EuroEconomica, Vol 33, No 1 (2014)
EuroEconomica
Issue 1(33)/2014 ISSN: 15828859
The economic convergence in European Union based on concentration and entropy approach
Mihaela SIMIONESCU^{1}
^{1}Institute for Economic Forecasting, Romanian Academy, mihaela.simionescu@ipe.ro
Abstract. The main objective of this study is to assess the economic convergence in European Union (EU28) using a frequent approach in literature based on Gini coefficients, Lorernz curve and Theil’s index. On the other hand, the entropy approach is quite new in the convergence field, but the results are relevant. The assumption of economic convergence is confirmed for EU28 in 20032012. According to Gini coefficient values the degree of concentration has decreased on the analyzed period, but there is an insignificant decrease in 2012 compared to 2003. The value of Theil’s index also confirmed the convergence. In the convergence analysis the increase in entropy translates into an emphasis of divergence process. In 2012 the entropy is lower than the value of entropy in 2003, the convergence being more relevant in 2012 compared to 2003.
Keywords: economic convergence, Gini coefficient, Theil’s index, Lorenz curve .
1 Introduction
The interest for economic convergence analysis increased in the last year mainly in the context of new integrations in the European Union. There are many ways to assess the degree of convergence, the approach based on Lorenz curve being considered relevant for many researchers, even if there is not a unique indicator to express the convergence intensity.
This paper brings us novelty the use of entropy indicators for evaluating the degree of convergence. Moreover, the convergence process refers to the countries of European Union in its extended form (EU28). The studies elaborated till now refer to EU27 or to other reduced forms from the European territory.
The structure of the paper follows a rational demarche: after the brief introduction, a short retrospective in the literature is made, giving also some theoretical basis. The application refers to the convergence in EU28 and the methods used for measuring the economic convergence are based on Lorenz curve, Gini coefficients, Theil’s index and entropy indicators.
2 The measurement of economic convergence in literature
The economic convergence is characterized by the decrease of the development gap between less developed economies compared to developed countries. The process is very well analyzed in the economic literature, the interest for convergence becoming higher in the context of the extension of the European Union in the last 10 years (Angeloni, Flad, Mongelli, 2005).
There is not still a unique indicator for measuring the degree of convergence process, but there are indicators that reflect the disparities between regions or countries: variance, coefficient of variance, Gini coefficient, Theil index, etc. (Castro, 2004). Theil index is an extensive indicator used to measure the inequality, being decomposable, but also additive.
(Barro & SalaiMartin, 1995) considered the theoretical background for studying the convergence of contributions to inequality. This approach was developed by (Islam, 1995) and (Nerlove, 1999) for panel analysis. The convergence test of inequalities based on the variation of Gini index was proposed by Bénabou (1996) and developed by Ravallion (2003). (Antonescu, 2012) used the spatial methods to measure the regional convergence in European Union and Romania, among the methods being the computation of Lorenz curve and Gini coefficients.
(Geppert & Stephan, 2008) assessed the overall convergence and the spatial concentration in the European Union using methods like Markov chain, crosssectional regressions and Kernel density estimation. The concentration of economic activities increased the disparities between the EU countries. (El ouardighi & SomunKapetanovic, 2009) obtained a weak convergence of contributions to inequality when they analyzed the international income inequality of 32 countries from Europe during 19892002.
(Albu, 2012a) proved that there is a general tendency of structural convergence in the EU during 20002011 using the Lorenz curve. Even if the actual economic crisis has a negative effect on convergence process, (Albu, 2012b) used the Lorenz curve and Gini coefficients to show that there is still significant convergence across EU countries.
(Ville, 2013) linked the convergence with the evolution in income distribution measured by Gini coefficient. In general, there was not found a correlation between convergence and changes in income repartition during 2000–2011.
(Buturac, 2013) confirmed the economic convergence in SouthEastern European countries during 20002010. The author used Theil’s index as inequality measure to analyze the macroeconomic convergence.
(Weatherspoon et al., 2003) used the Theil’s index to assess the economic convergence in OECD and then the computed indices for industrial employment, GDP per capita, government and investment expenditures were made dynamic by using pairwise cointegration and Johansen’s I(2) multicointegration tests.
(Maasoumi & Wang, 2008) proposed a new concept of convergence that takes into account the entropy measure described by (Granger et al., 2004) for assessing economic convergence in China.
Concentration is actually perceived as an accumulation more and more significant of means (incomes, real estate etc.) for a small number of holders, expressing an inequality state, a divergence. In the convergence economic approach, in a group of countries a convergence process in relation to income (GDP, output), if the proportion of each country in the population group has a closer and closer correspondent as measure in outcome proportion of that country in the overall outcomes of group. The concentration indicators close to zero show the equilibrium state or the proportionality between resources (population, surface, number of organizations etc.) and results (income, production, access to funds etc.) registered by group’s components. A simple indicator is the Gini indicator:
Equation 1 Formula for Gini coefficient
_{ } element’s weight (country, region i)
Equation 2 Formula for the weight
The maximal value of this coefficient is 1; the minimum value of the coefficient is _{ } which is obviously different from zero. The GiniStruck coefficient is between 0 and 1:
Equation 3 Formula for GiniStruck coefficient
Onicescu informational energy that is also known as Herfindahl coefficient is computed as:
Equation 4 Formula for Herfindahl coefficient
Each coefficient indicates a higher concentration if the value increases towards the superior limit. Lorenz curve refers to concentration and it is a useful tool in the economic analysis, showing the process intensity, but also a possibility of measuring the concentration degree. The procedure supposes the parallel analysis of the weights’ location regarding the two correlated variables.
In the convergence analysis, the concentration indicators provide limited information, these being defined to express states that are complementary to convergence. A comparative analysis of concentration coefficients calculated for successive periods could show indirectly a closer situation of convergence. This kind of situation could be confirmed by the slow diminish of the concentration level towards zero. In a direct way, the concentration indicators show how far we are of equality situation, of a proportional distribution of the economic results in the analyzed countries.
The convergence process in a group of spatial units (regions, countries) has a correspondent in physics, given by the entropy. It tends to increase all the time (it converges towards an equilibrium state, according to the second law of thermodynamics). The convergence measurement is somehow related to the way of getting a numerical measure of the indetermination degree (entropy). The level of development, synthetically measured by GDP per capita in each country from EU is assimilated to the independent realizations of a random variable _{ }. The Theils’ index is based on the additive entropy and on the reference unit given by the decimal logarithm base.
Equation 5 Formula for Theil’s index
(Dickey, 2001) proposed another version that takes into account the existence of more groups of spatial units that compose the entire region:
Equation 6 Formula for modified Theil’s index
_{ } the Theil’s index for group k
_{ } share of variable x (GDP per capita) to group k in the overall groups
If Theils’ index decreases towards zero, the divergence degree in the sense of diversity decreases, too. So, the countries converge to close values regarding the analyzed variable. This index expresses in a synthetic way a state of the system that could be correlated with the convergence process development. Moreover, the Theil’s index allows us to assess the divergence (differences in levels) in the case of a structured entire on groups of countries, regions etc. There are few limits of this indicator like: the all elements are considered as a closed system, the countries are independent from the economic point of view, the finish of the convergence process conducts to a “out of stock” system if the energy transfer is not possible any more.
3 The measurement of economic convergence in EU28
For measuring the degree of concentration and its evolution in time in a first stage the countries of EU28 were grouped according to GDP per capita in 2003 (reference base). These groups were maintained in 2012 for ensuring the comparability and for the lack of significant change in homogeneity in each group. Only the intervals’ limits changed. In the following table we mention the group number for the interval’ limits represented in 2003 the values (GDP per capita). The number of countries, weights for GDP, but also population in 2003 and 2012 are included in the table columns. The weights of GDP/capita for 2003 were kept.
Table 1 Weights for population and GDP per capita in 2003 and 2012
No. of group 
Number of countries 
GDP per capita weights in 2003 
Population weights in 2003 
GDP per capita cumulative weights in 2003 
Population cumulative weights in 2003 
GDP per capita weights in 2012 
Population weights in 2012 
GDP per capita cumulative weights in 2012 
Population cumulative weights in 2012 
1: Less than 9001 
2 
2.46% 
6.02% 
2.46% 
6.02% 
3.55% 
5.46% 
3.55% 
5.46% 
2: 900113000 
7 
14.06% 
13.31% 
16.53% 
19.34% 
17.47% 
12.84% 
21.01% 
18.29% 
3: 1300117000 
3 
9.05% 
4.30% 
25.57% 
23.64% 
8.87% 
4.27% 
29.88% 
22.56% 
4: More than 17000 
16 
74.43% 
76.37% 
100% 
100% 
70.11% 
77.43% 
100% 
100% 
2.46% of the GDP/capita is produced by only 6.02% of the EU28 population. but this situation is compensated by the fact that 76.37% of the EU population in 2012 produced 74.43% of the total production. In 3.55% of the GDP/capita was obtained by 5.46% of the EU28 inhabitants. while 77.43% of the population produced 70.11% of the GDP/capita.
The Gini coefficient in weighted variant was computed. The computations for concentration and entropy indicators were made in Wessa free statistical software.
Table 2 Concentration and entropy indicators in 2003 and 2012
Indicator 
2003 
2012 
2.691537 
2.686573 

3.332205 
3.332205 

0.807735 
0.806245 

0.067777 
0.068114 

0.092268 
0.092292 

0.058648 
0.058673 

0.600281 
0.601846 

0.622514 
0.624137 
The entropy is a measure of information uncertainty, a higher value of it implying a higher degree of uncertainty. In the convergence analysis this increase in uncertainty translates into an emphasis of divergence process. In 2012 the entropy is 2.6865, which is lower than the value of entropy in 2003 (2.6915). This means that the convergence process is a little more obvious in 2012 compared to 2003. For Gini coefficient a higher value was registered in 2012, even if the differences between indicator values are insignificant. The concentration coefficient indicates a slow increase in the degree of concentration in 2012 with respect to the situation presented in 2003.
The study of the absolute and relative indicators of convergence and entropy for each country does not allow us to draw a conclusion regarding the convergence for overall European Union.
Table 3 Absolute and relative indicators for concentration and entropy in 2003 and 2012
Category 
2003 
2012 


Elements (Absolute) 
Elements (Relative) 
Entropy (Absolute) 
Entropy (Relative) 
Elements (Absolute) 
Elements (Relative) 
Entropy (Absolute) 
Entropy (Relative) 
1 
1.035584e+7 
0.021168 
0.081607 
0.030320 
1.109485e+7 
0.022070 
0.084165 
0.031328 
2 
7.845841e+6 
0.016037 
0.066279 
0.024625 
7.327224e+6 
0.014575 
0.061631 
0.022940 
3 
1.019265e+7 
0.020834 
0.080652 
0.029965 
1.050544e+7 
0.020898 
0.080834 
0.030088 
4 
5.383507e+6 
0.011004 
0.049623 
0.018437 
5.580516e+6 
0.011101 
0.049962 
0.018597 
5 
8.253668e+7 
0.168708 
0.300230 
0.111546 
8.032790e+7 
0.159789 
0.293037 
0.109075 
6 
1.364678e+6 
0.002789 
0.016407 
0.006096 
1.333788e+6 
0.002653 
0.015739 
0.005858 
7 
3.964191e+6 
0.008103 
0.039020 
0.014497 
4.582707e+6 
0.009116 
0.042824 
0.015940 
8 
1.100638e+7 
0.022497 
0.085363 
0.031715 
1.112303e+7 
0.022126 
0.084322 
0.031387 
9 
4.182784e+7 
0.085497 
0.210261 
0.078119 
4.681822e+7 
0.093131 
0.221070 
0.082287 
10 
6.010184e+7 
0.122850 
0.257591 
0.095704 
6.340919e+7 
0.126134 
0.261149 
0.097205 
11 
4.305384e+6 
0.008800 
0.041652 
0.015475 
4.275984e+6 
0.008506 
0.040547 
0.015093 
12 
5.732107e+7 
0.117166 
0.251223 
0.093338 
5.939421e+7 
0.118147 
0.252342 
0.093927 
13 
713720.000000 
0.001459 
0.009527 
0.003539 
862011.000000 
0.001715 
0.010920 
0.004065 
14 
2.299390e+6 
0.004700 
0.025193 
0.009360 
2.044813e+6 
0.004068 
0.022391 
0.008334 
15 
3.431497e+6 
0.007014 
0.034789 
0.012925 
3.003641e+6 
0.005975 
0.030592 
0.011387 
16 
448300.000000 
0.000916 
0.006410 
0.002382 
524853.000000 
0.001044 
0.007167 
0.002668 
17 
1.014236e+7 
0.020731 
0.080357 
0.029855 
9.931925e+6 
0.019757 
0.077530 
0.028858 
18 
397296.000000 
0.000812 
0.005779 
0.002147 
417546.000000 
0.000831 
0.005892 
0.002193 
19 
1.619257e+7 
0.033098 
0.112808 
0.041912 
1.673035e+7 
0.033280 
0.113246 
0.042152 
20 
8.100273e+6 
0.016557 
0.067900 
0.025227 
8.408121e+6 
0.016726 
0.068421 
0.025468 
21 
3.821853e+7 
0.078120 
0.199168 
0.073998 
3.853845e+7 
0.076661 
0.196893 
0.073288 
22 
1.044459e+7 
0.021349 
0.082125 
0.030512 
1.054240e+7 
0.020971 
0.081045 
0.030167 
23 
2.162751e+7 
0.044207 
0.137877 
0.051226 
2.009600e+7 
0.039975 
0.128700 
0.047905 
24 
1.995033e+6 
0.004078 
0.022437 
0.008336 
2.055496e+6 
0.004089 
0.022486 
0.008370 
25 
5.374873e+6 
0.010986 
0.049561 
0.018414 
5.404322e+6 
0.010750 
0.048729 
0.018138 
26 
5.206295e+6 
0.010642 
0.048345 
0.017962 
5.401267e+6 
0.010744 
0.048708 
0.018130 
27 
8.940788e+6 
0.018275 
0.073141 
0.027175 
9.482855e+6 
0.018863 
0.074898 
0.027879 
28 
5.949020e+7 
0.121600 
0.256213 
0.095192 
6.349535e+7 
0.126306 
0.261333 
0.097274 
The cumulated indicators for concentration and entropy show that in general the convergence process emphasized as tendency in 2012 compared to 2003. However, for few countries an obvious regression of the convergence was observed during 20032012.
Table 4 Absolute and relative cumulated indicators for concentration and entropy in 2003 and 2012
Category 
2003 
2012 


Elements (Absolute Cumulated) 
Elements (Relative Cumulated) 
Entropy (Absolute Cumulated) 
Entropy (Relative Cumulated) 
Elements (Absolute Cumulated) 
Elements (Relative Cumulated) 
Entropy (Absolute Cumulated) 
Entropy (Relative Cumulated) 
1 
1.035584e+7 
0.021168 
0.081607 
0.030320 
1.109485e+7 
0.022070 
0.084165 
0.031328 
2 
1.820168e+7 
0.037205 
0.147886 
0.054945 
1.842207e+7 
0.036645 
0.145796 
0.054268 
3 
2.839433e+7 
0.058039 
0.228539 
0.084910 
2.892752e+7 
0.057543 
0.226630 
0.084356 
4 
3.377784e+7 
0.069043 
0.278161 
0.103347 
3.450804e+7 
0.068644 
0.276592 
0.102953 
5 
1.163145e+8 
0.237751 
0.578391 
0.214893 
1.148359e+8 
0.228433 
0.569629 
0.212028 
6 
1.176792e+8 
0.240540 
0.594799 
0.220988 
1.161697e+8 
0.231086 
0.585367 
0.217886 
7 
1.216434e+8 
0.248643 
0.633819 
0.235486 
1.207524e+8 
0.240202 
0.628192 
0.233826 
8 
1.326498e+8 
0.271140 
0.719182 
0.267201 
1.318755e+8 
0.262328 
0.712514 
0.265213 
9 
1.744776e+8 
0.356638 
0.929443 
0.345320 
1.786937e+8 
0.355459 
0.933584 
0.347500 
10 
2.345794e+8 
0.479488 
1.187034 
0.441025 
2.421029e+8 
0.481593 
1.194733 
0.444705 
11 
2.388848e+8 
0.488288 
1.228685 
0.456500 
2.463789e+8 
0.490099 
1.235280 
0.459798 
12 
2.962059e+8 
0.605454 
1.479909 
0.549838 
3.057731e+8 
0.608246 
1.487622 
0.553725 
13 
2.969196e+8 
0.606913 
1.489435 
0.553377 
3.066351e+8 
0.609961 
1.498543 
0.557790 
14 
2.992190e+8 
0.611613 
1.514628 
0.562737 
3.086799e+8 
0.614029 
1.520933 
0.566124 
15 
3.026505e+8 
0.618627 
1.549417 
0.575663 
3.116835e+8 
0.620004 
1.551526 
0.577511 
16 
3.030988e+8 
0.619544 
1.555827 
0.578044 
3.122084e+8 
0.621048 
1.558693 
0.580179 
17 
3.132412e+8 
0.640275 
1.636184 
0.607899 
3.221403e+8 
0.640804 
1.636223 
0.609037 
18 
3.136385e+8 
0.641087 
1.641962 
0.610046 
3.225579e+8 
0.641635 
1.642115 
0.611230 
19 
3.298310e+8 
0.674185 
1.754770 
0.651958 
3.392882e+8 
0.674915 
1.755360 
0.653383 
20 
3.379313e+8 
0.690742 
1.822670 
0.677186 
3.476963e+8 
0.691641 
1.823781 
0.678850 
21 
3.761498e+8 
0.768862 
2.021838 
0.751183 
3.862348e+8 
0.768302 
2.020675 
0.752138 
22 
3.865944e+8 
0.790211 
2.103962 
0.781695 
3.967772e+8 
0.789273 
2.101720 
0.782305 
23 
4.082219e+8 
0.834419 
2.241839 
0.832921 
4.168732e+8 
0.829248 
2.230419 
0.830210 
24 
4.102170e+8 
0.838497 
2.264276 
0.841258 
4.189287e+8 
0.833337 
2.252906 
0.838580 
25 
4.155918e+8 
0.849483 
2.313837 
0.859671 
4.243330e+8 
0.844087 
2.301635 
0.856718 
26 
4.207981e+8 
0.860125 
2.362182 
0.877633 
4.297342e+8 
0.854831 
2.350343 
0.874848 
27 
4.297389e+8 
0.878400 
2.435324 
0.904808 
4.392171e+8 
0.873694 
2.425241 
0.902726 
28 
4.892291e+8 
1.000000 
2.691537 
1.000000 
5.027125e+8 
1.000000 
2.686573 
1.000000 
According to Gini coefficient values the degree of concentration has decreased but with an insignificant decrease in 2012 compared to 2003 (a value of 0.601846 in 2012 compared to 0.600281 in 2003). Lorenz curve indicates a lower inequality of the wealth distribution in 2012 compared to 2003.
Table 5 Lorenz curve in 2003 and 2012
Cumulative % of population 
Cumulative % of variable (2003) 
Cumulative % of variable (2012) 


Expected 
Observed 
Expected 
Observed 
0% 
0.000000 
0.000010 
0.000000 
0.000010 
4% 
0.035714 
0.000812 
0.035714 
0.000831 
7% 
0.071429 
0.001728 
0.071429 
0.001875 
11% 
0.107143 
0.003187 
0.107143 
0.003589 
14% 
0.142857 
0.005977 
0.142857 
0.006243 
18% 
0.178571 
0.010055 
0.178571 
0.010310 
21% 
0.214286 
0.014755 
0.214286 
0.014399 
25% 
0.250000 
0.021769 
0.250000 
0.020374 
29% 
0.285714 
0.029872 
0.285714 
0.028880 
32% 
0.321429 
0.038672 
0.321429 
0.037996 
36% 
0.357143 
0.049314 
0.357143 
0.048740 
39% 
0.392857 
0.060300 
0.392857 
0.059490 
43% 
0.428571 
0.071304 
0.428571 
0.070591 
46% 
0.464286 
0.087341 
0.464286 
0.085166 
50% 
0.500000 
0.103899 
0.500000 
0.101892 
54% 
0.535714 
0.122174 
0.535714 
0.120755 
57% 
0.571429 
0.142905 
0.571429 
0.140512 
61% 
0.607143 
0.163739 
0.607143 
0.161409 
64% 
0.642857 
0.184907 
0.642857 
0.182380 
68% 
0.678571 
0.206256 
0.678571 
0.204450 
71% 
0.714286 
0.228754 
0.714286 
0.226576 
75% 
0.750000 
0.261852 
0.750000 
0.259857 
79% 
0.785714 
0.306059 
0.785714 
0.299832 
82% 
0.821429 
0.384179 
0.821429 
0.376493 
86% 
0.857143 
0.469676 
0.857143 
0.469624 
89% 
0.892857 
0.586842 
0.892857 
0.587771 
93% 
0.928571 
0.708442 
0.928571 
0.713906 
96% 
0.964286 
0.831292 
0.964286 
0.840211 
100% 
1.000000 
1.000000 
1.000000 
1.000000 
Figure 1 Lorenz curve in EU28 for 2003
Figure 2 Entropy of GDP per capita in EU28 in 2003
Figure 3 Lorenz curve in EU28 for 2012
Figure 4 Entropy of GDP per capita in EU28 in 2012
In order to determine the Theil’s index the GDP per capita of EU countries was used. For 2003 we got the value of 175.3 while for 2012 the Theil’s index is 181.2. fact that indicates convergence from the point of view given by GDP per capita.
Table 6 Standard deviations and coefficients of variation in 2011 and 2012
Year 
Standard deviation 
Coefficient of variation 
2011 
0.047565438 
5.30% 
2012 
0.041368457 
4.79% 
The standard deviation in 2011 is greater than the value in 2012. Moreover, the degree of variation decreased in 2012 compared to 2011, fact that indicates the economic convergence of the EU countries. A relationship of dependence is considered between the rate of growth in certain interval and the level of development of that particular region. The relationship is observable for more regions at a certain reference time t for a specific degree of development.
The convergence perspective brings that fact that the process of development levels closeness between regions is under hypothesis. According to Solow. the assumption of high rates of growth for the low developed countries is based on statistical data and on the economic theory.
4 Conclusions
The assumption of economic convergence is confirmed for EU28 when concentration and entropy indicators are used. According to Gini coefficient values the degree of concentration has decreased but with an insignificant decrease in 2012 compared to 2003. The value of Theil’s index for GDP per capita shows advancement in convergence process in 2012 with respect to 2003. The research could be continued by analyzing the economic convergence in EU28 from other perspectives, including the use of tools offered by the spatial econometrics.
5 References
Albu, L.L. (2012). Structural Convergence in European Union. Annals of the „Constantin Brâncuşi” University of Târgu Jiu, Economy Series, Issue 4/2012, 215.
Albu, L.L. (2012). The Convergence Process in the EU Estimated by Gini Coefficients. Romanian Journal of Economic Forecasting, 4, 516.
Angeloni, I., Flad, M., Mongelli, F. (2005). Economic and Monetary Integration of the New Member States: Helping to Chart the Route. European Central Bank Occasional Paper No. 36, 3045.
Antonescu, D. (2012). Measuring regional convergence an application to the European Union and Romania, Revista Economica. 2012, vol. Supplement, issue 1, 4659.
Barro, R. J., & SalaiMartin, X. (1995). Economic growth. London: The first MIT Press.
Bénabou, R. (1996). Inequality and Growth, In Bernanke, B. S. and Rotemberg, J. (ed), National Bureau of Economic Research Macroeconomics Annual. Cambridge: MIT Press,1174.
Buturac, G. (2013). Beyond the global recession: mutual trade and economic convergence. Ekonomski Pregled, 64 (4), 303326.
Castro, V. J. (2004). Indicators of Real Economic Convergence. A Primer. United Nations University, UNUCRIS EWorking Papers, w2004/2, 6067.
Dickey H. (2001). Regional earnings in Great Britain: A decomposition analysis. Regional Studies, 7, 5869.
El ouardighi, J. & SomunKapetanovic, R. (2009), Income inequality convergence in the development of European countries. Review of Applied Economics, Vol. 5, No. 12, (JanuaryDecember 2009)
Granger, C., Maasoumi, E. & Racine, J.C. (2004). A dependence metric for possibly nonlinear processes. Journal of Time Series Analysis 25, 649–669.
Islam, N. (1995). Growth Empirics: A Panel Data Approach. Quarterly Journal of Economics, 110: 11271170.
Maasoumi, E., & Wang, L. (2008). Economic Reform, Growth and Convergence in China. Econometrics Journal, 2008, vol. 11, issue 1, 128154.
Kurt, G., & Andreas S. 2008. Regional disparities in the European Union: Convergence and agglomeration, Papers in Regional Science, Wiley Blackwell, vol. 87(2), 193217.
Nerlove, M. (1999). Properties of Alternative Estimators of Dynamic Panel Models: An Empirical Analysis of Crosscountry Data for the Study of Economic Growth”, In Hsiao, C., Lahiri, K., Lee, LF. and Pesaran, H.M. (ed), Analysis of Panel and Limited Dependent Variables Models, Cambridge University Press, Cambridge, 136170.
Ravallion, M. (2003). Inequality Convergence. Economics Letters, 80, 351356.
Ville, K. (2013). Convergence, income distribution, and the economic crisis in Europe. ETLA Working Papers, no.4, 7896.
Weatherspoon, D., Seale, J., &Moss, C. B. (2003). Extending Theil's Inequality Index: Addressing Dynamic Convergence in the OECD. Journal of Agricultural and Applied Economics, 35, 189197.
Wessa.
P. (2014). Free Statistics Software. Office for Research Development
and Education.
version 1.1.23r7. Retrieved
from
http://www.wessa.net/
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