Inequality of Opportunity in Sub-Saharan Africa

Transcription

1 Inequality of Opportunity in Sub-Saharan Africa Paolo Brunori Flaviana Palmisano Vito Peragine December 2015 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. In this paper we evaluate inequality of opportunity in 11 Sub-Saharan Africa countries. According to our results, the portion of total inequality which can be attributed to exogenous circumstances is between 30% and 40% for the generality of countries considered. We also find a positive association between total consumption inequality and inequality of opportunity and we study the different sources of unequal opportunities. Finally, we address a number of methodological issues that typically arise when measuring inequality of opportunity with imperfect data, which is the typical case in developing countries. Keywords: Consumption inequality, Equality of opportunity, Sub-Saharan Africa. JEL codes: D63, E24, O15, O40. This work was supported by the World Bank in the framework of the Poverty in a rising Africa report. We are grateful to Francisco Ferreira, Kathleen Beegle, Isis Gaddis, and Camila Galindo Pardo for their comments and support. All errors remain our own. University of Bari. paolo.brunori@uniba.it. University of Luxembourg. flaviana.palmisano@gmail.com University of Bari. vitorocco.peragine@uniba.it 1

2 1 Introduction Sub-Saharan Africa (SSA) 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 on the argument that not all inequalities are the same: in particular, it has been convincingly argued (see World Bank, 2006; Ferreira et al., 2014; Marrero and Rodriguez, 2013) that the degree of the inequality caused by differences at birth (such as gender, ethnicity, or parental background) or, more generally, by factors beyond the individual control may be related to low growth, more so than other effort-based inequalities. The idea is that when exogenous circumstances play a strong role in determining individual outcome, there is a sub-optimal 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 the economic activity, is harmful to growth because they discourage effort and investment by individuals, provoke a loss of productive potential, and contribute to social and institutional instability. The arguments above suggest that analysing 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 Roemer, 1998; Fleurbaey, 2008), which provides a model to distinguish between that part of inequality caused by exogenous circumstances outside the individual responsibility, considered to be objectionable and therefore deserving a compensatory intervention, and the part of inequality generated by individual choices and effort, which is on the contrary considered to be fair and not to be eliminated. The EOp theory has spurred a huge amount of theoretical and empirical works focussing 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 opportunity inequality is not an easy task: its informational requirements are quite high if compared to the standard measurement of income or consumption inequality. 2 Therefore, these are more commonly met in surveys and databases that refer to 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 1 In particular, only two contributions exist in the literature, namely Cogneau and Mesplé-Somps (2008) and Piraino (2015) that propose an analysis of inequality of opportunity for African countries. 2 See on this Hassine (2011). 2

3 evaluate inequality of opportunity in a large set of SSA countries by using 13 different surveys that contain information about individual circumstances and outcomes. Our contribution to the literature is twofold. First, we contribute to the understanding of economic inequality in 11 SSA countries (i) by showing the portion of consumption inequality, which can be attributed to inequality of opportunities, and (ii) by identifying the most disadvantaged groups of the population in each country. This analysis can help to understand the social and economic mechanisms that generate inequalities and can help in identifying priorities in anti-poverty 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 realisation 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 socio-economic 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: Comoros, Democratic Republic of Congo, Ghana, Guinea, Madagascar, Malawi, Niger, Nigeria (two waves), Rwanda, Tanzania (two waves), and Uganda (two waves). Our estimates are shown on a sub-sample 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 index ranges from 0.55 for Comoros to 0.31 for Niger, but in general the Gini index is around 0.4 in all countries considered. The entire region of SSA 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 witness that the impact of exogenous circumstances is noticeable in every country, although this impact is quite variable across them: the portion of total inequality which can be attributed to (the observable) exogenous circumstances is between 30% and 40% for the generality of countries considered. This is a striking result, particularly if one considers that the computed measures are only 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 Comoros and Niger birthplace play a strongest role in determining IOp, while in Congo is clearly ethnicity to be 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 non-parametric) 3

4 and by proposing an adjusted inequality of opportunity measure, which takes into account the differences between countries in the number of the circumstances variables. This methodology should make the cross-country comparison more reliable. Our results differ substantially from the only previous contribution that has focussed on inequality of opportunity in SSA: 3 Cogneau and Mesplé-Somps (2008) analysed five SSA countries (Ivory Coast, Ghana, Guinea, Madagascar, and Uganda) by using data collected between 1985 and They use a very 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% and 20%. 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 organised as follows. Section 2 briefly reviews the concept of opportunity inequality and discusses some measurement issues. Section 3 describes the data, and the non-parametric and parametric analyses 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 SSA 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 Roemer, 1998; Van de gaer, 1993; Peragine, 2002). 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

5 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 characterise a population of individuals. For simplicity, let us treat effort, as well as each element of the vector of circumstances, as discrete variables. This would allow 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 speaking, the source of unfairness in this model is given by the effect that circumstance variables (which lie beyond individual responsibility) have on individual outcomes. However, there are different ways to measure such effect. This 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 to respect the outcome inequalities due to effort; the compensation principle, according to which all outcome inequalities due 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 opportunity inequality, namely the ex-ante and the ex-post approach. According to the ex-ante approach, there is equality of opportunity 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 reducing 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 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 socio-economic groups, possibly deserving special attention by policymakers. 4 This assumption is motivated by the theoretical argument that it would be hardly sustainable to hold people responsible for the factor e in a situation in which it were dependent on exogenous characteristics. 5

6 Alternatively, according to the ex-post approach, there is equality of opportunity 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 opportunity inequality 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, which are either consistent with 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 equality of opportunity 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, for the ex-post approach a measure of individual effort is required. 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 such approach, we use the between-types inequality measure, which was proposed, among others, by Peragine (2002), Checchi and Peragine (2010), and Ferreira and Gignoux (2011). 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 from 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 non-parametric method. These are discussed in the following section. 2.2 Parametric and non-parametric 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 due to 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 et al. (2009) and Peragine and Serlenga (2008) for empirical analyses based on different versions of the reward principle. 6

7 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 in 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, when inequality is measured on a distribution of type means, from which extreme values have been removed by the smoothing operation, it tends to be very underestimated by the MLD. For these reasons, in this paper we follow Aaberge et al. (2011) and use the Gini index, 6 which has well known desirable characteristics, although it is not perfectly decomposable in betweenand within-types inequality whenever the type income distributions overlap. 7 Therefore, in general: Gini(Y ) = Gini(Y within ) + Gini(Y s ) + K (3) Where K is a residual greater than zero when there is overlapping between the types distributions. It deserves to be noted that, 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 sub-vector 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 true inequality of opportunity, 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 when comparing, for instance, the IOp of a country with a large number of observable circumstances to the IOp of another country with only few observable circumstances. Moreover, the error made in comparing these two quantities might not be random but 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, when decomposing total inequality into a between 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 6 In the Appendix, for a robustness check we also compute the mean logarithmic deviation. 7 See Lambert and Aronson (1993) for an insightful discussion on the Gini decomposition. (2) 7

8 individual is a group. To overcome this problem they propose an adjusted 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 betweengroup 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 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 as 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 number of observable characteristics. Therefore, in the following we propose estimates of both IOp and Adj-IOp. The non-parametric 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 limitation on circumstances might seriously hamper the analysis, an alternative, parametric approach to the estimation of inequality of opportunity that economises on data requirement could be explored. It is based on the assumption that a simple linear relationship characterises equation (1), given that circumstances are exogenous by definition and they may also influence effort (see Bourguignon et al., 2007; Ferreira and Gignoux, 2011; Ferreira et al., 2011). Therefore, equation (1) could be re-expressed in reduced form as: y = φ(c, ɛ), and a linearised version of this equation would lead to: (4) y = βc + ɛ (5) The estimated ˆβ coefficient of the ordinary least square (OLS) estimation of equation (5) will incorporate both the direct effect of circumstances on outcome and its indirect effect through effort. Clearly, this will be true only if the ˆβs estimated with OLS are unbiased estimates of the real effect of circumstances. Inequality of opportunity 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: 8 8 See Ferreira and Gignoux (2011). IOp = I(ŷ) (6) 8

9 Relative inequality of opportunity will be equal to: IOp = I(ŷ) I(y) It is worth noticing that the parametric approach is fully consistent with the ex-ante utilitarian assumption used in the non-parametric modeling of IOp. Here, the only difference is that the expected outcome, given observable circumstances, is obtained using the predicted values from a linearised OLS model. Assuming a linear effect of circumstances we no longer need to construct types in order 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 recognised that also the parametric approach has some limitations, however. First, it indirectly imposes a precise functional form linking circumstances and outcome. Moreover, the OLS estimation of equation (5) requires that one controls for a number of dummy variables. In fact, the set of circumstances that is generally used in empirical analyses typically includes parental education, parental occupation, area of birth, and ethnicity. Such variables are not cardinal, and each one needs to be transformed into a number of dummy variables equal to the number of values it assumes in order to make equation (5) operational. When no cardinal circumstance is observable, estimating equation (5) through an OLS regression brings to the estimation of a shift in the regression intercept associated to 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 non-parametric approach. Thus, from one side the motivations for the use of a parametric approach appear to be clear when cardinal measures of circumstances are available (such as parental income). However, they are less convincing when all circumstances can be only modeled through dummies. From the other side, by assuming 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 their possible permutations. This method leads to a path-independent identification of the contributions of each circumstance. (7) 9

10 The discussion above suggests the adoption of both the parametric and non-parametric approaches. In fact, as underlined by Ferreira and Gignoux (2011), the two approaches may be considered complementary. 3 Data Our analysis is based on the following surveys: - Enquête Intégrale auprè des Ménages (EIM) for Comoros, carried out by the Statistical Office of the Ministry of Land Planning and Settlement; - Enquête sur la Consommation des Ménages (ECM) for Congo D. R. (year 2010), carried out by 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 auprè 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 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 10

11 Table 1: Data sources country survey year sample size documentation Comoros EIM ,373 IHSN Congo D. R. 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 link to the documentation. Our analysis is based on a sub-sample of the original data, obtained by considering only individuals aged 15 years or more for whom information about circumstances beyond individual control are available. The outcome considered is per capita consumption, which encompasses consumption for both food and non-food goods, that is, we assume a proportional intra-household distribution of consumption and zero economies of scales in consumption. Although we use different surveys, the results are comparable across countries since 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 inequality of opportunity 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, but nonetheless of prominent importance. For each country, in fact, we can observe a subset of the following: ethnicity, parental education and occupation, birthplace (see Table 2 for details). As for the specific circumstances, parental education and occupation are widely used as circumstances in the empirical literature on IOp that has dealt with developed countries. The importance of the socio-economic origin is emphasised also by the sociological literature on social stratification and social mobility, which focusses on occupation-based social classes. A vast amount of evidence has been produced on the effect of socio-economic background on children s outcomes during adulthood. This literature is however traditionally Western-centric and has rarely concentrated on SSA countries. Nevertheless, there 11

12 is also evidence supporting the argument that parental education and occupation act as circumstances on individual outcome in the specific SSA context. For instance, it has been shown that, in these countries, the nutritional status of a child is strongly correlated to parental occupation with obvious, although indirect, consequences on his outcome in the future (Madise et al., 1999). Parental education, instead, has been 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, among others, Glick and Sahn, 2000; Lloyd and Blanc, 1996; Lassibille and Tan, 2005; Schultz, 2004). Ethnicity and birthplace are variables of paramount importance in SSA, historically characterised by civil and ethnic conflicts, which arrest or even reverse the growth and development process of the this specific part of the African continent. Even today, SSA 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 SSA (Lacina and Gleditsch, 2005). In 2011, for instance, SSA has had 91 instances of this type of conflict, compared to the 89 of 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 characterised by regional disparities in access to opportunities. Hence, it appears natural to treat ethnicity and birthplace as circumstances in the context of our analysis. It is important to note that cross-country comparisons of IOp must be interpreted while bearing in mind that the subset of circumstances used may vary across countries, as different surveys usually collect different information on circumstances. 9 In order to provide meaningful non-parametric 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 non-parametric 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 their size. Tables 7 to 16 in the Appendix contain the details of the partition in types used for the non-parametric estimates in each country. These tables represents the so-called opportunity profile (Ferreira and Gignoux, 2011), a country specific list of types, their rank, and the value of their opportunity set. These profiles are interesting per se, as they 9 All individuals with missing information on the circumstances are dropped from the analysis. 12

13 country Comoros Congo DR Ghana Guinea Madagascar Malawi Niger Nigeria Rwanda Tanzania Uganda Table 2: Circumstances observed by country circumstances birthplace parental education parental occupation ethnicity Note: Ethnicity for Democratic Republic of Congo is observable but the documentation to decode it is missing thus rendering it impossible to construct the partition in types necessary for the non-parametric estimates of IOp. In Malawi, mother tongue is used as a proxy for ethnicity. Source: Surveys listed in Table 1. identify the most deprived groups in each society. 4 Results: the non-parametric approach 4.1 Consumption inequality and opportunity inequality Table 3 reports, for each country and wave, the estimates of total inequality, inequality of opportunity, and inequality of opportunity ratio (all computed by using the Gini index). Moreover, the first three columns contain information about the sample size, the average per capita consumption, and the number of types in which each country is partitioned. Note also that we do not report any estimate for Congo DR due to 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 index ranges from 0.55 for Comoros to 0.31 for Niger, but in general the Gini is around The entire region of SSA is confirmed as one of the most unequal regions in the world. For the three countries for 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 their 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 13

14 Table 3: Inequality and IOp, non-parametric estimates country sample consumption types inequality IOp IOp % max between-groups 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, Note: Per capita consumption is expressed in 2011 PPP $. Source: Authors calculation based on surveys listed in Table 1. III table 16), there is in fact only one instance of re-ranking occurring between Tanzania and Niger. As far as the inequality of opportunity is concerned, 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% for Rwanda and 44% for Malawi, and is more generally between 30% and 40% for the other SSA 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 inequality of opportunity. This is a striking result, particularly if one considers that the computed measures are only lower bound estimates of the inequality of opportunity level in each country. It is also interesting to look at the association between total consumption inequality and opportunity inequality as depicted in Figure 1. This figure could be interpreted as a generalisation of the so-called Great Gatsby curve (Corak, 2013), showing a negative relationship between income inequality and social mobility. Our results show that, although countries with higher consumption inequality are also characterised by a higher level (portion) of inequality of opportunity, there is also considerable re-ranking between countries taking place in passing from total inequality to IOp. Notable here is the case of 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 to divide the 10 SSA countries under analysis into three main groups. The first group is represented by the three countries with highest share of IOp, namely Tanzania, Malawi, and Uganda; Malawi and Uganda have also highest level of 14

15 Figure 1: Total inequality and inequality of opportunity Gini Madagascar Niger Rwanda Nigeria Ghana Nigeria Guinea Comoros Tanzania Tanzania Uganda Uganda IOp (absolute Gini) Malawi Source: Surveys listed in Table 1. total inequality. The second group is represented by the three countries with lower share of inequality of opportunity, namely Rwanda, Madagascar, and Comoros, that nevertheless exhibit a comparatively high level of consumption inequality; the third represented by all the other countries having relatively middle shares of IOp (i.e., 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 it share on total consumption inequality. As discussed above, the normalisation of inequality with respect to the number of types is particularly relevant in the present context, as we are comparing IOp in countries whose specific consumption distribution is partitioned into a very 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 it clear that the adjustment procedure does not add particularly relevant information in our context. The correction is never above 5% and it is smaller than 2% for countries with a number of types above 40. Hence, the higher the number of 15

16 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: Surveys listed in Table 1. types the lower the impact of the adjustment, and this result is rather general. To grasp this drawback consider Figure 3, plotting the difference between total Gini, twice the area between the black Lorenz curve and the diagonal, and the maximum between-group Gini, twice the area between the blue broken line, for three hypothetical group partitions: one group, five groups, ten 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 very 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 tens. 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 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 16

17 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. each circumstance can take. 10 The second part of the table contains the estimates of total inequality, IOp in absolute terms and as share of total inequality, using the Gini 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, Note: Per capita consumption is expressed in 2011 PPP $. Source: Authors calculation based on surveys listed in Table The analytical results of the OLS regression for each country are available from the authors upon request. 11 See Appendix III for a parametric estimate of IOp using MLD. 17

18 In general, non-parametric estimates tend to be lower than their parametric version; however, this must not be necessarily the case. Recall that parametric and non-parametric approaches differ in two aspects: the former imposes a linear relationship between circumstances and outcome, the latter aggregates some information contained in variables beyond individual control. Setting aside the problem of partial observability, both constraints imply that IOp is a downward bias estimate of the real IOp under very general conditions. Imposing linearity reduces the variability that can be explained by circumstances in all cases except when y is a linear function of c. Similarly, ignoring some of the circumstances variability decreases the ability of these variables to explain total inequality, unless the inequality between the groups aggregated is zero. Thus, when the bias implied by the assumption of linearity is smaller than the bias introduced aggregating circumstances, the parametric IOp is larger than the non-parametric IOp. However, there can be cases in which the linearity assumption implies a larger distortion than the aggregation of circumstances: in this case the non-parametric IOp will be larger. Figure 4 shows the discrepancy between the two approaches. Parametric estimates are reported on the vertical axis and the non-parametric estimates on the horizontal axis. The first clear feature that stands out is that, with the exception of Guinea, parametric estimates are always larger than non-parametric ones. As for the ranking, 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 very high number of regressors used to estimate equation (5) and the rather low number of types used to construct the counterfactual distribution for the non-parametric estimates. An extreme case is that of 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 non-parametrically 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, it must be noted that the high number of regressors in Madagascar is mainly due to the high number of possible birthplace, 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. Birthplace in this survey are cities (commune urbaines). Not surprisingly the coefficients for the dummies of such a detailed subdivision of the territory are generally not statistically significant. It seems, therefore, unreasonable to include all the possible birthplaces among the controls of the OLS estimation of equation (5), since 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 non-parametric approach: we trade-off some of our regressors variability with statistical significance. Therefore, in cases like that of 18

19 Figure 4: IOp parametric and non-parametric estimates parametric IOp % Rwanda Madagascar Nigeria Comoros Niger Ghana Tanzania Nigeria Tanzania Guinea Malawi Uganda Uganda non parametric IOp % Source: Surveys listed in Table 1. Madagascar, with few observable qualitative characteristics that can take a large number of values, it would be more advisable to follow a non-parametric approach, which has the additional quality of not imposing linearity, rather than a parametric one. This issue is examined for all countries in Figure 5 where we determine whether the difference between parametric and non-parametric estimates is really due to the difference between the number of types and the number of regressors. The vertical axis reports the ratio between the two estimates (non-parametric over parametric), and the horizontal axis reports the ratio between the number of types and the number of regressors. Indeed, the positive correlation between the two ratios suggests that the number of regressors does play a role in making parametric estimates. Obviously, 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 non-parametric one. The case of Guinea provides an example of how assuming a linear effect of circumstances on outcome actually provokes a downward bias of our IOp estimates, which is larger than the bias induced by aggregating circumstances when using the non-parametric 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 clearly 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 children outcome 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

20 Figure 5: Number of types and number of regressors non-parametric/parametric Guinea Nigeria Nigeria Uganda Comoros Uganda Ghana Rwanda Madagascar Tanzania Tanzania Niger Malawi types/regressors Source: Surveys listed in Table 1. Table 5: Non-linear impact of circumstances: the case of Guinea birthplace parental occupation per capita consumption rest of Guinea agriculture rest of Guinea other 1, Labe other 1, Labe agriculture 1, Note: This example is obtained by aggregating data in Table 9. best outcome prospects. The effect of birthplace and parental occupation on consumption are clearly not linear. This is not just a statistical feature, but it has a clear economic meaning: Labe one of the main centres of national and international agricultural trade flows (FEWS, 2013). Therefore, an individual who was born into a farming family in Labe has the best possible condition in terms of economic opportunities. It is clear that for the specific case of Guinea, the parametric procedure neglects the interaction between parental occupation and area of birth. In sum, among the main reasons for the possible inconsistency between the parametric and non-parametric approaches, we find that the small number of observable characteristics and the possible high number of values they can assume do play an important role. In fact, our results demonstrate that a high number of regressors tends to make parametric estimates higher than the non-parametric estimates. However, the assumption of a linear effect of circumstances on outcome, implicit in the parametric approach, can provoke a downward bias of IOp. 20