Inequality of Opportunity in Sub-Saharan Africa

Transcription

1 Policy Research Working Paper 7782 WPS7782 Inequality of Opportunity in Sub-Saharan Africa Paolo Brunori Flaviana Palmisano Vito Peragine Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Africa Region Office of the Chief Economist August 2016

2 Policy Research Working Paper 7782 Abstract In the last decades, inequality of opportunity has been extensively studied by economists on the assumption that, in addition to being normatively undesirable, it can be related to low potential for growth. This paper evaluates inequality of opportunity and the different sources of unequal opportunities in 11 Sub-Saharan Africa countries. The results indicate that the portion of total inequality that can be attributed to exogenous circumstances that is, circumstances outside the control of individuals control is between 30 percent and 40 percent in the countries considered. The results also indicate a positive association between total consumption inequality and inequality of opportunity. Finally, this paper addresses a number of methodological issues that typically arise when measuring inequality of opportunity with imperfect data, which is the typical case in developing countries. This paper is a product of the Office of the Chief Economist, Africa Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at The authors may be contacted at peragine.vito@gmail.com. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team

3 Inequality of Opportunity in Sub-Saharan Africa Paolo Brunori Flaviana Palmisano Vito Peragine JEL classification: D63, E24, O15, O40. Keywords: Consumption inequality, Equality of opportunity, Sub-Saharan Africa. University of Bari. University of Rome LUMSA. University of Bari.

4 1 Introduction Sub-Saharan African countries are especially known for their high levels of economic inequality and poverty (see, for instance, Ellis 2012; Moradi and Baten 2005; Thorbecke 2013). However, the specific features of these inequalities remain largely understudied. Yet, the understanding of the different sources of inequality is a necessary step toward the implementation of policies that may foster a sustained and shared growth in these countries. There is, in fact, a rooted consensus around the argument that not all inequalities are the same: in particular, it has been convincingly argued (see Ferreira et al. 2014; Marrero and Rodriguez 2013; World Bank 2006) that the degree of inequality caused by differences at birth (such as gender, ethnicity, or parental background) or, more generally, by factors beyond the control of individuals may be related to low growth, more so than other effortbased inequalities. The idea is that, when exogenous circumstances play a strong role in determining individual outcome, there is a suboptimal allocation of resources and lower potential for growth. To put it differently, the existence of inequality traps, which systematically exclude some groups of the population from participation in economic activity, is harmful to growth because it discourages effort and investment by individuals, provokes a loss of productive potential, and contributes to social and institutional instability. The arguments above suggest that analyzing the specific horizontal dimensions of inequality is particularly important in both developing and underdeveloped countries. One way to assess these kinds of inequalities is to implement the Equality of Opportunity (EOp) framework (see Fleurbaey 2008; Roemer 1998), which provides a model to distinguish between that part of inequality caused by exogenous circumstances outside the individual s responsibility, considered to be objectionable and therefore deserving a compensatory intervention, and the part of inequality generated by individual choices and effort, which is, in contrast, considered to be fair and should not be eliminated. The EOp theory has spurred a huge amount of theoretical and empirical work focusing on the measurement of inequality of opportunity (see the recent surveys by Ferreira and Peragine 2015; Ramos and Van de gaer 2015; Roemer and Trannoy 2015). However, most of the literature has been concerned with inequality of opportunity (IOp) in Western developed countries, with only a small set of studies dedicated to developing countries. 1 One reason for this is that measuring IOp is not an easy task: its informational requirements are quite high if compared with the standard measurement of income or consumption inequality. 2 Therefore, these are more commonly met in surveys and databases in wealthier countries. Hence, as argued above, such analysis would be particularly needed in developing countries. This paper is a contribution in this direction. Specifically, it is the first attempt to evaluate IOp in a large set of Sub-Saharan African countries by using 13 different surveys that contain information about individual circumstances and outcomes. 1 In particular, only two contributions exist in the literature, namely, Cogneau and Mesplé-Somps (2008) and Piraino (2015), that propose an analysis of IOp for African countries. 2 See Hassine (2011). 2

5 Our contribution to the literature is twofold. First, we contribute to the understanding of economic inequality in 11 Sub-Saharan African countries (i) by showing the portion of consumption inequality that can be attributed to IOp and (ii) by identifying the most disadvantaged groups of the population in each country. This analysis can help in understanding the social and economic mechanisms that generate inequalities and can help in identifying priorities in antipoverty policies in different countries. Second, this paper offers a methodological contribution to the literature on the measurement of inequality of opportunity by addressing a number of methodological issues that typically arise in the realization of this task in the presence of imperfect data, which is the typical case in developing countries. Our analysis is made possible through the availability of large-sample surveys built upon a common methodology and providing information on the socioeconomic background of adult individuals. We use a set of 13 surveys that were implemented during a period ranging from 2000 to 2013 and covering the following countries: the Comoros, the Democratic Republic of Congo, Ghana, Guinea, Madagascar, Malawi, Niger, Nigeria (two waves), Rwanda, Tanzania (two waves), and Uganda (two waves). Our estimates use a subsample of the original data, adult household members with observable relevant characteristics; nevertheless, they uncover a dramatic picture. Total consumption inequality is remarkable in all the countries, although quite variable across them: the Gini coefficient ranges from 0.55 for the Comoros to 0.31 for Niger, but, in general, the Gini coefficient is around 0.4 in all countries considered. The entire region of Sub-Saharan Africa is confirmed as one of the most unequal regions in the world. Moreover, for the three countries for which two waves are available (Nigeria, Tanzania, and Uganda), the results show an increase in inequality in recent years. As far as inequality of opportunity is concerned, our estimates show that the impact of exogenous circumstances is noticeable in every country, although this impact is quite variable across them: the portion of total inequality that can be attributed to (the observable) exogenous circumstances is between 30 percent and 40 percent for the countries considered. This is a striking result, particularly if one considers that the computed measures are lower bound estimates of the inequality of opportunity level in each country. We also look at the association between total consumption inequality and inequality of opportunity: although some re-rankings do exist, the data show a positive relationship between the two kinds of inequalities. The sources of unequal opportunities also differ across countries. For example, in the Comoros and Niger, birthplace plays the strongest role in determining IOp, while in Congo ethnicity is clearly the dominating circumstance. The ranking of countries in terms of inequality of opportunity is robust with respect to the inequality measure used, but our estimates are sensitive with respect to the estimation approach and to the choice of the exogenous circumstances. In this paper we address this issue by exploring two different estimation approaches (parametric and nonparametric) and by proposing an adjusted inequality of opportunity measure, which takes into account the differences between countries in the number of the circumstances variables. 3

6 This methodology should make the cross-country comparison more reliable. Our results differ substantially from the only previous contribution that has focused on cross-country comparisons of inequality of opportunity in Sub-Saharan Africa: 3 Cogneau and Mesplé-Somps (2008) analyzed five Sub-Saharan African countries (Côte d Ivoire, Ghana, Guinea, Madagascar, and Uganda) by using data collected between 1985 and They use a coarse set of circumstances (parental background), and, in fact, their results show a much lower level of inequality of opportunity: with some variation between countries, their estimates show that the portion of inequality attributed to exogenous circumstances is between 10 percent and 20 percent. Unlike Cogneau and Mesplé-Somps (2008), we extend the analysis to a larger set of countries and a bigger set of circumstances for each country; moreover, we provide a more data-extended and methodologically intensive analysis. The paper is organized as follows. Section 2 briefly reviews the concept of opportunity inequality and discusses some measurement issues. Section 3 describes the data, and the nonparametric and parametric analyzes of inequality of opportunity for the periods and countries considered are presented in Sections 4 and 5, respectively. Section 6 provides a summary of the current findings and concludes with suggestions for further research on IOp in Sub-Saharan African countries. 2 Methodology 2.1 A model of equality of opportunity The canonical model of EOp assumes that the outcome of an individual, y, is entirely determined by two classes of variables: circumstances and effort (see Peragine 2002; Roemer 1998; Van de gaer 1993). For simplicity, we refer here to the individual outcome as income, but any other interpretation of outcome, such as consumption, would in principle be possible. Circumstances are denoted by c and belong to a finite set Ω: examples are gender, age, ethnicity, region of birth, or parental background. These are factors beyond an individual s control, but nonetheless exogenously affect income. Effort is denoted by e and belongs to the set Θ, and it may be treated either as a continuous or a discrete variable. This is a factor that endogenously affects the individual income since it is the result of one s own choices. The different forms of luck that may affect the individual income can be classified either as circumstances or as responsibility characteristics. Individual income can then be expressed as follows: y = g(c, e) (1) The production function g : Ω Θ R + is assumed to be monotonic in both arguments, 3 See also Piraino (2015) for a study of IOp in South Africa. 4

7 while circumstances and effort are assumed to be orthogonal. 4 This is a reduced form model in which neither the opportunities themselves nor the individual decision process to exert a given level of effort are explicitly modeled. The model builds on the argument that (non-observable) individual opportunities can be inferred by observing joint distributions of circumstances, effort, and income, which fully characterize a population of individuals. For simplicity, let us treat effort, as well as each element of the vector of circumstances, as discrete variables. This allows the population to be partitioned in two ways: into types in which all individuals share the same circumstances and into tranches in which everyone shares the same degree of effort. Roughly, the source of unfairness in this model is given by the effect circumstance variables (which lie beyond individual responsibility) have on individual outcomes. However, there are different ways to measure this effect. The measurement exercise can be thought of as a two-step procedure. First, the actual distribution is transformed into a counterfactual distribution that reflects only and fully the unfair inequality, while all the fair inequality is removed. In the second step, a measure of inequality is applied to this counterfactual distribution. The construction of the counterfactual distribution should reflect two distinct and independent principles: the reward principle, which is concerned with the apportion of outcome to effort and, in some of its formulations, requires that one respects the outcome inequalities arising from effort and the compensation principle, according to which all outcome inequalities associated to exogenous circumstances are unfair and should be compensated for by society. In particular, the existing literature has developed two main versions of the compensation principle and two consequent approaches to the measurement of IOp, namely the ex ante and the ex post approach. According to the ex ante approach, there is EOp if the set of opportunities is the same for all individuals, regardless of their circumstances. Hence, in the ex ante version, the compensation principle is formulated with respect to individual opportunity sets: it requires that one reduce the inequality between these opportunity sets. In the model introduced above, the income distribution of a given type is interpreted as the opportunity set of all individuals with the same set of circumstances. Hence, the focus is on the inequality between types: the counterfactual distribution should eliminate the inequality within the types (reward) and reflect the inequality between the types (ex ante compensation). Let us underline here a dual interpretation of the types in the EOp model: on one hand, the type is a component of a model that, starting from a multivariate distribution of income and circumstances, allows us to obtain a distribution of (the value of) opportunity sets enjoyed by each individual in the population. On the other hand, given the nature of the circumstances typically observed and used in empirical applications, the partition into types may be of interest per se: they can often identify well-defined socioeconomic groups, possibly deserving special attention by policy makers. 4 This assumption is motivated by the theoretical argument that it would hardly be sustainable to hold people responsible for the factor e in a situation in which it is dependent on exogenous characteristics. 5

8 Alternatively, according to the ex post approach, there is EOp if and only if all those who exert the same effort end up with the same outcome. The compensation principle, in the ex post version, is thus defined with respect to individuals with the same effort but different outcomes. This means that IOp within this approach is measured as inequality within the tranches. Hence, the corresponding counterfactual distribution should reflect the inequality within the tranches (ex post compensation), but should eliminate the inequality between the tranches (reward). Different measures that are consistent with either the ex ante or the ex post approaches have been proposed in the literature (see Ferreira and Peragine, 2015; Ramos and Van de gaer, 2015): they express different and sometimes conflicting views on EOp, and, in fact, the rankings they generate may be different. In addition, their informational requirements are quite different: while, for the ex ante approach, one needs to observe the individual outcome and the set of circumstances, a measure of individual effort is required for the ex post approach. Therefore, in addition to normative considerations, the choice of which methodology to adopt should also reflect data availability. In our case, the database we use does not contain a satisfactory measure of effort. For this reason, we focus on the ex ante approach, and, among the various measures coherent with this approach, we use the between-types inequality measure, which was proposed, among others, by Checchi and Peragine (2010), Ferreira and Gignoux (2011), and Peragine (2002). It relies on a counterfactual distribution, which is obtained by replacing each individual s income by the average income of the type an individual belongs to, independently of the level of effort exerted. 5 This smoothing transformation, intended to remove all inequality within types, can be performed by using either a parametric or a nonparametric method. These methods are discussed in the following section. 2.2 Parametric and nonparametric approaches Given a distribution of income Y of size N, with n types indexed by i = 1,..., n, for each type i, the population size will be denoted by m i, its population share by q i, and its mean income by µ i (y). According to the between-types inequality measure, the counterfactual distribution Y s is obtained by replacing each individual income with the value of the opportunity set of that individual, that is, the mean income of the type to which the individual belongs. Hence, by ordering the types on the basis of their mean such that µ 1 (y)... µ j (y)... µ n (y), the counterfactual distribution corresponding to Y is defined as Y s = (µ 1 (y)1 1,..., µ i (y)1 i,..., µ n (y)1 n ), where 1 i is the unit vector of size m i. For a given measure of inequality I : R N + R +, the part of inequality arising from initial 5 The use of the average of the type for the smoothing transformation is justified, from a normative point of view, in light of the utilitarian reward principle, according to which society should express full neutrality with respect to inequalities due to effort. See Ferreira and Peragine (2015) for a discussion of the different formulations of the reward principle proposed in the literature and Lefranc, Pistolesi, and Trannoy (2009) and Peragine and Serlenga (2008) for empirical analyses based on different versions of the reward principle. 6

9 circumstances will be given by I(Y s ) or, in relative terms, by: IOp = I(Y s) I(Y ) Equation (2) measures the portion of overall inequality that can be attributed to unequal opportunities. In most empirical analyses, I(Y ) is represented by the mean logarithmic deviation (MLD), because it is perfectly decomposable into between- and within- types inequality. However, the MLD has some undesirable properties: in particular, it tends to be more sensitive to extreme values and is not bounded above; therefore, if inequality is measured on a distribution of type means from which extreme values have been removed by the smoothing operation, it tends to be underestimated by the MLD. For these reasons, in this paper, we follow Aaberge, Mogstad, and Peragine (2011) and use the Gini index, which has well-known desirable characteristics, although it is not perfectly decomposable into between- and within- types inequality whenever the type income distributions overlap. 6 Therefore, in general: Gini(Y ) = Gini(Y within ) + Gini(Y s ) + K (3) K is a residual greater than zero if there is overlapping between the type distributions. Given a set of selected circumstances defined on the basis of normative grounds and observability constraints, any within-type variation in individual outcome is attributed to personal effort. However, the vector of observed circumstances is likely to be a subvector of the theoretical (true) vector of all possible circumstances that determine a person s outcome. Hence, as in any other empirical analysis of this kind, we face the issue of omitted circumstance variables. This problem is often addressed by the argument that the IOp estimates should be interpreted as lower-bound estimators of the true IOp, that is, the inequality that would be captured by observing the full vector of circumstances. It can be shown, in fact, that increasing the number of observed circumstances increases IOp (see Ferreira and Gignoux 2011; Luongo 2011). However, this interpretation renders IOp estimates barely comparable across studies, particularly if comparing, for instance, the IOp of a country with a large number of observable circumstances to the IOp of another country with only a few observable circumstances. Moreover, the error made in comparing these two quantities might not be random, but might be correlated with data quality. Elbers et al. (2008) discuss this issue in a more general setting concerning any estimate of between-group inequality. They claim that, if decomposing total inequality into a between component and a within component, the estimate of between-group inequality might be artificially too low because it compares between-group inequalities with the inequality measured in a counterfactual population in which each individual is a group. To overcome this problem, they propose an adjusted 6 In the appendix, for a robustness check, we also compute the mean logarithmic deviation. See Lambert and Aronson (1993) for an insightful discussion on the Gini decomposition. (2) 7

10 measure of between-group inequality, which is equivalent to the actual between-group inequality normalized by the maximum possible between-group inequality that could be reached in the population, given the number of groups. The latter is defined as the extent of between-group inequality in a counterfactual distribution (Y a ) obtained by ranking outcomes from the lowest to the richest and then partitioning the distribution in such a way that the groups have the same population share as the actual group. Hence, adjusted IOp (Adj-IOp) can be expressed as follows: Adj-IOp = I(Y s) I(Y a ) Although the problem they are looking at does not exactly correspond to our problem of partial observability, their solution can be usefully applied to this context. This adjusted measure is appealing because it accounts for the number of types and their relative weights. Adj-IOp solves, at least in part, the problem of comparing IOp estimates based on different numbers of observable characteristics. Therefore, in the following, we propose estimates of both IOp and Adj-IOp. The nonparametric approach discussed so far is data-intensive: as the partition into types becomes finer, the population size of each type decreases, bringing about a decline in the precision of the estimates of the type mean, consequently giving rise to a bias in the estimation of IOp. In countries such as those considered in this paper, where data limitations on circumstances might seriously hamper the analysis, an alternative, parametric approach to the estimation of IOp that economizes on the data requirement could be explored. This is based on the assumption that a simple linear relationship characterizes equation (1), given that circumstances are exogenous by definition, and they may also influence effort (see Bourguignon, Ferreira, and Menendez 2007; Ferreira and Gignoux 2011; Ferreira, Gignoux, and Aran 2011). Therefore, equation (1) could be reexpressed in reduced form as y = φ(c, ɛ), and a linearized version of this equation would lead to: (4) y = βc + ɛ (5) The estimated ˆβ coefficient of the ordinary least squares (OLS) estimation of equation (5) will incorporate both the direct effect of the circumstances on the outcome and the indirect effect through effort. Clearly, this will be true only if the ˆβs estimated through OLS are unbiased estimates of the real effect of circumstances. IOp will then be obtained by applying an index of inequality to the distribution of the predicted values ŷ from the OLS estimation of equation (5), that is 7 7 See Ferreira and Gignoux (2011). IOp = I(ŷ) (6) 8

11 Relative IOp will be equal to IOp = I(ŷ) I(y) The parametric approach is fully consistent with the ex ante utilitarian assumption used in the nonparametric modeling of IOp. Here, the only difference is that the expected outcome, given observable circumstances, is obtained using the predicted values from a linearized OLS model. Assuming a linear effect of circumstances, we no longer need to construct types to predict this outcome, and we can exploit all information contained in the variables describing circumstances, that is, all values assumed by each circumstance. The literature has also recognized that the parametric approach has some limitations, however. First, the approach indirectly imposes a precise functional form linking circumstances and outcome. Moreover, the OLS estimation of equation (5) requires that one control for a number of dummy variables. In fact, the set of circumstances generally used in empirical analyses typically includes parental education, parental occupation, area of birth, and ethnicity. Such variables are not cardinal, and, to make equation (5) operational, each one needs to be transformed into a number of dummy variables equal to the number of values it assumes. If no cardinal circumstance is observable, estimating equation (5) through an OLS regression brings to the estimation of a shift in the regression intercept associated with each category of every circumstance, for instance, having white-collar parents or being a first-generation immigrant. This implies a severe restriction in the construction of the counterfactual distribution because it imposes a fixed effect for each circumstance. For example, it could be the case that being a first-generation immigrant has a completely different meaning depending on whether one s parents are university professors or construction workers. On the other hand, in a parametric approach, this effect is defined to be the same. To take into account the interaction between circumstances, one needs to interact dummies. However, once all dummies have interacted, one intercept is estimated for each type, and our OLS estimate becomes equivalent to the nonparametric approach. Thus, on one side, the motivations for the use of a parametric approach appear to be clear if cardinal measures of circumstances are available (such as parental income). However, they are less convincing if all circumstances can only be modeled through dummies. On the other side, if we assume a fixed effect of each circumstance, the output of the parametric approach can be easily used to estimate the partial effect of each circumstance on outcome: for example, following Wendelspiess and Soloaga (2014), we could implement a Shapley-Shorrocks decomposition based on the average marginal effect of each circumstance over all the possible permutations. This method leads to a path-independent identification of the contributions of each circumstance. The discussion above suggests the adoption of both the parametric and nonparametric approaches. In fact, as underlined by Ferreira and Gignoux (2011), the two approaches may be considered complementary. 9 (7)

12 3 Data Our analysis is based on the following surveys: - Enquête Intégrale auprès des Ménages (EIM) for the Comoros, carried out by the Statistical Office of the Ministry of Land Planning and Settlement; - Enquête sur la Consommation des Ménages (ECM) for the Democratic republic of Congo (year 2010), carried out by the National Institute of Statistics (Ministry of Planning); - Ghana Living Standards Survey (GLSS) for Ghana (year 2013), carried out by the Ghana Statistical Service - National Data Archive (GSS); - Enquête Integré de Base pour l Evaluation de la Pauvreté (EIBEP) for Guinea (year 2003), carried out by the National Directorate of Statistics (Ministry of Economics and Finance) - Enquête Périodique auprès des Ménages (EPM) for Madagascar (year 2005), carried out by the National Institute of Statistics (INSTAT); - Third Integrated Household Survey (IHS3) for Malawi (year 2010), carried out by the National Statistical Office of Malawi; - National Survey on Household Living Conditions and Agriculture (ECVM) for Niger (year ), carried out by the National Institute of Statistics of Niger; - General Household Survey (GHS) for Nigeria (years and ), carried out by the National Bureau of Statistics of Nigeria; - Enquête Intégrale sur les Conditions de Vie des Ménages (EICV) for Rwanda (year 2000), carried out by the National Institute of Statistics of Rwanda (NISR); - National Panel Survey (NPS) for Tanzania (years and ), carried out by the National Bureau of Statistics of Tanzania; - Uganda National Panel Survey (UNPS) for Uganda (years and ), carried out by the Uganda Bureau of Statistics. They are all representative at a national level and cover both urban and rural areas. Table 1 lists the surveys used, the year they refer to, their original sample size, and a link to the documentation. Our analysis is based on a subsample of the original data, obtained by considering only individuals aged 15 years or more on whom information about circumstances beyond an individual s control are available. The outcome considered is per capita consumption, which encompasses consumption for both food and non-food 10

13 Table 1: Data sources Country Survey Year Sample size Documentation Comoros EIM ,373 IHSN Congo, Dem. Rep. ECM ,529 IHSN Ghana GLSS ,826 GSS Guinea EIBEP ,319 INSG Madagascar EPM ,271 INSTAT Malawi IHS ,137 World Bank Niger ECVM ,118 World Bank Nigeria GHS ,916 World Bank Nigeria GHS ,560 World Bank Rwanda EICV ,69 INSR Tanzania NPS ,175 World Bank Tanzania NPS ,394 World Bank Uganda UNPS ,268 World Bank Uganda UNPS ,509 World Bank goods, that is, we assume a proportional intrahousehold distribution of consumption and zero economies of scale in consumption. Although we use different surveys, the results are comparable across countries because the consumption variable has been adjusted for inflation and translated into 2011 purchasing power parity (PPP) international dollars (World Bank, 2015). A fundamental step in the measurement of IOp is the identification of the vector of observable circumstances. This is a normative choice, subject to the constraint of data availability. Our data contain information on a small set of basic circumstances that are important. For each country, in fact, we can observe a subset of the following: ethnicity, parental education and occupation, birthplace (see Table?? for details). Parental education and occupation are widely used as circumstances in the empirical literature on IOp that deals with developed countries. The importance of socioeconomic origin is emphasized also by the sociological literature on social stratification and social mobility, which focuses on occupation-based social classes. A vast amount of evidence has been produced on the effect of socioeconomic background on children s outcomes during adulthood. This literature is, however, traditionally Western-centric and has rarely concentrated on Sub-Saharan African countries. Nevertheless, there is also evidence supporting the argument that parental education and occupation act as circumstances in individual outcomes in the specific Sub-Saharan African context. For instance, it has been shown that, in these countries, the nutritional status of a child is strongly correlated with parental occupation with obvious, although indirect, consequences on the outcome in the future (Madise, Matthews, and Margetts 1999). Parental education, meanwhile, has been 11

14 Table 2: Circumstances observed by country Country Circumstances birthplace parental education parental occupation ethnicity Comoros Congo, Dem. Rep. Ghana Guinea Madagascar Malawi Niger Nigeria Rwanda Tanzania Uganda Source: Surveys listed in Table 1. Note: Ethnicity for the Democratic Republic of Congo is observable, but the documentation to decode it is missing, thus rendering impossible the construction of the partition in the types necessary for the nonparametric estimates of IOp. In Malawi, mother tongue is used as a proxy for ethnicity. shown to be an important factor in determining whether or not a child is currently attending school; whereas, school improvements in parental education have been shown to increase the schooling of children, which, in addition to improving their health and reducing the status of extreme poverty, has direct effects on the outcome prospects of these children (see Glick and Sahn 2000; Lassibille and Tan 2005; Lloyd and Blanc 1996; Schultz 2004). Ethnicity and birthplace are variables of paramount importance in Sub-Saharan Africa, historically characterized by civil and ethnic conflicts, which arrest or even reverse the growth and development process of the Sub-Saharan part of the African continent. Even today, Sub-Saharan African countries face impressive challenges to peace and stability and have fallen prey to continuous armed ethnic conflicts. Between 1946 and 2002, not less than 1.37 million battle-related deaths occurred in 47 civil wars in Sub-Saharan Africa (Lacina and Gleditsch 2005). In 2011, for instance, Sub-Saharan Africa suffered 91 instances of this type of conflict, compared with 89 in 2010 (see Brautigam and Knack 2014; De Ree and Nillesen 2009). Moreover, previous studies have shown that high levels of ethnic diversity are strongly linked to high informal market premiums, poor financial development, low provision of infrastructure, and low levels of education. Ethnicity has a strong influence on inequality in Africa, where ethnic fractionalisation has given rise to a political economy of unequal subsidies and discrimination (Easterly and Levine 1997; Milanovic 2003). The area is also characterized by regional disparities in access to opportunities. Hence, it appears natural to treat ethnicity and birthplace as circumstances in the context of our analysis. 12

15 Cross-country comparisons of IOp must be interpreted while bearing in mind that the subset of circumstances used may vary across countries because different surveys usually collect different information on circumstances. 8 To provide meaningful nonparametric estimates of IOp, the circumstances observed for each country require some additional treatment. While the parametric approach, assuming a linear effect of circumstances on outcome, can exploit all the information contained in the variables that describe circumstances, the nonparametric approach is forced to aggregate some of this information. Thus, to estimate the mean of each type with a sufficient degree of confidence, the sample size of each type should not be too small. Circumstances are therefore aggregated to reduce the number of types and to increase the size. Tables 7 to 16 in the appendix contain the details of the partition in types used for the nonparametric estimates in each country. These tables represents the opportunity profile (Ferreira and Gignoux 2011), a country-specific list of types, the rank, and the value of the opportunity set. These profiles are interesting per se because they identify the most deprived groups in each society. 4 Results: the nonparametric approach 4.1 Consumption inequality and inequality of opportunity Table 3: Inequality and IOp, nonparametric estimates Country Sample Consumption Types Inequality IOp IOp % Max between-group Adj-IOp % per capita Gini Gini Gini Gini Gini Comoros 5,936 2, Ghana 42,519 1, Guinea 24,866 1, Madagascar 28, Malawi 30, Niger 11,774 1, Nigeria ,916 1, Nigeria ,560 1, Rwanda 14, Tanzania ,119 1, Tanzania ,391 1, Uganda ,194 1, Uganda ,454 1, Source: Calculations based on the surveys listed in Table 1. Note: Per capita consumption is expressed in 2011 PPP U.S. dollars. Table 3 reports, for each country and wave, the estimates of total inequality, IOp, and 8 All individuals with missing information on circumstances are dropped from the analysis. 13

16 the IOp ratio (all computed using the Gini coefficient). Moreover, the first three columns contain information about the sample size, the average per capita consumption, and the number of types into which each country is partitioned. We do not report any estimate for the Democratic Republic of Congo because of the already mentioned impossibility of aggregating ethnic groups to obtain types. Total inequality is remarkable in all the countries, although quite variable across them: the Gini coefficient ranges from 0.55 for the Comoros to 0.31 for Niger, but, in general, the Gini is around The entire region is confirmed as one of the most unequal regions in the world. 9 For the three countries on which observations for more than one year are available (Nigeria, Tanzania, and Uganda), the results bear witness to an increase in inequality; hence, the recent dynamics, where available, show a regressive pattern. The ranking of countries according to the level of inequality seems to be robust to the choice of the inequality measure (whether the Gini or the MLD index, the latter reported in appendix III table 16); there is, in fact, only one instance of re-ranking between Tanzania and Niger. For IOp, the estimates show an equally dramatic albeit different picture. The share of inequality that can be attributed to different exogenous factors is extremely high and variable across all countries: it ranges between 26 percent for Rwanda and 44 percent for Malawi, and is more generally between 30 percent and 40 percent for the other Sub- Saharan African countries. In other words, according to the observed circumstances, more than one-third of the observed inequalities in consumption can be attributed to exogenous factors, that is, to IOp. This is a striking result, particularly if one considers that the computed measures are only lower-bound estimates of the IOp in each country. The association between total consumption inequality and IOp is depicted in Figure 1. This figure could be interpreted as a generalization of the so-called Great Gatsby curve (Corak 2013) showing a negative relationship between income inequality and social mobility. Our results demonstrate that, although countries with higher consumption inequality are characterized by a higher level (portion) of IOp, there is also considerable re-ranking between countries taking place in passing from total inequality to IOp. Notable here is the case of the Comoros, which has the highest total inequality, but it has the second to lowest IOp of all countries examined here. In sum, our estimates allow the division of the 10 Sub-Saharan African countries under analysis into three main groups. The first group is represented by the three countries with the highest share of IOp, namely, Tanzania, Malawi, and Uganda; Malawi and Uganda also have the highest level of total inequality. The second group is represented by the three countries with a lower share of IOp, namely, Rwanda, Madagascar, and the Comoros, that nevertheless exhibit a comparatively high level of consumption inequality. The third 9 For instance, the most recent estimates of the Gini coefficient are around 0.30 for advanced countries, such as the EU-28, Australia, or the United States. They are around 0.35 for Eastern Europe, and about 0.40 for East Asia. Only the Latin American countries are characterized by an average Gini coefficient above 0.50, which is higher than the Gini for Sub-Saharan African countries (see Tsounta and Osueke 2014). 14

17 Figure 1: Total inequality and IOp Gini Madagascar Niger Rwanda Nigeria Ghana Nigeria Guinea Comoros Tanzania Tanzania Uganda Uganda IOp (absolute Gini) Malawi Source: Calculations based on the surveys listed in Table 1. is represented by all the other countries having relatively middle shares of IOp (that is, Ghana, Guinea, Niger, and Nigeria). 4.2 Adjusted inequality of opportunity The last two columns of the third part of Table 3 report, respectively, the adjusted IOp according to the Gini index and its share in total consumption inequality. As discussed above, the normalization of inequality with respect to the number of types is particularly relevant in the present context because we are comparing IOp in countries in which the specific consumption distribution is partitioned into a different number of types: from a minimum of 20 in Nigeria to a maximum of 64 in Malawi. Figure 2 plots the difference between IOp and Adj-IOp as a percentage of IOp against the number of types. Figure 2 also shows a clear pattern for this correction (approximated with a fractional polynomial curve), approaching zero as the number of types increases. The figure makes clear that the adjustment procedure does not add particularly relevant information in our context. The correction is never above 5 percent, and it is smaller than 2 percent in countries with a number of types above 40. Hence, the higher the number of types, the lower the impact of the adjustment, and this result is rather general. To grasp this drawback, consider Figure 3, which plots the difference between the total Gini (twice the area between the black Lorenz curve and the diagonal) and the maximum 15

18 Figure 2: Adj-IOp correction and number of types correction (%) Ghana Nigeria Nigeria Rwanda Uganda Uganda Madagascar Guinea Comoros Niger Tanzania Tanzania Malawi number of types Source: Calculations based on the surveys listed in Table 1. between-group Gini, twice the area between the blue broken line, for three hypothetical group partitions: 1 group, 5 groups, 10 groups. The difference between the two possible denominators of IOp will depend on the shape of the original Lorenz curve; the example clarifies that this difference approaches zero quickly as the number of types increases. Therefore, the adjustment proposed by Elbers et al. (2008) loses relevance whenever the number of types is in the order of 10s. 5 The parametric approach Table 4 reports, for each country and wave considered, the results of the parametric estimates of IOp. The first part of the table contains information about sample size, mean per capita consumption, and the number of regressors (all dummies) used to assess the share of total inequality explained by circumstances. The number of regressors is given by the number of observable circumstances, multiplied by the number of values that each circumstance can take. 10 The second part of the table contains the estimates of total inequality and IOp in absolute terms and as a share of total inequality, using the Gini 10 The analytical results of the OLS regression for each country are available from the authors upon request. 16

19 Figure 3: Lorenz curve and maximum between-type inequality Lorenz curve 2 types 5 types 10 types Note: Lorenz curves for the maximum between-group inequality (light blue) are drawn assuming a population partitioned into equally sized types. coefficient. 11 Table 4: Inequality and IOp, parametric estimates Country Sample Consumption Number of Total inequality IOp IOp (%) per capita regressors Gini Gini Gini Comoros 5,936 2, Congo DR 39,578 1, Ghana 42,519 1, Guinea 24,866 1, Madagascar 28, Malawi 30, Niger 11,774 1, Nigeria ,916 1, Nigeria ,560 1, Rwanda 14, Tanzania ,119 1, Tanzania ,391 1, Uganda ,194 1, Uganda ,454 1, Source: Calculations based on the surveys listed in Table 1. Note: Per capita consumption is expressed in 2011 PPP U.S. dollars. 11 See appendix III for a parametric estimate of IOp using MLD. 17

20 In general, nonparametric estimates tend to be lower than their parametric version; however, this is not necessarily the case. Recall that parametric and nonparametric approaches differ in two aspects: the former imposes a linear relationship between circumstances and outcome; the latter aggregates some information contained in variables beyond an individual s control. Setting aside the problem of partial observability, both constraints imply that IOp is a downward bias estimate of the real IOp under general conditions. Imposing linearity reduces the variability that can be explained by circumstances in all cases except if y is a linear function of c. Similarly, ignoring some of the variability of the circumstances decreases the ability of these variables to explain total inequality, unless the inequality between the groups aggregated is zero. Thus, if the bias implied by the assumption of linearity is smaller than the bias introduced by aggregating circumstances, the parametric IOp is larger than the nonparametric IOp. However, there can be cases in which the linearity assumption implies a larger distortion than the aggregation of circumstances: in such cases, the nonparametric IOp will be larger. Figure 4 shows the discrepancy between the two approaches. Parametric estimates are reported on the vertical axis, and the nonparametric estimates on the horizontal axis. The first feature that stands out is that, with the exception of Guinea, parametric estimates are always larger than nonparametric ones. With the considerable exception of Guinea, Ghana, and Madagascar, there is a clear positive relationship between the rankings generated by the two approaches. The discrepancy between the two approaches seems to be driven by the high number of regressors used to estimate equation (5) and the rather low number of types used to construct the counterfactual distribution for the nonparametric estimates. An extreme case is Madagascar, in which the number of regressors is the highest, 462, while the number of types is 30, one of the lowest. Moreover, Madagascar jumps from being one of the least unequal countries when IOp is parametrically estimated to being one of the most unequal when IOp is nonparametrically estimated. Such a difference should be expected whenever the number of regressors (which by definition increases the total variability explained) is much larger than the number of types. However, the high number of regressors in Madagascar is mainly driven by the high number of possible birthplaces, that is, 397 dummies, far more than the six provinces in which Madagascar was divided at the time of the survey (now 22 regions), and also more than three times the 111 districts of the country. Birthplaces in this survey are cities (communes urbaines). The coefficients for the dummies of such a detailed subdivision of the territory are generally not statistically significant. It therefore seems unreasonable to include all the possible birthplaces among the controls of the OLS estimation of equation (5) because the estimates of their effect on circumstances would not be reliable. A viable solution consists of aggregating birthplaces into districts or provinces. Indeed, this is exactly what we do with the nonparametric approach: we trade some of the variability of our regressors to gain statistical significance. Therefore, in cases such as Madagascar, with 18

21 Figure 4: IOp parametric and nonparametric estimates parametric IOp % Rwanda Madagascar Nigeria Comoros Niger Ghana Tanzania Nigeria Tanzania Guinea Malawi Uganda Uganda non parametric IOp % Source: Calculations based on the surveys listed in Table 1. few observable qualitative characteristics that can take a large number of values, it would be more advisable to follow a nonparametric approach, which has the additional quality of not imposing linearity. This issue is examined for all countries in Figure 5, where we determine whether the difference between parametric and nonparametric estimates is really associated to the difference between the number of types and the number of regressors. The vertical axis reports the ratio between the two estimates (nonparametric over parametric), and the horizontal axis reports the ratio between the number of types and the number of regressors. The positive correlation between the two ratios suggests that the number of regressors does play a role in making parametric estimates. The correlation is far from perfect, and Guinea is an interesting case. Although, for this country, we have 113 regressors and 32 types, the parametric estimate of IOp is smaller than the nonparametric one. The case of Guinea provides an example of how assuming a linear effect of circumstances on outcome actually provokes a downward bias in our IOp estimates, which is larger than the bias induced by aggregating circumstances in using the nonparametric approach. The literature has traditionally judged the assumption of linearity to be less important in determining the magnitude of IOp than the issue related to the number of circumstances. However, the case of Guinea highlights that there are cases in which the opposite can happen. Table 5, a simplified version of the opportunity profile presented in Table 9 in appendix II, clarifies this point. The effect of parental occupation on child outcomes depends on area of birth: on average, in Guinea, having a father employed in agriculture is associated with low consumption. By contrast, being born in the region of Labe to parents working in the agricultural sector implies that one belongs to the type with the 19