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Using fractionalization indexes: deriving methodological principles for growth studies from time series evidence

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Abstract

Recent cross-country growth studies have found that ethnolinguistic fractionalization is an important explanatory variable of long-run growth performance. This paper highlights some limitations of cross-country studies by focusing on the time series evidence for South Africa. In presenting variation over time in a number of social dimensions, this paper adds longitudinal evidence on a range of dimensions that have been linked to long run economic development. Given South Africa’s history of ethnic and racial politics, it constitutes a useful case study to explore the dynamics of the possible effects of ethnolinguistic fractionalization on growth. We introduce several new sets of fractionalization indicators for South Africa: ethnolinguistic, religious and cultural fractionalization, and a polarization measure. The results of this study provide important nuance to the existing body of evidence, for the use of fractionalization indices in growth studies.

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Fig. 1

Notes

  1. 1.

    On the impact of political instability on investment, see Fielding (2000), and Fedderke (2004). On the impact of political instability, and changes in political rights on short and long-term capital flows as well as capital flight, see Fedderke and Liu (2002). On the impact of political instability on human capital production in black schooling in South Africa, see Fedderke and Luiz (2002). On the interaction of political instability, political rights and economic growth in South Africa see Fedderke, De Kadt and Luiz (2001b).

  2. 2.

    A fractionalization index measures the probability that any two randomly selected members of a statistical population will possess different properties in the dimension that is being measured.

  3. 3.

    This study is part of a larger project that has been concerned to address the institutional dimensions of long-term economic growth in South Africa. See Fedderke, de Kadt, Luiz (1999, 2000, 2001a, b, 2002, 2003).

  4. 4.

    See Alesina and La Ferrarra (2005).

  5. 5.

    See Alesina and Spolaore (2003) and Alesina and La Ferrara (2005).

  6. 6.

    See Annett (2001) and Rodrik (1999).

  7. 7.

    See Alesina et al. (1999) and La Porta, Lopez de Silanes, Shleifer, and Vishny (1999).

  8. 8.

    See Easterly and Levine (1997).

  9. 9.

    Alesina and Spolaore (2003).

  10. 10.

    See Collier (2000, 2001).

  11. 11.

    See Aghion, Alesina, and Trebbi (2004).

  12. 12.

    See Leeson (2005).

  13. 13.

    See Easterly (2001).

  14. 14.

    See the extensive discussion in Posner (2004).

  15. 15.

    See Chandra and Boulet (2003).

  16. 16.

    For instance, Mauro (1995) and Easterly and Levine (1997) assume ethnic identity to be fixed and unchanging.

  17. 17.

    Thus Scaritt and Mozaffar (1999) argue identity is malleable over time and heterogeneous—particularly in Africa.

  18. 18.

    Thus Posner (2004) has proposed the use of “politically relevant” ethnic groups—though here the danger of selection bias is ever present.

  19. 19.

    See Posner (2004).

  20. 20.

    There are alternative empirical operationalizations (on different underlying data). See for instance Atlas Naradov Mira (1964); Alesina, Devleeschauwer, Easterly, Kurlat, and Wacziarg (2002), Roeder (2001). The measure is defined as:

    $$ {\hbox{ELF}}\, = \,1 - \sum\limits_{i = 1}^N {\pi _i } $$

    where ⊥ i denotes the proportion of the total population of group i, and N denotes the total number of groups in the population.

  21. 21.

    See Montalvo and Reynal-Querol (2005). Note that Alesina and La Ferrara (2005) suggest that ELF is more robustly correlated with GDP than RQ—while RQ is more strongly correlated with civil war. The measure is defined as:

    $$ {\hbox{RQ}}\, = \,1 - \sum\limits_{i = 1}^N {\left( {\frac{{0.5 - \pi _i }} {{0.5}}} \right)} ^2 \pi _i $$

    where ⊥ i denotes the proportion of the total population of group i, and N denotes the total number of groups in the population.

  22. 22.

    See Fearon (2003). The measure is defined as:

    $$ {\hbox{CF}}\, = \,1 - \sum\limits_{i = 1}^N {\sum\limits_{j = 1}^N {\pi _i \pi _j r_{ij} } } $$

    where ⊥ i denotes the proportion of the total population of group i, N denotes the total number of groups in the population, and rij = (k/m)ϑ, with k denoting the number of shared characteristics between i and j, and m the highest number of characteristics of any in-sample group.

  23. 23.

    See Laitin and Posner (2001).

  24. 24.

    Thus Fearon (2003) points out that the same index value emerges from quite distinct population proportions.

  25. 25.

    See Bush and Reinhardt (1999), Mozaffar et al. (2003), Rogowski and Kotin (1999), Toft (2003).

  26. 26.

    For instance Scaritt and Mozaffar (1999) argue for the importance of national, middle and lower levels of fractionalization.

  27. 27.

    For instance due to the incentive to migrate created by relative economic success or failure—see Alesina and La Ferrara (2004); Glaeser, Scheinkman, and Shleifer (1995).

  28. 28.

    See for instance Ensminger (1992).

  29. 29.

    See the Leeson (2005) argument on colonialism above.

  30. 30.

    See Deutsch (1953), Anderson (1983), Gellner (1983), Weber (1976), and also the discussion in Posner (2004).

  31. 31.

    See Bockstette and Putterman (2002) and also the discussion in Posner (2004).

  32. 32.

    See Diamond (1997), Bloom and Sachs (1998), Easterly and Levine (2002), and also Posner (2004).

  33. 33.

    Though both Posner (2004) and Fearon and Laitin (1996) find low correlation between civil war and diversity.

  34. 34.

    For instance Posner (2004) points our that Malaysia created incentives for ethnic Chinese to convert to Islam: so that identity changed from race to religion.

  35. 35.

    The first and most widely used in growth studies is the Atlas Narodov Mira (1964) measure, developed by Russian ethnological scholars. More recent measures include Alesina et al. (2003), Fearon (2003), Roeder (2001) and Montalvo and Reynal-Querol (2005). Furthermore, Posner (2004) has developed a new fractionalization index but only for Africa.

  36. 36.

    Under Apartheid attempts were made to create “independent” political entities defined ethnically, officially referred to as “homelands.” Only a small number of the projected homelands pursued the goal of independence to any extent.

  37. 37.

    Such deliberations are valuable. But they do beg the question of what practical significance errors of measurement might be in empirical work investigating the impact of fractionalization on economic growth, say. This question become all the more pressing if it is indeed true that fractionalization matters (in distributional conflict, say), and if the measurement problems the literature refers to are as widespread as this and other studies suggest. We calculate two initial sets of consideration from the South African case study that lend themselves to shedding some light on the practical question posed. We compute the contrast between the uncorrected and the corrected census computations of Black and total South African linguistic fractionalization indexes. Note that the exclusion of the homeland populations from the official South African census resulted in a substantial under enumeration. Up to 50% of a set of linguistic groups that together constituted approximately 40% of South Africa’s black population was thereby excluded from official census data (hence approximately 20% of the total population). Unsurprisingly therefore, a divergence between uncorrected and corrected fractionalization indexes for the black population emerges. But given the size of the underlying measurement error (20% of the total population excluded), on the other hand the divergence is arguably surprisingly small: 0.78 on the uncorrected fractionalization index versus 0.83 on the corrected index constitutes the maximal divergence, for the black population in South Africa. Moreover, for the aggregate total population fractionalization index, the divergence between the corrected and the uncorrected index is negligible: 0.86 versus 0.85. An immediate implication that follows is that while measurement error in the computation of fractionalization indexes is undoubtedly a serious concern, and should of course be minimized, the fractionalization indexes used in the literature might also be argued to be in fact fairly robust to measurement error. Of course bias emerges in the fractionalization indexes—but it appears that the error of measurement would have to be fairly substantial before a significant divergence between the true and the biased fractionalization measure emerges.

  38. 38.

    Various authors have attempted to deal with these limitations and have developed alternative measures to capture polarization and cultural fractionalization as discussed in Sect. 2.

  39. 39.

    We follow the standard measure given by\( F\, = \,1 - \sum\limits_{i = 1}^n {\left( {\frac{{n_i }} {N}} \right)} \left( {\frac{{n_i - 1}} {{N - 1}}} \right) \), where n i denotes the number of members of households that cite the i’th language as the principal medium of communication within the household, N denotes the number of members in the population. F thus computes the probability that two randomly chosen individuals speak different first languages. Symmetrically for religious fractionalization. Note that for linguistic fractionalization we suppressed the 1936 observation, and for religious fractionalization the 1921 observation. While available, data collection problems resulted in clear outlier observations relative to the rest of the series.

  40. 40.

    See Fielding (2000), Fedderke (2004), Mariotti (2002), Kularatne (2002), Fedderke and Luiz (Unpublished).

  41. 41.

    The measure of political instability is obtained from Fedderke, De Kadt and Luiz (2001a). One objection might query whether the measure of political instability is indeed a measure of distributional conflict. Instead political conflict in South Africa may be conceived of as a conflict not over access to resources but over political rights. However, Fedderke and Luiz (Unpublished) demonstrate that the primitive here is property rights, which influence both growth and political conflict, while political rights are an outcome variable from the interaction of economic and property rights developments. Effectively the exclusion of most racial groupings in South Africa from access to resources by denying them relevant property rights renders questionable the suggestion that conflict was, at least exclusively, concerned with political rights, and not with rights over resources.

  42. 42.

    We recognize that this might lead to the conjecture that rising religious fractionalization might have led to distributional conflict—though with a lag. Two reasons suggest that this is unlikely. Barro and McCleary (2003) find that religious beliefs do influence economic performance and certainly this association goes back to the seminal work of Max Weber. The decision to measure religious diversity was in part occasioned by the fact that South Africa has historically been characterized by a considerable diversity of religions. It should be noted that, notwithstanding this diversity of religions, the country does not have a history of significant conflict between religious communities. Instead religious communities and institutions have been mobilized around political issues, notably with respect either to supporting or criticizing Apartheid. In this regard, many religious organizations came into conflict with the government. Some supported the Apartheid project and some were internally divided over the issue. The important point, however, is that these divisions were not primarily divisions between religious movements on specifically religious matters. They were divisions on the matter of the morality of Apartheid. See for instance the discussions in Research Institute for Theology and Religion (2000). We reflect further on questions of causality below.

  43. 43.

    In South Africa, this resulted firstly in the Tricameral parliament of 1983 (which co-opted Coloureds and Asians into the formal legislative structures in the hopes of building new alliances and building critical mass) and then in 1989 in the unbanning of the African resistance movements (including the African National Congress and the Pan African Congress). The unbanning of these anti-apartheid movements in turn paved the way for the constitutional negotiations which led to democratic elections in 1994.

  44. 44.

    See also the discussion in Pesaran (1997) and Pesaran and Shin (Unpublished, b) and Pesaran et al. (2001). Suppose that the question is whether there exists a long run relationship between the set of variables y t , x 1, t ,...,x n,t . Univariate time series characteristics of the data are not known for certain. The PSS approach to testing for the presence of a long run relationship proceeds by estimating the error correction specification given by

    $$ \Delta y_t = \alpha _0 + \sum\limits_{i = 1}^p {\beta _i \Delta y_{t - 1} } + \sum\limits_{j = 1}^n {\sum\limits_{i = 1}^p {\gamma _{j,i} \Delta x_{j,t - 1} } + \left( {\delta _1 y_{t - 1} + \sum\limits_{k = 2}^{n + 1} {\delta _k x_{k,t - 1} } } \right) + \varepsilon _t } $$

    The test proceeds by computing the standard F-statistic for the joint significance of δ1 = δ2 = ··· = δ n + 1 = 0, under all feasible alternative LHS variables. While the distribution of the test statistic is non-standard, with x i,t  ∼ I(0) ∀i providing a lower bound value, x i,t  ∼ I(1) ∀i an upper bound value to the test statistic. The test is analogous to a Granger causality test, but in the presence of non-stationary data. This renders the PSS F-test suitable in the current context.

  45. 45.

    This direction of association is further favored by the fact that emigration from South Africa accelerated during the 1980s and 1990s, considerably after the process of racial homogenization of the population began.

  46. 46.

    A cursory examination of the international political landscape readily demonstrates that it is unlikely that ethnolinguistic fractionalization is necessarily the defining social fault line. Whilst ethnolinguistic fractionalization may be the social cleavage which resulted in conflict in Rwanda and Burundi, it is not clear that this is the case in other conflicts. The long lasting conflict in Northern Ireland was ostensibly waged between Protestants and Catholics and was thus driven by a religious cleavage. The balkanization of Yugoslavia and the Soviet Union had many dimensions including ethnolinguistic and religious cleavages. The Huntington (1997) hypothesis of the clash of civilizations supports a number of fundamental cleavages in world politics and these could easily be translated intra-country, although not his intention. The current conflict in the Sudan likewise reveals a complex network of cleavages including religious and racial. It is simplistic therefore to assume that the default cleavage for distributional conflict will necessarily be ethnolinguistic rather than other forms of social and political cleavages including the most obvious of race and religion.

  47. 47.

    The study employs the Apartheid racial classificatory system of African, Asian, Coloured and White, given the prevalence of data collection under these categories.

  48. 48.

    In the case of Asians, additional factors would have included the policy decision in 1948 to terminate immigration from India, and to decrease to the point of elimination funding for private Indian schools (see Fedderke et al., 2000). Both measures prevented Indian linguistic usage from being sustained through investment in the stock of primary language users.

  49. 49.

    Economic incentives toward linguistic assimilation need not be restricted to minorities. Sufficient economic pay-off may induce even majorities to change. A tempting means of independent verification lurks here. Currently the African population of South Africa has unprecedented access to schooling resources. A predicted change which follows from the interpretation of the data series presented above is that the African population too should come to manifest reduced levels of linguistic fractionalization, since the prevailing language of education, industry and commerce, and government in South Africa is English. This latent change in linguistic fractionalization would be hidden in current and past census data, since the primary language use of households is collected on heads of households. Only once the current population of school children and university students forms its own households, would the change become evident.

  50. 50.

    Questions surrounding the direction of association between variables in growth contexts are both pervasive and crucial. For discussions surrounding methodological and estimation issues in these contexts see Awokuse (2005), Chang and Cuadill (2005), Shan (2005), and Wahab (2004).

  51. 51.

    So for example, Zulu is classified as follows: Niger-Congo, Atlantic-Congo, Volta-Congo, Benue-Congo, Bantoid, Southern, Narrow Bantu, Central, S, Nguni, Zulu. Afrikaans, on the other hand, is classified: Indo-European, Germanic, West, Low Saxon-Low Franconian, Low Franconian, Afrikaans. The languages are therefore unrelated since they share no common characteristics as classified by linguistic grouping. By contrast, Ndebele is classified as: Niger-Congo, Atlantic-Congo, Volta-Congo, Benue-Congo, Bantoid, Southern, Narrow Bantu, Central, S, Northern, Ndebele, and hence has a high degree of commonality with Zulu.

  52. 52.

    This is a question we explore in greater detail in a separate paper (Fedderke & Luiz, 2007).

  53. 53.

    See for instance the discussion in Hamilton and Wright (1993) on the South African context.

  54. 54.

    A caveat that Alesina et al. (2002: 18) is conscious of.

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Fedderke, J., Luiz, J. & de Kadt, R. Using fractionalization indexes: deriving methodological principles for growth studies from time series evidence. Soc Indic Res 85, 257–278 (2008). https://doi.org/10.1007/s11205-007-9090-x

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JEL Classification

  • O4
  • O11
  • Z13

Keywords

  • Fractionalization
  • Distributional conflict
  • Social and political dimensions of economic growth
  • South Africa