income inequality and macroeconomic activity in greece

7/28/2019 Income inequality and macroeconomic activity in Greece

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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


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


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


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


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


criterion

SB - Short run

C2 C3 C4 C5 C6 ECM


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


criterion

SB - Long run

C2 C3 C4 C5 C6


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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