The South African implementation of affirmative action policies is unique in that it characterises a situation in which the historically disadvantaged constitute a majority of the population.  In applications of Affirmative Action in the US, for example, the point has always been to get minorities into positions in which they can hopefully have positive spillovers for their communities, act as role models, and improve the well-being not only of themselves and their own families, but also of those around them. 

One of the ultimate questions to do with race in society, and specifically in the workplace, is whether affirmative action policies will do anything to alter the landscape of society itself, i.e. whether it will assist us in ending persistent inequalities and getting rid of segregation in our society.  A forthcoming paper from Sam Bowles, Glenn Loury and Rajiv Sethi examines  the "conditions under which inequality across social groups can emerge and persist across generations despite equality of economic opportunity" (1).  This is particularly pertinent for South Africa.  What else does the paper set out to do? It argues that these persistences can arise from the extent of segregation in social networks, the strength of interpersonal spillovers in human capital accumulation and the level of complementarity between high and low skill labour in production.

To foreshadow, their crucial result is that if the size of the disadvantaged group is relatively small then integration can occur with increasing levels of human capital for both advantaged and disadvantaged groups.  However, if the disadvantaged group is large then segregation worsens and incentives to invest in human capital diminish.  I'm hoping that their model is wrong, as much as I think it is rigorously constructed and elegantly derived.

As Bowles et al. comment, "In South Africa under Apartheid group membership based on a system of racial classification was a critical determinant of economic opportunity" (2).  The authors differentiate persistence of inequality (consistent lack of convergence of incomes) from its emergence (the factors that lead inequailty to arise from an initial elagitarian distribution of wealth).  What then is the problem? To quote again, "A liberal judicial system cannot prohibit an individual's choice of a date, a spouse, an adopted child, a role model, a friend, membership in a voluntary association or residence in a neighbourhood."(1-2) So the issue is that even in a world in which individuals face no statutory discrimination, and even have access to equality in all other realms, social networks - the connections that individuals have with one another - may be segregated.  As the authors explain, "Voluntary discrimination in contact can give rise to persistent group inequality even in the absence of discrimination in contract." (2, original italics)

So how does discrimination in social networks result in persistent group inequality?  The short answer is, "Through the human capital mechanism." What I mean here is that even if individuals have the same innate ability because they are surrounded by individuals with different levels of human capital (for historic or other reasons) this disparity may give rise to persistence of group inequality over time.  The model proposed by Bowles, Loury and Sethi provides a rigorous mathematical exemplification of this.  They model an overlapping generations model with a competitive, non-discriminating (i.t.o. 'group') labour market.  They separate workers into two arbitrary groups, both of which have the same underlying distribution of 'ability'.  Employment depends entirely on one's investment in human capital, which they take as a decision by one's 'parents' (in the model).  There are 'spillovers' of one's own investment in human capital to those in one's group. 

Their first insight from the model is that there is a threshold level of segregation above which there will be persistent group inequality, below which group inequalities will tend to converge - i.e. equality will emerge between groups.  What this means though is that if your 'economy' has a level of segregation that is close to this threshold then little interventions will surely assist in overcoming the persistent group inequality and equality will emerge over time.  If you are particularly distant from the threshold level, then even large attempts to eradicate segregation may not bring you closer to greater equality unless they are large enough to take you under the threshold.  What does this mean for South Africa? Are the attempts by government and civil society sufficiently large to take us towards the threshold? I don't know.  I'd suspect not.

They then take a look at a situation in which, instead of there being only two 'equilibria' (i.e. states to which society tends) as in the above, there are multiple potential equilibria.  Here the insight becomes that the size of the historically 'disadvantaged' (in terms of human capital in its social networks) group becomes a critical determinant of the persistence of group inequality over time.  Quoting extensively from the text,

Here we find that the population share of the initially disadvantaged group plays a critical role. If this share is sufficiently small, integration can result not only in the equalization of income distributions across groups, but also in an increase in the levels of human capital in both groups. Under these conditions integration might be expected to have widespread popular support. On the other hand, if the population share of the initially disadvantaged group is sufficiently large, integration can give rise to a decline in human capital in both groups and, if this result is anticipated, may face widespread popular resistance. (4)

Reading this paper gave me one of those "I really hope this is wrong" moments that I occasionally get when reading academic work.  I don't want to go into any great detail on the rest of the material from the paper, the paper is mainly mathematical modelling.  A final conclusion worth noting is their comment that, "equal opportunity alone cannot ensure the convergence of group outcomes even in the long run." (20) Additionally, one of the issues with human capital accumulation is that they are often strongly determined by parents, siblings and other kin.  These connections are often highly segregated (inter-racial marriage is not particularly prevalent in SA or the US). 

But let's leave on a positive note.  They argue that we can still do something:

Finally, as we observed above, contrary to the assumptions we have made here, the degree of segregation may be affected by group differences in human capital attainments. For this reason, temporary policies to reduce these differences, such as lowering the cost to members of the disadvantaged group of attaining human capital, could reduce segregation of social networks which in turn would further reduce or eliminate group differences in levels of human capital. (21) 

So, as long as we get rid of those pesky human capital accumulation costs in the short run, we might still be able to get rid of group inequality and eradicate segregation!  Speculate freely on what this means for policy.  Vouchers? Subsidization of education? Cash grants?