INEQUALITY IN EDUCATION IN THE MENA REGION: A MACROECONOMETRIC INVESTIGATION USING NORMATIVE INDICATORS IBOURK, Aomar^{1 } AMAGHOUSS, Jabrane^{2} _____________________________________________________________________
Abstract.
After the initial explosion of literature discussing the quantity and quality of education, recent research has begun to attach importance to the potential role of equity in education in developing countries. The purpose of this paper is to analyze the impact of inequality in education on economic growth. Based on a sample of Arab countries and on the Barro and Lee data (2014), the results of estimates using several panel econometrics techniques show that the significant and negative effect of educational inequality on economic growth differs from a group of countries to another and depends on the level of sensitivity and aversion to inequality. In terms of involvement, In terms of involvement, taking into consideration the unequal dimension of education in the development of public education policies is needed.
JEL Codes: Inégalité educative, normative indicators, economic growth, MENA
1. Introduction
Since the second half of the 20th century, several studies have focused on how the accumulation of human capital could be beneficial to individuals, businesses and society. The benefits of education takes many forms: education increases individual earnings (Mincer, 1958, 1974 Arrow, 1973; Spence, 1973, Acemoglu and Angrist, 2001), improves productivity (Moretti, 2002, Aghion and Cohen, 1998; Dearden et al 2000. Martins, 2004)3 and stimulates economic growth^{4} (Mankin, Romer and Weil (MRW), 1992, Benhabib and Spiegel, 1994; Temple, 1999; Cohen and Soto, 2007; De la Fuente and Domenech, 2006). In addition to these measurable effects, investment in human capital is a source of positive externalities. In fact, investment in education improves health ( Taubman and Rosen, 1982; Desai, 1987, Christensen and Johnson, 1995 ; Deaton and Paxson , 2001; Elo and Preston , 1996; Rogers , Hummer and Nam , 2000; Lleras  Muney , 2002) reduces crime ( De la Fuente , 2003; Behrmann and Stacey, 1997) , and promotes freedoms (Campbell et al , 1976; Rizzo and Zeckhauser , 1992).
Policy makers are forced to consider educational indicators to establish the guidelines and objectives for education systems (Chevallier, 1999). Therefore, the
1 Aomar Ibourk, aomaribourk@gmail.com, Cadi Ayyad University, Morocco
2 Jabrane Amaghouss, jabrane_widadi@yahoo.fr, Cadi Ayyad University, Marrakech, Morocco.
3 For more details see Aghion and Cohen (2004).
4 For Diebolt and Jaoul (2004 ), education is both cause and consequence of economic growth.
Indeed, it is a condition for increasing production but also increasing the available stock of human capital requires financial resources from the proceeds of growth.
debate about the evaluation of the performance of education systems has dominated the economic literature. However, it has faced a series of challenges. Generally, we are confronted with two main difficulties. The first is the choice of indicators (Psaharopoulos, 1984, Hanushek, 1998 and 2000; Michaelowa, 2000). The second challenge is the availability of reliable data (Bailly and Chatel, 2004).
If the studies carried on income inequality are abundant5 (UNDP, 2002, Adams and Page, 2003; Benar, 2007, Page 2007; UNDP, 2009a; Nabli and Bibi, 2010). To our knowledge, no work has been forced to analyze the dynamics of these inequalities in education in Arabic region. However, some separate studies have attempted to analyze the distribution of education in some countries, but they did it in a superficial way (Trabelsi et al , 2011 in Turkey . Krichen et al, 2012. )^{6}. From our literature review, we find a paucity of studies that build inequality measures for a larger sample of Arab countries.
This work differs from others in that it mobilizes the most recent data (Barro and Lee, 2014) and the most appropriate panel data techniques. When Arab countries are not a homogenous group, and in order to study the different growth trajectories, we divided our sample into two groups: the group of highincome countries and the group of middleincome countries.
The objective of this paper is to explore the unequal dimension of education weakly discussed in the Arab countries in a comparative perspective. We mainly study the dynamics of these inequalities by studing its impact on economic growth. We first start by calculating indicators to measur inequality in terms of education. Measuring inequality was not unanimity among researchers. In our opinion, the most developers’
indicators include not only those of Gini but also Atkinson and the generalized entropy indicators. We then conduct an analysis in an international comparative perspective.
Address the issue of inequality in education implies a reflection on its dynamics.
Through an econometric model, we empirically test the extent to which these alternative indicators can help us to improve the relation between education and economic growth. Finally, the fifth section concludes our work.
2 Quantification of inequalities in education in Arab countries : a downward trend
It is impossible to provide an exhaustive list of all measures of inequalities. The objective of this section is to provide an empirical measure of inequality for some Arab countries using indicators commonly used in the literature. First, we present an overall assessment of the extent of these inequalities ( 2.2 ), but before detailing these results,
5 Other research has studied the evolution of economic inequality in an international perspective including Arab countries. See, for example, the recent work of the World Bank (2006, World Development Report 2006.), Milanovic (2005), Deininger and Squire (1996), Summers, Kravis and Heston (1984), Schultz (1998 ), SalaiMartin (2005), Bourguignon and Morrisson (2002).
6 They conducted a comparative approach of the distribution of inequalities in education for Algeria, Egypt, Tunisia and Turkey.
we propose a description of the indicators used in this study and the methodology of the calculation (2.1).
2.1 Measuring inequality in education: data and methodology
Although the inclusion of several measures is desirable for understanding the dynamics of inequality in the field of education, the present investigation is focused on four indicators: Gini index of education (Thomas et al, 2002; Qian and Smyth, 2005.
Morrison et al, 2010), the standard deviation of schooling (Checchi 2000 standard;
Thomas et al, 2002; Castello and Domenech 2002), the index of generalized entropy (developed by Shorrocks, 1980; Cowell, 1988) and the Atkinson index (developed by Atkinson, 1970). The first two indices are the most used in the literature and they are easy to interpret. The last two have the property of decomposability7 . Expressions ( 1) to (4) respectively describe the formula for each indicator as adapted to the field of education :
j i
j
j i n
i
P Y Y P
GINI
i
1
1 2
1
(1)
n
i
n
i i i i
i y p y
p SDS
1 1
))2
(
( (2)
1
) (
) ( ) 1 ( ) 1 (
1 1
n
i i n
i i i
py y p GE
(3)
n
i i i n
i
p i
y p
y A
i
1 1
) 1 (
) 1 ( 1 ) 1
( (4)
With GINI is the Gini index of education, SDS is the standard deviation of schooling, GE (α) is the index of the generalized entropy (α is a parameter of aversion for inequality) and A (1) is the Atkinson index for the parameter 1.
Pi and Pj denote the proportion of the population with education i and j. Yi and Yj are the accumulation of years of schooling according to each level of education. n is the number of levels of education. The classification of Barro and Lee (2014) identifies seven levels of education. In this work, we assumed that the duration of each level of study Yi is constant throughout the period and is the same for all countries.
2.2 A sustained decline in inequality in education
7 Very recent work (Dagum, 1997; Dagum et al, 2003; Deutsch and Silber, 1999) tried to verify ownership of the decomposability of the Gini index.
This section provides statistical analysis for indicators of educational inequality.
Table (1) describes the general evolution of the Gini index (divided by level of income) between 1970 and 2010. As a trend, the level of inequality in education is reduced between 1970 and 2010. In Indeed, in 1970, the countries in our sample have very high indices of inequality of education. Countries where education inequalities are most pronounced are Morocco (0.90), Egypt (0.88) and Iraq (0.87). They are all middle income countries.
It also notes that in 2010, the situation was improved significantly for all countries.
This reflects a form of regional homogenization. This finding is largely shared with the results of Thomas et al. (2002). It should be noted that the lowest values are observed in the highincome countries. However, the rate of decline in the Gini index of education varies between countries. For countries like the United Arab Emirates, Bahrain, Egypt, Jordan and Algeria, the Gini index has declined at least 45% between 1970 and 2010. For other countries such as Morocco, the inequalities slowly decline between 1970 and 2010.
The discrepancies between these countries reflect differences in the effectiveness of efforts devoted by each country to reduce inequalities in access to different levels of education.
The table (1) shows that Morocco, compared to the sample of this study, is the country where education inequalities are most pronounced. This fact is easy to understand if we consider the fact that this country has the highest rate of illiteracy and the lowest average year of schooling in the sample.
Table 1: Evolution of the Gini index of education, selected countries, 19702010
Pays 1970 1975 1980 1985 1990 1995 2000 2005 2010 Jordanie 0,68 0,64 0,59 0,53 0,46 0,41 0,36 0,33 0,3 Turquie 0,66 0,6 0,55 0,5 0,46 0,41 0,35 0,31 0,3 Iran 0,82 0,77 0,7 0,63 0,57 0,52 0,45 0,4 0,36 Syrie 0,71 0,66 0,6 0,53 0,48 0,43 0,42 0,39 0,37 Algérie 0,82 0,76 0,7 0,63 0,56 0,5 0,45 0,41 0,38 Tunisie 0,82 0,75 0,67 0,65 0,6 0,54 0,49 0,45 0,41 Egypte 0,88 0,84 0,76 0,66 0,61 0,56 0,5 0,46 0,42 Iraq 0,87 0,83 0,77 0,69 0,62 0,57 0,53 0,52 0,49 Middle
income countries
Maroc 0,9 0,87 0,83 0,79 0,74 0,69 0,65 0,61 0,56 Moyenne groupe 0,80 0,75 0,69 0,62 0,57 0,51 0,47 0,43 0,40 Bahreïn 0,71 0,63 0,56 0,51 0,45 0,33 0,25 0,22 0,2 Émirats Arabes Unis 0,8 0,76 0,71 0,66 0,59 0,5 0,41 0,33 0,28 Arabie Saoudite 0,69 0,65 0,6 0,54 0,48 0,46 0,41 0,36 0,3 Kuwait 0,62 0,68 0,61 0,55 0,52 0,5 0,44 0,36 0,33 Libye 0,76 0,7 0,65 0,6 0,53 0,48 0,45 0,42 0,4 Qatar 0,71 0,67 0,63 0,59 0,57 0,52 0,49 0,45 0,42 High
income country
Moyenne groupe 0,72 0,68 0,63 0,58 0,52 0,47 0,41 0,36 0,32 sample
average 0,76 0,72 0,66 0,60 0,55 0,49 0,44 0,40 0,37 Source: Direction of the author, based on our calculations
Although these countries have managed to lower the Gini index of education between 1970 and 2010, they are still far from the performance achieved by countries in other regions of the world especially the countries of East Asia (for example in 2010, South Korea shows a Gini index of 0.15, 0.26 in Philippines, 0.29 in Singapore, 0.25 in Bolivia and 0.3 in Brazil (Table 2)).
Table 2: Evolution of the Gini index of education between 1970 and 2010, selected countries
Pays 1970 1975 1980 1985 1990 1995 2000 2005 2010 Bolivie 0,61 0,57 0,51 0,46 0,40 0,38 0,35 0,29 0,25 Brésil 0,55 0,48 0,50 0,48 0,45 0,42 0,38 0,33 0,30 Burundi 0,86 0,83 0,82 0,81 0,79 0,73 0,68 0,65 0,62 Canada 0,24 0,23 0,21 0,20 0,19 0,18 0,17 0,16 0,15 Chine 0,57 0,52 0,45 0,42 0,41 0,35 0,30 0,27 0,24 Danemark 0,28 0,28 0,27 0,25 0,25 0,25 0,24 0,24 0,24 Finlande 0,25 0,27 0,26 0,26 0,25 0,25 0,25 0,23 0,22 France 0,27 0,31 0,32 0,34 0,34 0,28 0,23 0,21 0,18 Gambie 0,95 0,93 0,91 0,89 0,83 0,78 0,77 0,73 0,68 Indonésie 0,59 0,55 0,51 0,57 0,59 0,52 0,44 0,40 0,38 Korea 0,39 0,33 0,29 0,26 0,27 0,20 0,19 0,17 0,15 Mali 0,95 0,93 0,91 0,89 0,88 0,87 0,85 0,81 0,75 Philippines 0,44 0,39 0,37 0,35 0,32 0,31 0,30 0,28 0,26 Singapore 0,51 0,51 0,49 0,41 0,33 0,33 0,33 0,32 0,29 Taillande 0,43 0,40 0,39 0,41 0,40 0,40 0,41 0,39 0,37 Viet Name 0,50 0,45 0,40 0,39 0,35 0,33 0,32 0,31 0,30 Source: Direction of the author, based on our calculations
The use of other indicators (the Atkinson index and the index of the generalized entropy) provide almost the same results. The distribution of education in the countries of our sample follows the same trend as the Gini index: inequalities tend to fall in all countries. However, despite this general trend, middleincome countries are more unequal than highincome countries. It should be noted that the situation of Morocco is very alarming (Table 3 and Table 4).
Table 3: Gini index, the entropy index (GE (a)) and Atkinson (A (e)), selected countries, 1970
Country GE(1) GE(0) GE(1) GE(2) Gini A(0.5) A(1) A(2)
Algérie 5,30E+07 13,55 1,52 2,21 0,82 0,76 1 1
Bahreïn 1,02E+08 11,79 1,07 1,08 0,71 0,64 1 1
Egypte 5,35E+07 15,08 1,89 3,27 0,88 0,84 1 1
Iran 7,36E+07 14,05 1,5 1,93 0,82 0,77 1 1
Iraq 5,59E+07 15,04 1,85 3,02 0,87 0,83 1 1
Jordanie 1,00E+08 11,18 0,97 0,92 0,68 0,6 1 1
Koweït 8,47E+07 8,62 0,76 0,72 0,62 0,49 1 1
Lybie 5,12E+07 12,4 1,28 1,62 0,76 0,7 1 1
Maroc 4,46E+07 15,83 2,17 4,23 0,9 0,88 1 1
Qatar 1,20E+08 11,95 1,06 1,04 0,71 0,64 1 1
Arabie Saoudite 8,98E+07 10,51 0,95 0,96 0,69 0,59 1 1
Syrie 6,45E+07 10,93 1,03 1,13 0,71 0,62 1 1
Tunisie 6,40E+07 13,87 1,52 2,06 0,82 0,77 1 1
Turquie 7,74E+07 10,36 0,91 0,87 0,66 0,57 1 1
Emirats Arabes Unis 9,10E+07 14,01 1,45 1,76 0,8 0,75 1 1 sample average 7,97E+07 12,69 1,27 1,5 0,77 0,69 1 1
Note: A (e), with e> 0 is the parameter of aversion to inequality. GE (a), with a is the sensitivity parameter to the difference in level of education
Table 4: Gini index, the entropy index (GE (a)) and the Atkinson index (A (e)), selected countries, 2010
Country GE(1) GE(0) GE(1) GE(2) Gini A(0.5) A(1) A(2)
Algérie 4,23E+07 2,42 0,3 0,25 0,38 0,2 0,91 1
Bahreïn 2,88E+07 1,2 0,1 0,07 0,2 0,08 0,7 1
Egypte 1,13E+08 6,11 0,42 0,29 0,42 0,33 1 1
Iran 7,52E+07 3,63 0,29 0,21 0,36 0,22 0,97 1
Iraq 8,97E+07 6,03 0,48 0,38 0,49 0,35 1 1
Jordanie 9,19E+07 3,98 0,25 0,16 0,3 0,21 0,98 1
Koweït 1,95E+07 1,23 0,21 0,18 0,33 0,13 0,71 1
Lybie 9,46E+07 4,79 0,35 0,25 0,4 0,27 0,99 1
Maroc 1,14E+08 8,52 0,66 0,53 0,56 0,46 1 1
Qatar 1,13E+08 6 0,42 0,29 0,42 0,32 1 1
Arabie Saoudite 5,39E+07 2,57 0,21 0,15 0,3 0,16 0,92 1
Syrie 2,95E+07 2,27 0,26 0,23 0,37 0,17 0,9 1
Tunisie 7,96E+07 4,5 0,35 0,26 0,41 0,27 0,99 1
Turquie 4,23E+07 2,19 0,2 0,15 0,3 0,15 0,89 1
Emirats Arabes Unis 8,50E+07 3,56 0,22 0,14 0,28 0,19 0,97 1 sample average 7,48E+07 3,95 0,31 0,23 0,38 0,24 0,98 1
Note: A (e), with e> 0 is the parameter of aversion to inequality
GE (a), with a sensitivity parameter is the difference in level of education.
One of the most desired property for an indicator of inequality is the decomposability. By construction, the index of the generalized entropy8 and Atkinson index obey this property. They are broken down into intragroup (inequality within each country) and intergroup inequalities (inequalities between countries). The results indicate that intragroup inequalities dominate inequalities between groups except for the Atkinson index of order 1 both in 1970 and in 2010 (Table 5 and Table 6).
Therefore, we can say that a strong heterogeneity prevails in 15 countries, although there is relative homogeneity between the different countries.
Table 5: Decomposition of entropy index and Atkinson, 1970, entire sample
GE(1) GE(0) GE(1) GE(2) A(0.5) A(1) A(2)
8 For this indicator, Shorrocks defines the concept of additive decomposability and consistently decomposability into subpopulations that meet the axioms inherent inequality measures, namely the "transfer axiom PigouDalton (denoted PD), the axiom Dalton population (PP), the axiom of anonymity or symmetry (SM), the axiom for Standardization (NM) and the axiom of invariance relative (IR).
Intragroupes 7,48e+07 3,93 0,29 0,21 0,22 0,92 1,00
Intergroupes 0,01 0,01 0,01 0,01 0,01 0,74 0,28
Source: Calculation of the author, based on our calculations
Table 6: Breakdown of the entropy index and Atkinson, 2010, total sample
GE (1) GE(0) GE(1) GE(2) A(0.5) A(1) A(2)
intragroupes 7,97e+07 12,61 1,19 1,42 0,65 0,99 1,00
intergroupes 0,09 0,08 0,08 0,08 0,11 0,89 0,03
3 Inequalities in education and economic growth : A Literature Review
Economic theory suggests a strong link between education and economic growth, but the empirical results are mixed, fragile and sometimes contradictory. Few studies have examined the specific link between the distribution of education and economic growth.
Several indicators were used in the literature to measure the impact of different aspects of education on economic growth: enrollment rates at different levels of education, completion rates , the survival rate the final grade , the average number of years of schooling, and scores in international standards tests. By cons, work measuring the impact of inequality in education on economic growth are less numerous. In fact, we distinguish two types of impact assessment, those relating to gender inequality (Barro and Lee, 1993, 1997; Lagerlöf, 1999; Klasen and Lamanna, 2008) and those of distribution (Thomas et al (2002).
Implicitly, Schultz (1993) argues that low investment in girls' education is not economically efficient. It stresses that no study has shown that the performance of the education of girls is lower than boys.
Lopez et al. (1998) calculate the Gini index of education by using the educational level of the population. The authors seek to show why the impact of education on economic growth is so mixed. They build a model of resource allocation which implements the importance of the distribution of education in economic growth. They are based on panel data from 12 countries in Asia and Latin America between 1970 and 1994. Results show that the distribution of education plays a very important role in explaining the fragile link between education and economic growth. They also show that inequality in the distribution of education has a negative effect on GDP per capita for most countries in the sample. Thus, the impact of education on economic growth is much more significant when equal distribution of education is high. It appears that the economic policy is not intended to reduce the uneven distribution of education reduces or adversely affect the impact of human capital on economic growth.
Based on crosssectional data and panel data, Kalsen (1999) examines the impact of gender inequality in education (measured by the female ratio of gross primary enrollment rates) on the growth and economic development. The results suggest a direct and negative impact on economic growth. On the other hand, economic growth is indirectly affected by the impact of gender inequality on investment and population growth. The results also show that gender inequality negatively affects reduction strategies fertility and infant mortality.
In the same analysis, Castello and Domenech (2002) framework build the Gini index for 108 countries from 1960 to 2009. Results show a decrease in inequality of human capital. Then they estimate a standar model of economic growth. Econometric estimates suggest a negative impact of inequality of human capital on economic growth. These results are robust to changes in explanatory variables, excluding outliers and the use of instrumental variables to control for endogeneity problems.
For their part, De Gregorio and Lee (2002) provide empirical evidence on how education can affect the distribution of income for a panel of countries studied from 1960 to 1990. Findings support a high level of instruction and a more equal distribution of education allow a better distribution of income.
By extending the analysis to 1995, Checchi (2004) discusses the relationship between inequality in education and income inequality. The study focused on a sample of 117 countries. They find that when the negative correlation between the average level of education and its dispersion is taken into account, the relationship between income inequality and the average number of years of education takes the form of U.
Based on a theoretical model of the production technology of human capital, Park (2006) empirically examines the impact of the standard deviation of schooling on the growth rate of GDP per capita. The study involved 94 countries during 19601995. The author found that the dispersion index used (SDS) positively affects productivity growth. In terms of implications, educational policies that create greater dispersion of human capital promote growth.
Starting from a sample of 57 developing countries (crosssectional data), Bowman ( 2007) estimates a growth model that endogenizes the formation of human capital.
Empirical analyzes suggest that initial inequalities in education (as measured by the Gini index) slow economic growth.
Based on a spatial approach, Yang and Li (2007) estimate a model of convergence of thirty one Chinese provinces during 19962004. They find a negative and statistically significant elasticity of output with respect to the distribution level of education. Thus, economic inequalities are largely due to inequality in education as measured by the Gini index.
Based on the Gini index and the standard deviation of schooling, Shahzad and Hassan (2005) estimate a model of standard spatial growth for four provinces of Pakistan from 1973 to 1998. Estimates show that public spending on education has a strong impact on reducing educational inequalities and, consequently, economic growth. The authors therefore recommend that educational reforms in Pakistan are focused on universal primary education rather than higher education for a limited segment of the population.
In another more recent study, Klasen and Lamanna (2009) try to update the results of previous work by analyzing the impact of inequality in education on economic growth. The results suggest that inequality in education reduces the potential growth countries. This negative impact is much felt in the MENA and South Asia region. The
9 They only use four levels of study to calculate inequality in education: no education, primary, secondary and higher education level.
economic growth rate decreased by 0.1% when inequalities of education increased by 0.9%.
Baliamoune Lutz and Mc Grillivray ( 2009) use panel data for thirty one countries in subSaharan Africa and ten Arab countries to empirically assess the impact of literacy ratio (female/male, aged 1524 years) on economic growth. The results point that gender inequalities in literacy have a negative and significant impact on the potential for economic growth. The results point that this negative effect is very strong in the Arab countries. These findings obtained are robust to changes in model specification. They also note that the interaction between trade openness and gender inequality has a positive impact. In this sense, induced by trade openness growth may be accompanied by greater inequality between the sexes.
Examining the determinants of economic growth, income inequality, and their relationship to inequality in education ( as measured by the Gini index ) Digdowiseiso (2009 ) indicates that a high level and relative dispersion of human capital reinforce inequality in income distribution . Based on twenty three Indonesian provinces over the period 19962005, estimates suggest that economic policies should target not only the level of education but also its distribution.
By combining the Gini, Theil and Atkinson education, Duarte and Simões (2010) prove the existence of a positive relationship between the initial level of inequality in education and growth for thirty Portuguese regions studied from 1995 to 2007.
Based on time series econometrics, Changzheng and Jin (210) operate macroeconomic data from China during the period 19782004 to test the link between equity in education and the quality of economic growth. From the calculation of the Gini index, the model concluded that equity in education is significantly and positively associated with the quality of economic growth in China. From these facts, the authors propose several adjustments to the Chinese education system.
Placed in a broader regional context, Rodriguez Pose and Tselios (2010) examine the relationship between, on the one hand , the distribution of income and education and, secondly , the economic growth of for 102 regions from Western Europe during the period 19962002. Their results tend to confirm an increase in the income of a region and inequality in education are positively associated with economic growth. The estimates also show that inequalities in education are more important for economic growth than the average level of education . These findings are not only robust to the definition of the income distribution, but also to different measures of inequality in education.
It is this intuition that leads Güngör (2010) to pursue the logic of spatial inequalities. It focuses on the impact of inequality in education on economic growth for sixtyseven Turkish provinces during the period 19752000 by estimating a neoclassical production function. Inequality in Education (approximated by the Gini and Theil index) has emerged as an important factor in explaining the variation in output growth in all provinces of Turkey. According to this author, there is evidence that inequality in education affects negatively and significantly growth not only through its impact on capital accumulation but mainly through the channel of inefficiency.
Measuring inequality in education by the Gini index, the quantile distributions, Castelló (2010b ) found a negative effect of inequality in education and income on economic growth both across the sample and in the countries with low and middle income , an effect that disappears or becomes positive in the sample of highincome countries .
More recently, Sauer and Zagler (2011) studied the relationship between economic development and the average level of education and the degree of inequality in the distribution of education (Gini index) for a dynamic panel of 137 countries from 1950 to 2010. Results suggest that the impact of inequality in education on economic growth depends on the average level of human capital. For developing countries with low levels of education, inequality is positively related to economic growth. While for highly skilled countries, this relationship is not statistically significant. It follows a slight increase in inequality in education is required to move the less educated from the poverty trap.
4 Reducing inequalities in education: Prerequisite for economic growth
The purpose of this section is to assess the impact of inequality in education on economic growth for a panel of Arab countries from the estimation of a growth model.
The indicator used to measure inequality is the Gini index. Furthermore, to confirm our results, we also undertake an estimate based on the Atkinson index and the indices of the family of generalized entropy. To control the bias due to endogeneity of explanatory variables, we used the method of instrumental variables in panel data^{10}.
We begin by describing the model used, the data sources and methodology (4.1).
We then present a discussion of the results obtained (4.2).
4.1 Models, data and methodology 4.1.1 Model
The specification used is based on that of Foldvari and Leeuwen (2011). It is written after adaptation to our approach, as follows:
it t i S it it
it kit
it
s pop S G
Lny
_{0}
_{1}ln
_{2}ln
_{3}
_{4}
(5) Lnyit is the logarithm of per capita GDP, lnskit is the logarithm of the rate of investment in physical capital, lnpop is the logarithm of the population, Sit is the average number of years of schooling, G is a measure of inequality, ηi is individual fixed effect, ui refer to time fixed effect and εit is idiosyncratic measurement error.
Data for yit, skit and popit come from Penn World Table 6.3. Data on the average number of years of schooling are from Barro and Lee (2014). Data on inequalities in education are those built in the second section of this work. All data are calculated on fiveyear averages from 1966 to 2010. Study covers 15 countries, 9 are middleincome
10 Early work using panel data econometrics eliminate all observations for an individual, when one of them was missing or appeared as an outlier. The development of new techniques and econometric programs was used to limit the use of this practice and to work with non displacement observations. Indeed, the elimination of certain individuals whose observations are missing or atypical results in the loss of a lot of information, and hence to biased estimators.
countries and 6 are highincome countries. To better understand the impact of inequality in education on economic growth, we also considered to calculate the impact of gender inequalities on economic growth.
4.1.2 Methodology
Taking into account multiple possible biases, estimating our model leads us to use several econometric methods. Purging the fixed effects models, we introduce dummy variablesindividualin the growth equation adapted to our sample. This makes it easier to estimate the model taking into account the heterogeneity of behaviors. For all regressions, the Fisher test confirm the existence of fixed effects ( Ftest values are not reported ) . To control the bias due to endogeneity of explanatory variables, we used the method of instrumental variables in panel data. A sensitivity analysis was also conducted to test the robustness of our results by approaching educational inequalities by several measures.
4.1.3 The data and their sources
The study covers 15 countries , Algeria , Egypt, Libya , Morocco , Tunisia, Jordan , Iran, Kuwait , Bahrain , Iraq, Qatar , Saudi Arabia, Syria, Turkey, United Arab Emirate . The study is carried out by dividing into 2 subgroups countries. The middle income countries (9 countries : Morocco, Jordan, Tunisia, Turkey, Algeria, Iran, Iraq, Egypt and Syria) and highincome countries (6 countries : Qatar, Bahrain , Saudi Arabia, UAE, Kuwait, Libya).
To study the longrun relationship between inequality in education and economic growth, we have built fiveyear averages for each variable. For the fiveyear data, Islam (1995) emphasizes that these quinquennial data avoid disruptions due to economic as well as autocorrelations that might have in the annual data cycles.
4.2 Estimation Results
Regressions (1), (2) and (3) of Table (7) relate to the estimation of the model (5) for the entire sample using three measures of inequality in education: the Gini index of men, the Gini index of women and the total Gini index. The results show that the impact of the physical capital stock is negative and significant regardless of the extent of inequality in education restraint. It can be explained by the fact that the stock of physical capital across countries is lower than the longrun equilibrium.
The impact of the population has a negative sign but not significant when one considers the total Gini index. This is explained by the fact that in the countries of our sample, the population growth is not conducive to economic growth in the sense that any additional population is not productive employment and are added to the already existing million unemployed . Indeed, the countries in our sample has one of the highest unemployment rates in the world ( Salehi  Isfahani 2010).
The educational level of the population and the distribution of education negatively and significantly impact economic growth in the regressions (1) and (3). These results confirm the findings of Pritchett (1999) and Makdissi (2006). For them, education does not contribute to economic growth. We also tested the equation (5) on the highincome
countries11 and middleincome countries12 in order to identify possible differences between the two subgroups. For highincome countries, the results suggest that only the Gini index of men has a negative and significant impact on economic growth. This result can be explained by the fact that in some highincome countries, the Gini index is lower for women than men. For its part, the educational level of the population has not changed sign and remained significant while the impact of the physical capital stock is no longer significant.
For middleincome countries, the negative impact of inequality in terms of education is significant when considering the inequality of women and the total Gini index. Indeed, the distribution of education is much more unequal among women in middleincome countries. For example, in Morocco, the level of inequality in women's education in 2010 is 0.64 while it is only 0.32 for men. In these countries, the level of accumulation of physical capital does not generate economic growth but negatively contributes to economic growth. As to the population level, the impact is negative and significant.
Table 7: Regression results: panel model with fixed effects. Measure of inequality: Gini index
Ensemble de l'échantillon Pays à revenu élevé Pays à revenu intermédiaire
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Ln( I/y)
0,177^{**} 
0,180^{**} 0,186^{**} 0,109 0,075 0,125 0,142^{*} 0,119 0,128^{*} (2,49) (2,35) (2,51) (0,90) (0,59) (0,99) (1,84) (1,55) (1,71) 0,171 0,086 0,223^{*} 0,208 0,367^{**} 0,248 0,473 0,814^{**} 
0,873^{***}
Ln(pop)
(1,377) (0,59) (1,67) 1,22 2,07 1,39 (1,96) (2,58) (3,01) 0,138^{**} 0,108 0,15^{**} 
0,253^{***} 0,064 0,26^{**} 0,053 0,065 0,065 S
(2,47) 1,49 (1,88) (3,48) 0,48 (2,26) (0,63) (0,97) (0,67)
3,005^{***} 2,306^{**} 1,643
Gini
homme (4,17)  
(2,30)  
(1,51)  
0,725 2,523 2,055^{*}
Gini
femme 
0,78  
1,6  
(1,91) 
3,036^{***} 1,917 4,004^{**}
Gini
 
(2,84)  
(1,23)  
(2,61) 13,426^{***} 9,51^{***} 14,175^{***} 11,73^{***} 6,14^{***} 11,384^{***} 14,093^{***} 17,87^{***} 20,36^{***}
6,34 7,52 8,62 5,58 4,92
Const
11,41 5,39
2,75
(5,47)
N 135 135 135 54 54 54 81 81 81
R sq:
Withim 0,2 0,26 0,21 0,2 0,4 0,41 0,43
Betuen 0,14 0,3 0,19 0,18 0,02 0,008 0,02
Overall 0,14 0,06 0,05 0,04 0,001 0,002 0,001
Source: work of the author
11 régression (4) , (5) et (6)
12 régression (7) , (8) et (9)
By construction, the estimation of equation (5) provides biased estimators in the measure where the rate of investment in physical capital (explanatory variable) depends on the level of GDP per capita (dependent variable). To control this problem of collinearity, we use the technique of instrumental variables in panel data. We opt for the lagged value of the investment rate in physical capital and the logarithm of the population as a tool for physical capital investment rate (Foldvari and Leeuwen, 2011) to ensure the proper choice of instruments, we proceed to Sargent trst. The estimation results are reported in Table (8).
For the sample of all countries (column 1, 2 and 3), the results obtained by the method of least squares panel data confirm those obtained by OLS for variables measuring inequalities in education. However, the negative impact of education is significant in the presence of the Gini index of men. The results confirm and amplify the magnitude of the negative coefficient associated with the physical capital stock.
For highincome countries (columns 4, 5 and 6), the sign and significance associated with coefficients measuring inequalities in education, the educational level of the population and physical capital investment rate have not changed. Only the positive coefficient associated with the population has lost significance.
Table 8: Regression results of fixedeffects model using the method of Instrumental Variables in panel data. Measure of inequality : Gini index
(1) (2) (3) (4) (5) (6) (7) (8) (9)
0,587^{**} 0,546^{**} 0,578^{**} 0,468 0,376 0,479 0,65 0,556 0,558 Ln I/y
(2,30) (2,08) (2,22) (1,57) (1,22) (1,50) (1,42) (1,23) (1,38) 0,384^{*} 0,285 0,455^{**} 0,122 0,069 0,065 0,344 0,537 0,69 Ln (pop)
(1,95) (1,29) (2,17) (0,46) 0,27 (0,24) (1,03) (1,02) (1,83) 0,123^{*} 0,068 0,145 0,195^{**} 0,025 0,229^{*} 0,063 0,048 0,075 S
(1,64) (0,82) (0,25) (2,22) (0,17) (1,68) (0,34) (0,6) (0,56)
3,085^{***} 2,522^{**} 2,541
Gini
homme (3,46)  
(2,18)  
(1,21)  
0,0713 1,296 1,236
Gini
femme 
(0,07)  
(0,74)  
(0,86) 
3,483^{***} 2,461 3,316
Gini
 
(4,05)  
(1,33)  
(1,7) 16,476^{***} 12,959^{***} 17,483^{***} 14,97^{***} 10,092^{***} 14,81^{***} 15,29^{***} 15,98^{***} 19,16 Const
(9,86) (5,77) 6,589 (6,8) (3,57) (5,11) (4,62) (3,09) (4,31)
N 120 120 120 48 48 48 72 72 72
Test de Hansen / Sargent de validité des instruments
validé validé validé validé validé validé validé validé validé
Source: work of the author
For middleincome countries (column 7, 8 and 9), the negative impact of physical capital stock becomes insignificant, the coefficient associated with the population becomes insignificant in the presence of the Gini index for men and women. After correction the bias due to the presence of collinearity between variables, the coefficient associated with the Gini index of women loses its significance.
The results show that the negative impact of the Gini index of men for high income countries and the total Gini index for all countries and middleincome countries are robust to changes in the method of estimate confirming the heterogeneity of countries' performance on the impact of inequality in education on economic growth.
Thus, the low egalitarian distribution of education characterizing most economies in the region has certainly been an obstacle to the development process in the region.
To test the robustness of our results, we estimated our model using different measure of inequality. Table (9) reports the estimation results using the generalized entropy indices. As can be seen, the main statistics of R² (Within, Between and Overall) are generally satisfactory. On this criterion, the adjustments are acceptable.
The OLS and Doubles Least Squares methods results were almost similar. Columns (1), (2) and (3) report the fixed effects estimeted by OLS. As regards the estimates with Double Least Squares instrumental variables, we obtain very robust results (column (4), (5) and (6)). In general, the signs of the main parameters for the various steps of entropy indices are consistent with our predictions. They are associated with a negative and significant sign. The results show that the impact of inequality in education, as measured by the indices of the generalized entropy, the trend of per capita GDP is lower by OLS estimation.
Table 9: Regression results of the panel model with fixed effects, total sample, measuring the inequality index entropy G ( 0), G ( 1) and G ( 2).
MCO IV
(1) (2) (3) (4) (5) (6)
Ln( I/y) 0,181** 0,175** 0,181** 0,575** 0,581** 0,573**
Ln(pop) 0,169 0,182 0,142 0,361* 0,359* 0,307
S 0,031 0,053 0,001 0,02 0,029 0,012
GE(0) 0,059**   0,060*  
GE(1)  0,661***   0,638** 
GE(2)  0,232***   0,265**
Const 11,872** 12,077*** 11,169*** 14,693*** 14,696*** 13,736***
N 135 135 135 120 120 120 R sq:
Within 0,11 0,16 0,15 0,13 0.12 0.11
Between 0,41 0,44 0,48 0,41 0,42 0,43
Overall 0,38 0,41 0,43 0,38 0,39 0,39
Source: work of the author
Table (10) reports the results of estimating the model approaching inequalities in education by the Atkinson index. Overall, the estimates by the two methods are of good quality and the results are robust. The model can easily be used to analyze the relationship between inequality in education and trajectories of GDP per capita of selected countries. It appears that the effects of inequality in education on growth are consistent with those obtained using the Gini index and the generalized entropy, that is to say, a negative and significant impact. This result is consistent with most theoretical and empirical analysis.
The results show that when the fixed effects are controlled, the variable " average years of schooling " (measuring the amount of education) has no significant effect on growth , confirming the fragility of the relationship linking education and economic growth when reasoning in terms of quantity of education.
Table 10: Regression results of the panel model with fixed effects , total sample Measure of inequality : Atkinson index A (0.5) and A ( 1)
MCO IV
1 2 (3) (4)
Ln( I/y) ,182** ,1943** ,580** ,562**
Ln(pop) 0,181 0,127 ,385* 0,289
S 0,059 0,052 0,045 0,047
A(0,5) 1,467**  1,509** 
A(1)  0,493  1,440621*
Const 12,308*** 11,135*** 15,231*** 14,605***
N 135 135 120 120
R sq:
Withim 0,12 0,09 0;1 0,11
Betuen 0,41 0,5 0,41 0,43
Overall 0,38 0,45 0,38 0,39
Source: work of the author
The negative impact of inequality in education on economic growth can be explained by several reasons. Thus, Lagerlöf (1999) confirms that inequalities in education affect growth via the channel of fertility. Economic growth is indirectly affected by inequality in through investment and population growth (King and Mason, 2001). Other studies have focused on the role of inequality in education in strengthening income inequality (and dallar Datti, 1999; Rehme, 2007). More recently, Castelló (2010a) confirm that this negative impact is heightened in countries where individuals have difficulty accessing credit.
We can identify several reasons according to which gender equality in education promotes economic growth. Assuming that men and women have an identical distribution of innate abilities and that individuals with more talent are more likely to receive better quality and / or more education, gender inequality in education implies that men with lower that women are more likely to be enrolled in the schooling process capabilities. Therefore, the average level of human capital stock held by an economy would be lower than in the context of equal opportunities in education between the sexes, which in turn could slow economic growth ( Thévenon and O. by the same reasoning al. (2012). , gender inequality in education can reduce the impact of male education on economic growth and increase the impact of women's education ( dollar and Gatti, 1999 and Knowles et al , 2002). adverse effects on investment rates could also contribute to slow growth because of low returns on investments. Finally, greater gender equality in the accumulation of human capital will also lead to higher growth if the accumulation of male and female human capital are imperfect substitutes and if the marginal returns to education are declining (Knowles et al. , 2002).
Note that the divergence of growth trajectories is not only the fact of educational policies. It is the product of the combination of natural factors, socioeconomic policies that influence national educational investment strategies. We recall that the fixed effects13 estimation can mobilize the country information (A. Pirotte, 2004, Greene 2006). It should be noted that these effects should be treated with caution. Indeed, estimates of the individual effects thus obtained must be strictly construed , in relation to different individual achievements and not in absolute terms . in other words, the individual fixed effects estimator of a country applies only with respect to individual effects in the group to which it belongs and has no particular significance in relation to himself.
Tables (11), (12) and (13), in the Annex, report the fixed effects estimation of each country for different inequality measures and for the three identified groups. On the entire sample, fixed effects of Morocco, Bahrain, Iraq, Tunisia, and Turkey are not significant compared to those of the reference countries (Algeria). Only Egypt specificities significantly reduce the potential for growth over Algeria. The fixed effects estimation for the sample of middleincome countries provides almost the same results except that the fixed effects of Tunisia and Jordan become significant. For high income countries, only Qatar maintains significant fixed effects (positive) relative to the reference country (Bahrain).
13Only the individual fixed effects are reported.
Generally, the fixed effects reflect the socioeconomic, political, institutional and geographic differente for each country. From these findings, it naturally comes to mind to tap into the study of each case. Since we belong to Morocco, we propose to study its characteristics in future work.
5. Conclusion
Empirically, after declining the construction methodology of our indicators taking into account the unequal da dimension of education, we discussed to analyze their evolution in some Arab countries in a comparative perspective. The results suggest that inequalities in education have declined in Morocco for both men and women regardless of age. It also appears that the distribution of education is more unequal in our country compared to other countries with which we share common cultural values.
In a third step, we estimated the impact of inequality in education on economic growth with panel data. The results suggest that the Gini index of men negatively and significantly affects the growth of highincome countries. The total Gini index negatively and significantly impact economic growth as well as for all countries to highincome countries. A sensitivity analysis was conducted to test the robustness of our results by using both technical instrumental variable in panel data and more sophisticated indicators. The main conclusion to be made is to emphasize this dimension of education in the development of educational policies.
While significant progress has been made in the field of education in recent years, Morocco is at a turning point in the development of its educational system. The first challenge that continues to arise in the development of the Moroccan education system is the fact that access to education is unfair.
The estimation of countryspecific fixed effects shows the existence of different educational paths. Thus, deviations enter the country leads us to suppose the existence of divergence even within a country. Thus, a general understanding of spatial patterns may be necessary. This issue is the subject of future work.
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Annex on line at the journal Website
Table 11: Fixed Effects Estimation for each country according to the measure of inequality, whole sample, OLS method.
gini
homme
gini
femmes gini G(0) G(1) G(2) A(0,5) A(1)
Bahreïn 0,679 0,923 0,244 0,608 0,511 0,651 0,527 0,673
Egypte 0,337 0,57*** 0,408* 0,381* 0,406* 0,493** 0,389* 0,555 Iran 0,667*** 0,437** 0,543*** 0,560*** 0,517*** 0,445** 0,551*** 0,443
Iraq 0,214 0,101 0,094 0,146 0,112 0,092 0,127 0,078
Jordanie 0,466 0,419 0,668** 0,454 0,563* 0,533 0,506 0,504 Koweït 1,689*** 1,800*** 1,230*** 1,497*** 1,398*** 1,505*** 1,428*** 1,560***
Lybie 1,119*** 1,252*** 0,921*** 1,116*** 1,024*** 1,089*** 1,064*** 1,147***
Maroc 0 0,234 0,146 0,107 0,095 0,153 0,119 0,253
Qatar 2,103*** 2,014*** 1,528*** 1,782*** 1,636*** 1,724*** 1,714*** 1,788***
Arabie
Saoudite 1,296*** 1,284*** 1,177*** 1,263*** 1,210*** 1,223*** 1,229*** 1,246***
Syrie 1,502*** 1,05*** 1,604*** 1,36*** 1,419*** 1,30*** 
1,435***
 1,207***
Tunisie 0,088 0,071 0,247 0,128 0,203 0,179 0,164 0,137 Turquie 0,217 0,07 0,252 0,047 0,113 0,074 0,104 0,003 Emirats
Arabes Unis 2,015 *** 1,855*** 1,544*** 1,764*** 1,660*** 1,682*** 1,713*** 1,703***
Note: Reference country is Algeria, Source: work of the author
Table 12: Fixed Effects Estimation of middleincome countries, OLS method.
gini
hommes gini
femmes gini G(0) G(1) G(2) A(0,5) A(1) Egypte 0,072 0,145 0,292 0,057 0,079 0,142 0,075 0,094 Iran 0,800***
0,867**
* 1,033***
0,763**
* 0,743***
0,692**
*
0,861**
*
0,739**
* Iraq 0,152 0,013 0,055 0,118 0,088 0,083 0,109 0,122 Jordani
e 1,268**
 2,10***

2,154***

1,322** 1,407 1,345* 1,535*
 1,295**
Maroc 0,117 0,083 0,227 0,085 0,071 0,038 0,147 0,048 Syrie

1,459***
 1,73***

1,982***
 1,37***

1,415***
 1,35***
 1,54***
 1,29***
Tunisie 0,421  0,887**

0,897*** 0,465 0,521* 0,487*

0,584** 0,429 Turqui
e 0,165 0,329 0,201 0,288 0,266 0,263 0,292 0,298
Note: Reference country is Algeria Source: work of the author
Table 13: Fixed Effects Estimation of highincome countries, OLS method.
gini
homme gini
femme gini G0 G1 G2 A05 A1
Koweït 0,329 0,206 0,174 0,132 0,202 0,184 0,136 0,00
Lybie 0,624

1,012** 0,662 0,746 0,627 0,669 0,738 ,890*
Qatar 1,268*** 1,022*** 1,122*** 1,037*** 1,030*** 0,997*** 1,041*** 1,067***
Arabie Saoudite 0,784 
1,434** 0,85 0,99 0,812 0,879 0,978 1,234*
Emirats Arabes
Unis 0,584* 0,101 0,415 0,318 0,392 0,321 0,323 0,264
Note: Reference country is Bahrain Source: work of the author