Horizontal inequalities in Africa: measurement issues SK Tetteh-Baah, K Harttgen, I Günther Chair of Development Economics ETH Zurich, Switzerland Abstract This study estimates different indicators of horizontal or between-group inequality to track the progress made against inequality of opportunity across 38 African countries between 1990 and 2016. Such progress largely depends on the assumptions held in measuring horizontal inequality [HI]. Previous studies have shown with traditional methods of measurement that HI has been generally falling in Africa. The traditional use of a relative measure of inequality assumes that people are sensitive to relative, not absolute, differences when comparing distributions. The traditional use of plutocratic method of weighting also assumes that majority groups count more than, not equal to, minority groups. Using data from the Demographic and Health Survey program, the study demonstrates that the traditional approach to the measurement of HI embellishes the progress made against unequal opportunities over time, compared to what more egalitarian approaches would suggest. Much of the reduction in horizontal inequalities in educational attainment and wealth in Africa, as shown in previous studies, is being driven by overall growth in living standards, and not necessarily the narrowing of absolute gaps in sub- national regional, ethnic, gender, or religious outcomes over time. However, the study finds falling horizontal inequalities in child non-stunting and child survival, which is robust to the measure of inequality applied, indicating greater equality of opportunity for the new generation of African people. JEL codes: D63 Equity, Justice, Inequality, and Other Normative Criteria and Measurement J71 Discrimination Key words: horizontal inequality, inequality of opportunity, gender, ethnicity, sub-national region, religion, Africa, educational attainment, wealth, child non-stunting, child survival 1. Introduction and background literature The cause of social development has, more than ever, been geared toward the equalization of opportunities for all. As is articulated in the Sustainable Development Goals [SDGs], the leaders of world have pledged to “leave no one behind” by 2030 (United Nations, 2015, 2017). Equality of opportunity is achieved if the outcomes of people depend solely on their choices and not on circumstances they face outside of their control, usually determined at birth, such as their gender, ethnicity, and parental background (Roemer, 1998, 2013; Roemer, Trannoy and Haven, 2015). There are both intrinsic and instrumental reasons to reduce inequality of opportunity. For the former, it is fair to work toward a world where all people, everywhere, enjoy sufficient freedom to pursue the lives of their choosing, regardless of their gender, ethnicity or race, place of birth, and religious beliefs. For the latter, a large body of empirical literature suggests (somewhat) negative relationship between inequality of opportunity and social, economic and political outcomes (Stewart, 2000, 2008; Klasen, 2002; Murshed and Gates, 2005; Østby, 2006; Mancini, 2008; Cederman, Weidmann and Gleditsch, 2011; Marrero and Rodríguez, 2013; Ferreira et al., 2018). This study identifies the estimation of horizontal inequality across developing countries over time as a means of tracking progress toward equality of opportunity in the developing world. Horizontal inequality [HI] is inequality in social outcomes observed between socio-cultural groups defined by identity cleavages, such as gender, religion, ethnicity, geographical location, among others. HI may reflect inequality of opportunity directly; e.g., gender inequality in educational attainment observed in a country may indicate the lack of equal opportunity for females to access formal education. HI may also reflect inequality of opportunity indirectly; e.g., the fact that inequality in outcomes today translates into inequality in opportunities in the next generation (Atkinson, 2015). In 2014, the United Nations University - World Institute for Development Economics Research (UNU-WIDER) echoed the salience of HI in developing countries, which was originally documented by Stewart (2000), and revived research on HI when it launched the project, “Group-based inequalities: patterns and trends within and across countries” (Gisselquist, 2014). In the years that followed, there has been a spike in the number of studies providing estimates of horizontal inequalities for developing countries (e.g., Gachet et al., 2016; Leivas and dos Santos, 2016; Maliti, 2016; Argaw, 2017; Thi and Hoai, 2017; Canelas and Gisselquist, 2018; Günther, Harttgen and Tetteh-Baah, forthcoming). These studies find relatively low and generally falling horizontal inequalities across most developing countries, especially in non-income indicators of well-being. This impressive conclusion is, however, driven by underlying measurement assumptions. Thus, the aim of this study is to highlight how horizontal inequality [HI] levels and trends may differ markedly depending on the assumptions held in constructing inequality indices for the measurement of HI. 1 In a preceding study, we take a more comprehensive approach to the measurement of HI, compared to previous studies in this body of literature, expanding the country and time coverage, analyzing data from 70 developing countries between 1990 and 2016, while expanding the indictors of well-being and group categories (Günther, Harttgen and Tetteh-Baah, forthcoming). The preceding study provides estimates of sub-national regional, gender, religious, and ethnic inequalities in terms of educational attainment, wealth, child non-stunting, and child survival. The results show that countries in Africa, though they have relatively high levels of HI, have seen large reductions in horizontal inequalities over time, though progress is slow. Similar to previous studies, the preceding study measures HI using the Group Gini (GGini) Index, following the recommendations of the pioneering works in this literature (Mancini, Stewart and Brown, 2008; Stewart, Brown and Mancini, 2010). This inequality index follows the same idea of the well-known Gini Index, which obtains the average of all pairwise absolute differences in individual outcomes, normalized by the overall mean, yielding a relative measure of inequality. However, with the GGini Index, group mean outcomes take the place of individual outcomes in constructing the Index, and group mean outcomes enter the GGini Index formula with plutocratic weights equal to the corresponding shares of groups in the population. By convention, economists select inequality indices that fulfill “axioms” or “desirable properties” of inequality measurement, including transfer principle, population principle, anonymity, decomposability, scale independence, and translation independence (Harrison and Seidl, 1994; Cowell, 2016).1 The variance, for instance, is a measure of dispersion but is not a standard measure of inequality because it does not fulfill the scale independence axiom of inequality measurement (Harrison and Seidl, 1994; Cowell, 2016). The scale independence axiom states that the level of inequality remains unchanged if all outcomes change by the same proportion; say, the doubling of all incomes. Each axiom is predicated on an assumption or judgment about distributions. Thus, the axioms are inherently value-laden and could be contested philosophically. For the scale indepedence axiom, this assumption is that people are sensitive to relative differences when comparing distributions. If the income of the rich doubles and the income of the poor also doubles, the ratio of their incomes is the same as before, and the level of inequality 1 Transfer principle, population priniciple, and decomposability, are not relevant for the purposes of the study and are not discussed any further than the following. The transfer principle states that a mean-preserving, rank- preserving transfer from a poorer individual or group to a richer one must increase inequality; conversely, a similar transfer from a richer individual or group to a poorer one must decrease inequality (Pigou, 1912; Dalton, 1920). The population principle, also known as “replication invariance axiom”, states that the level of inequality in distribution 퐴 is the same for another distribution 퐵 that is a combination of 퐴 and 퐴’s replication (Cowell, 2011). The decomposability axiom can be described in the following way. Take two distributions 퐴 and 퐵 with the same population size and the same mean, but 퐴 is more unequal than 퐵. If another distribution 퐶 with the same mean (but not necessarily the same population size) is merged with 퐴 and 퐵, separately, 퐴 merged with 퐶 will also be more unequal than 퐵 merged with 퐶 (Cowell, 2011). 2 remains unchanged in a relative sense. A relative measure of inequality conforms to the scale independence axiom of inequality measurement (e.g., the Relative GGini Index). The translation independence axiom of inequality states that the level of inequality remains unchanged if all outcomes change by the same amount; say, a lump-sum transfer of $100 to every employee in an organization (Harrison and Seidl, 1994; Cowell, 2016). The assumption underlying this axiom is that people are sensitive to absolute differences when comparing distributions. With a lump-sum transfer, the absolute difference between the incomes of the rich and the poor remains the same as before, and the level of inequality remains unchanged in an absolute