I was asked recently to advise on some ongoing work on human development, equal opportunities, and universal coverage. The work was building on previous work undertaken by the World Bank in its Latin America and the Caribbean (LAC) region that had developed a new index known as the Human Opportunity Index (HOI).
The core idea underlying the HOI isn’t new. The argument is that inequalities are inequitable insofar as they’re the result of circumstances beyond the individual’s control (inequality in opportunity), but not if they reflect factors that are within the individual’s control. The object of the exercise is to separate empirically the two.
Children and the HOI
The first part of the LAC study – where the HOI is operationalized – focuses on children and on a subset of goods and services that all children should start out life as having. These “basic opportunities” include things like access to education, safe water, and vaccinations. The study argues that “universal provision of basic opportunities is a valid and realistic social goal” and that “for children, access defines “opportunity,” because children (unlike adults) cannot be expected to make the efforts needed to access these basic goods by themselves.” (p.3). So when we see inequalities in, say, immunization coverage or primary school completion, we should regard these inequalities as unjust, and think of them as reflecting inequalities in opportunity.
I’m sure these value judgments are likely to command a lot of support. After all, in many countries parents are legally required to ensure their children are provided with at least some of these basic opportunities. For example, even in the US where government interference in individual decisions is a highly charged topic, children are required to attend school until at least 16, and must be fully immunized to attend school (there is scope to obtain an immunization exemption on medical and religious grounds, and 20 states allow philosophical exemptions too).
Given that the LAC study began arguing that coverage of basic services ought to be universal, I was expecting it to simply measure inequalities in immunization, primary completion, access to safe water, etc. But it didn’t. Instead, it went on to develop and compute the HOI.
The HOI captures two things: the level of coverage of the variable in question; and how unequally it is distributed across groups of children defined by combinations of variables capturing their circumstances, such as race, gender, parents’ income and education, and the like. The average across groups of the absolute deviations from the population mean is divided by twice the population mean to get the “index of dissimilarity” – an index of inequality used by sociologists. When inequality is non-existent the index is 0. One minus the index is multiplied by the population mean to get the HOI. The larger the inequality, the larger the shortfall of HOI from the population mean. Countries with unequal distributions across groups of childhood circumstance are penalized.
I’m puzzled why the study went down this route, because this index of dissimilarity will inevitably pick up only part of the inequality in the variable being analyzed. Yet we’ve agreed that all the inequality in these childhood variables is unjust.
An easy way to see how much inequality is being mislabeled as equitable is by computing and then decomposing the Gini coefficient. Following Lambert and Aronson , we can think of the Gini as breaking down into a between-group component, a within-group component, and a reranking component due to the fact that some kids in some of the more disadvantaged groups may actually have a higher value of the variable of interest than those in less disadvantaged groups.
Let’s take a specific example: a full course of immunization in Cambodia in 2010. According to the Demographic and Health Survey (DHS), 79% of kids aged between 1 and 2 had been fully immunized. The Gini is 0.210. (Because immunization is a binary variable, the Gini in this case equals one minus the mean.) Let’s next construct groups based on HOI-type groups based on variables defining childhood circumstances. I used the household’s “wealth” quintile, the child’s gender, whether the household’s locality is urban, and the mother’s education (which I coded as secondary schooling completed or not). The between-group contribution to the Gini coefficient is just 0.075 – only 36% of the inequality is attributable to variation in immunization across HOI groups. So the HOI is dramatically under-penalizing Cambodia, letting it off the hook for 64% of the inequality in immunization, even though we agreed at the start that all inequality in immunization is unfair.
HOI and policy
But doesn’t the grouping exercise underlying the HOI help identify the unequal circumstances that contribute to inequality and hence need to be addressed by policy? I’m not so sure.
The process of forming groups based on combinations of variables makes it hard to dig down and see what’s going on. In the example above we know that the inequalities in wealth, gender, location, and mother’s education together account for 36% of the inequality in immunization coverage. But we’ve no idea which underlying inequalities matter most. As it turns out, it looks like wealth inequalities are largely responsible in my example. If instead of defining groups using all 4 variables, we include just the five quintiles of wealth, we get 34% of the Gini accounted for by between-group immunization differences. Repeating the exercise defining the groups on the basis just of mother’s education gives us just 15% of the inequality accounted for between-group differences.
Suppose we didn’t lump variables together like the HOI does but repeated the exercise one variable or circumstance at a time. This is what the team seems to do in chapter 3 of the LAC report. As I and others argued  over 20 years ago, there is a problem with the index of dissimilarity, namely that it doesn’t tell us which way the outcome gradient runs (rural to urban, poor to rich, least educated to most educated), or indeed if there’s a gradient at all. It surely matters whether as in most countries immunization rates are lower among poorer groups, or whether as in some countries – like Moldova  – the opposite is true. The index of dissimilarity would give the same score to an immunization distribution across wealth quintiles equal to [.1,.2,.3,.4,.5] as it would to the distribution [.5,.4,.3,.2,.1]. Yet the first suggests the need for a pro-poor policy and the second does not. The between-group component of the Gini, where the groups are defined on the basis of wealth quintiles, would have the same numerical value in these two cases, but in the first would put a plus sign in front of the contribution, and in the second would put a negative sign in front of it. That’s quite a useful piece of information for a policymaker! It’s actually this part of the Gini – the part picking up shares going to different quintiles of the “wealth” or income distribution, captured by the “concentration index” – that the Bank’s Human Development sector focuses on in its work on inequalities in education , health  and social protection .
Outcome and opportunity inequalities after childhood
The LAC report doesn’t stop at childhood. It argues that we adults exert some influence over outcomes but are also constrained by factors beyond our control; only inequalities in outcomes caused by factors beyond our control should be deemed inequitable. The report focuses on six such factors (gender, race or ethnicity, birthplace, educational attainment of the father, and educational attainment of the mother) and looks at four outcomes (income, consumption and earnings for adults, and the educational achievement of 15-year olds).
This part of the report doesn’t use the HOI but rather a decomposition method, even though both analyses in practice seem to share the same goal. The aim of the decomposition is to isolate the part of the inequality in the outcome attributable to inequalities in factors beyond the individual’s control. The claim is that “in an ideal world, inequality in outcomes should reflect only differences in effort and choices individuals make, as well as luck.” (p15).
I feel rather uncomfortable saying that inequalities in the educational achievement of 15-year olds are unacceptable insofar as they reflect inequalities in the six aforementioned factors that are beyond the individual’s control but acceptable insofar as they reflect inequalities in effort, choices, and luck. First, the educational achievement of a 15-year old reflects a lot of decisions over the previous 14 years over which the individual had little if any control, including the family’s living standards. These will be partly captured by the six “exogenous” factors, but only partly – the family’s living standards will also reflect choices made by the parents. Second, while kids do, of course, have some control over their own educational achievement, it’s surely the case that even kids from relatively privileged backgrounds can get distracted from their efforts by their peers, can make mistakes in their choices, and can hit patches of bad luck – a near-fatal illness, a car accident, a parental breakup, a bout of depression, a spell of anorexia, etc. Do we really want to hold teenagers accountable for their decisions on effort, their choices in general, and their luck? I’m even more inclined to be skeptical in the case of health outcomes: there’s simply a huge random component to the health outcomes, a point that led Julian Le Grand 20 years ago to argue that while risky behaviors might warrant additional taxation, we shouldn’t attempt to decide which health outcome inequalities are just and which are unjust – a position that still seems to resonate today .
But at the end of the day it’s not the value judgments of World Bank staff members that count – it’s the views of the people living in the countries we’re working with that count. Perhaps they’re all tough as nails, in which case it’s fine to label as equitable inequalities that are the result of inequalities in effort, choices, and luck. But if there are a lot of softies like me out there, we’ll dramatically underestimate the amount of inequality that’s unfair. And that could hold governments back from addressing inequalities that their citizens would like them to address.