054353 3.6485 [.001]
Financial Development -.0022669 .0033658 -.67350 [.505]
Inflation -.023687 .0064304 -3.6836 [.001]
Inflation (-1) -.014150 .0064304 -1.6105 [.116]
Inflation (-2) -.015110 .0082045 -1.8417 [.073]
Population .11964 .095015 1.2592 [.216]
intercept .018672 .0047723 3.9125 [.000]
The diagnostic tests for the underlying ARDL model are:
Table 7. Diagnostic tests
Test Statistics Test Statistics F Version
A:Serial Correlation CHSQ( 1)= .49166[.483] F( 1, 37)= .38291[.540]B:Functional Form CHSQ( 1)= .96419[.326] F( 1, 37)= .75846[.389]C:Normality CHSQ( 2)= 12.9720[.002] Not applicableD:Heteroscedasticity CHSQ( 1)= 2.0967[.148] F( 1, 46)= 2.1011[.154]R-squared .98558
The r-squared statistic yields a very high value meaning the good fitness of the model.
The Breusch-Godfrey Serial Correlation LM Test suggests that there is no serial
correlation of the residuals (autocorrelation). The model also seems to pass the test for
the presence of heteroscedasticity, since that the null hypothesis is not rejected.
Moreover, the Ramsey RESET test indicates that the functional form is suitable.
Nevertheless, the model does not pass the test for normality of the residuals.
The stability of the coefficients was tested by applying the CUSUM and CUSUM of
squares test (Brown, Durbin, and Evans, 1975). In both tests movement outside the
critical lines is suggestive of parameter or variance instability.
Figures 1 and 2 present the results for CUSUM and CUSUM of squares test.
Figure 1. Plot of Cumulative Sum of Recursive Residuals
The straight lines represent critical bounds at 5% significance level
-5
-10
-15
-20
0
5
10
15
20
1962 1967 1972 1977 1982 1987 1992 1997 2002 2007
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The model succeeds in all diagnostic tests, except normality, and according to
CUSUM and CUSUM of squares test the stability of the coefficients is satisfactory;
the specification of the model seems robust enough.
Since the ARDL model is chosen, we proceed in the estimation of the equation (10)
and then in the estimation of the long-run coefficients. The following table presentsthe long-run estimates of the selected ARDL model for the case of intercept.
Table 8. Estimated long run coefficients of ARDL (1,1,0,0,2,0) based on Schwarz Bayesian Criterion
Regressors Coefficient Standard error T-ratio [prob]
Real GDP per capita -.0028337 .9293E-3 -3.0493 [.004]
Openness (trade % GDP) .080561 .028594 2.8174 [.008]
Financial Development (credit
% GDP)
-.0092090 .014756 -.62407 [.536]
Inflation (CPI rate) -.21509 .033824 -6.3592 [.000]
Population (population rate) .48604 .38795 1.2528 [.218]
intercept .075852 .0059700 12.7056 [.000]
The statistical significance of the intercept indicates that it should be included in the
equation. Growth seems to relate with income inequality. The real GDP per capita has
an impact on the long term, since the coefficient is statistical significant at 1% level.
The relationship with the proxy of income inequality is negative. A significant impact,
also, yields the openness of economy. Trade as a percentage of GDP influences
positively top income shares. Like the two previous independent variables, inflation,
expressed as the growth rate of CPI, is statistical significant at 1% level and it yields
negative sign. On the contrary the pattern of financial development (domestic credit to
private sector as percentage of GDP) and population (growth rate of population) doesnot affect income inequality in the long run; their coefficients does not differ
statistically from zero.
The next step is the estimation of the short-run coefficients associated with the long-
run relationships (equation (11)). The results for the case of intercept are illustrated
below
Table 9. Error correction representation for the selected ARDL model (1,1,0,0,2,0) based on Schwarz Bayesian Criterion
Regressors Coefficient Standard error T-ratio [prob]
D(Real GDP per capita) -.0024391 .8042E-3 -3.0330 [.004]
D(Openness) .019831 .0054353 3.6485 [.001]D(Financial Development ) -.0022669 .0033658 -.67350 [.505]
Figure 2. Plot of Cumulative Sum of Squares of Recursive Residuals
The straight lines represent critical bounds at 5% significance level
-0.5
0.0
0.5
1.0
1.5
1962 1967 1972 1977 1982 1987 1992 1997 2002 2007
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D(Inflation) -.023687 .0064304 -3.6836 [.001]
D(Inflation)(1) .015110 .0082045 1.8417 [.073]
D(Population) .11964 .095015 1.2592 [.215]
D(intercept) .018672 .0047723 3.9125 [.000]
ECM(-1) -.24616 .052755 -4.6661 [.000]
The coefficient of ECM is statistically significant at 1% level and yields the correct
sign. This is important because in a different case there would not be an adjustment
back to the long-run equilibrium after a short-run shock. The equilibrium correction
coefficient implies a significant speed of adjustment to equilibrium after a shock.
Approximately 25% of disequilibria from the previous years shock converge back to
the long-run equilibrium in the current year. The impact of the movements of growth,
openness and inflation is significant in the short term as well. The signs of the short-
run dynamic impacts are similar to the corresponding ones of the long-run
equilibrium. Once again, the movements of financial development and population donot affect income inequality.
6. Control of empirical results
ARDL approach with alternative inequality measures
In this section the ARDL approach for cointegration is applied for alternative
inequality measures. The aim is to verify if the empirical findings hold for other
proxies of income inequality. The ARDL procedure will be tested with three top
income shares: 0,1%, 2,5% and 10%. Furthermore the approach will be applied with
three aggregate income inequality measures: Gini and Atkinson with risk aversion
parameter of 0,5 and 1,5. Gini coefficient is more sensitive in transfers around
median. A low value of inequality aversion parameter e is used when there is
sensitivity to changes at the top end of distribution and a high value is employed when
there is sensitivity for the transfers at the low end of the distribution.
All time series were tested for the order of integration with ADF and PP test. The
results4 indicate that the order of integration for all variables is one, that is I(1) for 1%
statistical significance level. As in the case of the main proxy of income inequality
(1% top income share) no variable is integrated above order one, therefore the ARDLapproach of cointegration can be implemented.
The three steps of ARDL approach to cointegration are applied for each alternative
measure.
The null hypothesis of no long relationship5 is rejected for 0,1% (tis_001) and 2,5%
(tis_025) top income share whereas it is not conclusive for 10% (tis_010) top income
share. Setting Gini coefficient and Atkinson (0,5) index as the dependent variable
seems to establish long-run relationship; the results are inconclusive for the case of
Atkinson (1,5) index.
4Results are available upon request
5Results are available upon request
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Having establish the existence of a relationship in the long term the ARDL models are
estimated. The choice of the appropriate lags has been made according to Schwarz
Bayesian Criterion (SBC). The following tables illustrate the long-run coefficients
and the short-run dynamics for the alternative inequality income proxies.
Table 10. Results for long-run coefficients and short-run dynamics
TIS ARDL
max lag
exogenous Schwarz
Bayesian
criterion
SB - Long run
C2 C3 C4 C5 C6
rgdp_pc trade credit cpir popr
Tis_001 2 C (1,0,0,0,1,0) -.0010888 .024455 no -.051780 no
sig1 sig5 no sig1 no
Tis_025 3 C (1,3,0,0,0,0) -.0049202 .16233 no -.29034 no
sig5 sig5 no sig1 no
Tis_10 2 C (1,1,0,0,0,0) no no no no no
TIS ARDL
max lag
exogenous Schwarz
Bayesian
criterion
SB - Short run
C2 C3 C4 C5 C6 ECM
rgdp_pc trade credit cpir popr
Tis_001 2 C (1,0,0,0,1,0) -.2577E-3 .0057878 no no no -.23667
sig2 sig2 no no no sig1
Tis_025 3 C (1,3,0,0,0,0) -.00492106
.036287 no -.064901 no sig5
sig2 sig1 no sig1 no sig5
Tis_10 2 C (1,1,0,0,0,0) -.013009 .058650 no -.11183 no no
sig2 sig5 no sig1 no no
Note: sig1: 1%, sig2: 2%, sig5: 5% and sig10: 10% significance.
Table 11. Results for long-run coefficients and short-run dynamicsTIS ARDL
max lag
exogenous Schwarz Bayesian
criterion
SB - Long run
C2 C3 C4 C5 C6
rgdp_pc trade credit cpir popr
GINI 3 C+T (1,0,0,2,1,2) no .15791 -.081795 -.49906 5.7475
no sig10 sig5 sig1 sig1
ATK_05 2 C+T (1,0,0,2,1,2) .0056802 .099282 -.062659 -.34511 3.7559
sig10 sig10 sig5 sig1 sig1
ATK_15 2 C+T (2,1,1,0,0,0) -.046182 no .30562 .88567 -3.9933
sig1 no sig1 sig1 sig10
TIS ARDL
max lag
exogenous Schwarz Bayesian
criterion
SB - Short run
C2 C3 C4 C5 C6 ECM
rgdp_pc trade credit cpir popr
GINI 3 C+T (1,0,0,2,1,2) no .063817 -.16262 no 2.87957
-.40414
no sig10 sig5 no sig1 sig1
ATK_05 2 C+T (1,0,0,2,1,2) .0025995 no -.13621 no 2.05868
-.45764
sig10 no sig10 no sig1 sig1
ATK_15 2 C+T (2,1,1,0,0,0) .044205 no .29075 .84259 -3.7991 -.95137
sig2 no sig1 sig1 sig10 sig1
Note: sig1: 1%, sig2: 2%, sig5: 5% and sig10: 10% significance.
The independent variables that impose a statistically significant effect on the long-run
are the same for0,1% and 2,5% top income shares. Growth, openness and inflation
influence these two upper shares, while there is no evidence for a long-runrelationship for financial development and population. The real GDP per capita, the
sum of imports and exports (as a percentage of GDP) and the rate of CPI yield a
negative, positive and negative sign correspondingly. It is noted that the same
variables are significant with the same type of relationship for the main proxy of
income inequality, that is 1% top income share. Nevertheless, none of the variables is
imposing a significant effect on the long-run for the 10% upper share. The effects of
the short-run dynamics are similar for all three top income shares. Growth, openness
6
Also coefficient with positive sign at 5%: .00446057Also coefficient with negative sign at 1%: -4.1016
8Also coefficient with negative sign at 1%: -3.4847
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and inflation is significant on the short run (with the exception of inflation for 0,1%
tis), while financial development and population is not. The signs of the coefficients
are the same as in the case of long-run equilibrium. Once again, the same variables
are significant with the same type of relationship for the 1% top income share.
The findings for the aggregate income inequality measures ofGini andAtkinson (0,5)indicate the following. On the long-run, openness, financial development, inflation
and population influence the Gini coefficient and the Atkinson (0,5), whereas growth
is statistically significant only for the Atkinson (0,5) index. The sum of imports and
exports (as a percentage of GDP), the domestic credit to private sector (as a
percentage of GDP), the rate of CPI and the growth rate of population yield a positive,
negative, negative and positive sign correspondingly. The real GDP per capita affects
positively the Atkinson (0,5) index. On the short-run, financial development and
population have an impact on both indices, while inflation is not statistically
significant. Growth affects only Atkinson (0,5) while openness affects only the Gini
coefficient. The sings of the coefficients are similar to the corresponding ones of the
long-run equilibrium. The behavior ofAtkinson (1,5) index is different. The long-run
coefficients suggest that growth, financial development and inflation have positive
impact, population has negative impact while openness does not affect the inequality
index. The short-run dynamics indicate that the statistically significant independent
variables are the same as in the case of long-run equilibrium; the regressors yield the
same sign with the exception of growth which has a positive effect on the short-run.
Comparing the aggregate income inequality measure with the 1% top income share on
the long-run certain similarities and differences are detected. Growth imposes a
positive effect on Atkinson (0,5) index, a negative effect on Atkinson (1,5) indexwhile is not significant for the Gini coefficient. The top 1% yields a negative
relationship with real GDP per capita. Openness affects positively all aggregate
measures (except Atkinson (1,5) which has no effect) and the upper share. On the
contrary, inflation affects negatively all aggregate measures (except Atkinson (1,5)
which has positive effect) and the upper share. It is reminded that financial
development and population are not related in the long-run with 1% top income share,
while the effects for aggregate income inequality measures are described above. The
comparison for the short-run dynamics indicates, also differences. Growth has a
positive effect for the two Atkinson indices, no effect for Gini coefficient and
negative effect for the 1% upper share. Openness yields no relationship with the two
Atkinson indices, while is positively related for Gini and top 1%. Inflation is
negatively related to top 1%, positively related to Atkinson (0,5) index and no related
with the other two inequality measures. It is noted that financial development and
population are not related in the short-run with 1% top income share.
Detecting the different (opposite) impact that growth exerts on the two Atkinson
indices due to the variation of the inequality aversion parameter we estimate the
ARDL model for the lower part of the upper decile. The construction of the tis_90_95
is the result of the subtraction of the 5% top income share from the 10% upper share,
that is tis_90_95=tis_10-tis_05. This time series is integrated of order one and the
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results from Wald restrictions implies a long run relationship. Applying the procedure
for the selection of the appropriate lags, the ARDL model is
Table 12. Results for long-run coefficients and short-run dynamicsTIS ARDL max
lag
exogenous Schwarz Bayesian
criterion
SB - Long run
C2 C3 C4 C5 C6
rgdp_pc trade credit cpir popr
tis_90_95 2 C (2,0,0,0,0,0) .0047820 no -.041226 no no
sig5 no sig10 no no
Note: sig1: 1%, sig2: 2%, sig5: 5% and sig10: 10% significance
The effect of the growth on the lower part of the high income class is positive and
statistically significant. This is consistent with the estimations of the Atkinson index
with low inequality aversion parameters (e=0,5) which is sensitive with transfers in
the upper part of the distribution.
Supplementary econometric approach: VAR and VECM
This section describes the cointegration method in a Vector Autoregression (VAR)
framework. The aim is to control the robustness of the results of the ARDL approach.
The mathematical representation of a VAR is:
where is a k vector of endogenous variables, is a d vector of exogenousvariables and B are matrices of coefficients to be estimated, and is avector of innovations that may be contemporaneously correlated but are uncorrelated
with their own lagged values and uncorrelated with all with all of the right-hand side
variables.
In order to proceed to cointegration analysis two assumptions are to be fulfilled
- The variables are non-stationary
- The variables are integrated in the same order
Engel and Granger (1987) pointed out that a linear combination of two or more non-
stationary series may be stationary. If such a stationary linear combination exists, thenon-stationary series are said to be cointegrated. The stationary linear combination is
called the cointegrated equation and may be interpreted as a long-run equilibrium
relationship among the variables.
Two common tests for the identification of a long-run relationship is the Engel-
Granger residual based test and the Johansen-Juselius test. Engel and Granger (1987)
identify that the cointegrated variables must have an Error Correction Model (ECM)
representation. In this study, the cointegration analysis according to Johansen (1991)
(1995) is applied.
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The typical VAR can be rewritten as
Where
Grangers representation theorem asserts that if the coefficient matrix has a reduced
rank r
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Table 13. Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.610683 53.66299 40.17493 0.0013
At most 1 0.121581 8.381636 24.27596 0.9371
At most 2 0.042436 2.159334 12.32090 0.9376
At most 3 0.001622 0.077925 4.129906 0.8188
Table 14. Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.610683 45.28135 24.15921 0.0000
At most 1 0.121581 6.222303 17.79730 0.8799
At most 2 0.042436 2.081409 11.22480 0.9139
At most 3 0.001622 0.077925 4.129906 0.8188
The empirical results indicate that one cointegration equation exists. This is an
evidence of long-run relationship between aggregate income inequality, growth, trade
and inflation in Greece during the investigated period. Having detected cointegration
for the variables we proceed to the estimation of the restricted VAR, that is the
estimation of Vector Error Correction Model.
The estimated long-run function is reported below.
Table 15. Long-run estimates of the VAR model
Variable Income inequality Growth Trade Inflation
Proxy tis_01 rgdp_pc_r (import+export) % GDP cpi_r
Estimate -0.735910 -0.059285 -0.051437
SE (0.04606) (0.00805) (0.02520)
t-statistic [-15.9777] [-7.36595] [-2.04077]
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The VECM is presented in the following table
Table 16. VECM estimates of the VAR model
(Dependent: d(tis_01)) Coefficient Std. Error t-Statistic Prob.
ECM -0.064846 0.027889 -2.325119 0.0249
D(TIS_01(-1)) 0.369398 0.133822 2.760375 0.0085
D(RGDP_PC_R(-1)) -0.025430 0.013771 -1.846620 0.0717
D(TRADE(-1)) -0.001098 0.011198 -0.098019 0.9224
D(CPI_R(-1)) -0.020446 0.010857 -1.883184 0.0665
The diagnostic tests for the VECM are included in the following table
Table 17. Diagnostic tests for VECM
Fitting R-square 0.216492
Normality Jarque-Bera 3.966050 Probability 0.137652
Autocorrelation Durbin-Watson 2.033106
Breusch-Godfrey 2.962735 Prob. Chi-Square(2) 0.227327Heteroscedasticity ARCH Test 0.265023 Prob. Chi-Square(1) 0.606690
White Test 10.27782 Prob. Chi-Square(16) 0.851723
Table 16 presents the short-run dynamic adjustment of all the variables. The
significant and negative error correction term (ECM) is an indication of the existence
of stable long-run relationship between the variables. The feedback coefficient shows
that 6,5% of disequilibrium on average is corrected in the next years.
The diagnostic tests for the VECM are presented in table 17. The JarqueBera test
indicates normal distribution of the residuals while the model does not suffer fromautocorrelation. Moreover, there is no evidence of heteroscedasticity. Nevertheless,
the value of r-square is not very high.
The long-run estimates indicate that the 1 % top income share is related with negative
sign with all the independent variables, that is growth, trade and inflation. In all cases
the coefficients are statistically significant.
These results are consistent to a significant degree with the results of the ARDL
approach. In the ARDL framework the 1% top income share is associated with these
independent variables (growth, trade, inflation) in the long-run. The ECM term of the
short-run dynamics is also statistically significant. Both growth and inflation are
associated negatively with income inequality. The only difference in the ARDL
approach is that trade imposes positive effect on the 1 % top income share.
7. Conclusions
The goal of the paper is the examination of the relationship between income
inequality and macroeconomic activity. The macroeconomic indicators of most
interest are the economic growth and the openness of the economy. Other control
variables such as financial development, inflation and the growth of population wereincorporated in the econometric modeling.
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This study employed the Autoregressive Distributed Lag (ARDL) (or bounds testing)
cointegration procedure for the empirical analysis of the long-run relationships and
dynamic interacting among the variables of interest. This procedure was popularized
by Pesaran and Pesaran (1997), Pesaran and Smith (1998), Pesaran and Shin (1999)
and Pesaran et al (2001).This approach consists of three steps. The first step in the ARDL bounds testing
approach is to examine for the existence of a long-run relationship among the
variables of interest by conducting an F-test for the joint significance of the
coefficients of the lagged levels of the variables. The estimated F-statistic with Wald
restrictions is then compared with the critical values provided by Pesaran (2001). In
the second step, once cointegration is established the appropriate ARDL long-run
model is estimated. This step involves selecting the orders of the ARDL model in the
variables using Schwarz Bayesian criterion. The choice of the appropriate lags
according to Akaike information criterion has been, also, conducted. In the third and
final step, the short-run dynamic parameters have been obtained by the estimation of
an error correction model associated with the long-run estimates.
The empirical findings for the relationship of income inequality and macroeconomic
activity suggest the following. Income inequality (estimated applying 1% top income
share as a proxy) is the dependent variable. Growth seems to relate with income
inequality. The real GDP per capita has an impact on the long term and the
relationship is negative. A significant impact, also, yields the openness of economy.
Trade as a percentage of GDP influences positively top income shares. Like the two
previous independent variables, inflation, expressed as the growth rate of CPI, is
statistical significant and it yields negative sign. On the contrary the pattern offinancial development (domestic credit to private sector as percentage of GDP) and
population (growth rate of population) does not affect income inequality in the long
run; their coefficients do not differ statistically from zero.
The coefficient of ECM is statistically significant at 1% level and yields the correct
sign. This is important because in a different case there would not be an adjustment
back to the long-run equilibrium after a short-run shock. The equilibrium correction
coefficient implies a significant speed of adjustment to equilibrium after a shock.
Approximately 25% of disequilibria from the previous years shock converge back to
the long-run equilibrium in the current year. The impact of the movements of growth,
openness and inflation is significant in the short term as well. The signs of the short-
run dynamic impacts are similar to the corresponding ones of the long-run
equilibrium. Once again, the movements of financial development and population do
not affect income inequality.
The VAR-approach of cointegration analysis (Johansen test) was implemented as a
supplementary econometric methodology to control the robustness of the results. The
Johansen test for cointegration was applied for the variables that were found to have a
long-run relationship with the ARDL approach: 1% Top Income Share, real GDP per
capita growth rate10, the sum of imports and exports as a percentage of GDP and CPI
10In ARDL approach this proxy was real GDP per capita
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rate. The empirical findings are consistent to a significant degree with the results of
the ARDL approach. The Johansen test indicates one cointegration relationship for all
four variables (1% tis, growth, trade, inflation) similarly to the ARDL framework in
the long-run. The ECM term of the short-run dynamics is also statistically significant.
Both growth and inflation are associated negatively with income inequality. The onlydifference in the ARDL approach is that trade imposes positive effect on the 1 % top
income share.
The ARDL approach for cointegration was applied for alternative inequality
measures. The aim was to verify if the empirical findings hold for other proxies of
income inequality. The ARDL procedure was tested with three top income shares
(0,01%, 2,5% and 10%) and with three aggregate income inequality measures (Gini
and Atkinson with risk aversion parameter of 0,5 and 1,5). Gini coefficient is more
sensitive in transfers around median. A low value of inequality aversion parameter e
is used when there is sensitivity to changes at the top end of distribution and a high
value is employed when there is sensitivity for the transfers at the low end of the
distribution.
The empirical findings in the long-run equilibrium suggest that growth is negatively
associated with the very upper income shares (0,01%, 1% and 2,5%) but no with top
10%. Moreover, growth imposes a positive effect on Atkinson (0,5) index, a negative
effect on Atkinson (1,5) index while is not significant for the Gini coefficient. There
are two explanations for these results; the fist has to do with the underlying properties
of the indices and the second with the certain limitations of tax data for measuring
inequality in all distribution, since tax data are truncated below a threshold level of
income. Moreover, the evidence indicate that the lower part of the very high incomeclass (tis_90_95) is related positively with growth. Therefore, growth influences in
different patterns the various parts of the income distribution. The very top parts are
affected negatively, while the lower parts of high income class and upper parts of
middle class are related positively with economic growth. On the contrary, it seems to
exist a negative relationship with lower sectors of the distribution. Growth does not
seem to pose an impact on the Gini coefficient, which is more sensitive in transfers
around median, implying that the inequality is unaffected for the main parts of the
middle class. It should be noted that the conclusions for the specific parts of the
income distribution are derived according to the properties of the aggregate inequality
indices since there are no estimations for the actual shares of income; therefore these
limitations should be taken into consideration. These results are partly consistent with
the findings of Voitchovsky (2005) who has found evidence that while top-end
inequality is positively associated with growth, bottom-end inequality may be
negatively related to growth.
The effects ofopenness of economy in the long-run are clearer. In almost all cases the
impact is positive; except in 10% upper share and Atkinson (1,5) where the long-run
relationship does not seem to hold. The results are similar to the findings of Bergh and
Nilsson (2010), Barro (2000), Hurrell and Woods (2000) and Carter (2007).
The empirical findings for inflation suggest that income inequality is affected
negatively. Almost all proxies imply this type of relationship; once again the
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exception is the 10% top income share (no relationship) and Atkinson (1,5) (positive
relationship). The results are consistent with the findings of Easterly and Fisher
(2001) and Beck et al. (2007).
The empirical results forfinancial developmentandpopulation are contradictory. The
main proxy of income inequality (1% upper share) and the alternative three topincome shares does not relate at the long run. Nevertheless, the aggregate income
inequality measures indicate a relationship. Credit affects negatively the Gini
coefficient and Atkinson (0,5) and positively the Atkinson (1,5). The effect is reverse
for the population; positive impact for the Gini coefficient and Atkinson (0,5) and
negative for the Atkinson (1,5) index.
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