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  Figure 5.1. The Relationship Between Individual Circumstances, Opportunities, and Outcomes

  In this framework, inequality of opportunity corresponds to the diversity of individual circumstances and the way it maps onto unequal outcomes. However, in a dynamic setting, unequal outcomes may themselves map onto unequal individual circumstance. For instance, the thin dotted line (8) in Figure 5.1 may stand for the inter-generational transmission of inequality: successful people in the current generation provide better circumstances to their children in the next. Within a generation, that link may also stand for a random event at some point of life, which, given individual preferences (in particular with respect to risk), affects future earning potential, as in the case of poverty trap phenomena.

  In the economic inequality literature, a key distinction is made between defining inequality in the space of circumstances and in the space of outcomes. This distinction clearly matters from the point of view of moral philosophy and normative economics.1 For some authors, only inequality of individual circumstances should matter, as they are, to some extent, forced upon individuals, and people are not morally responsible for them. Social justice thus requires these sources of inequality to be compensated in the outcome space, for instance through cash transfers. In contrast, outcome inequality that arises from individual decisions or efforts should not be a matter of social concern as it essentially results from individuals’ free will or preferences, so that individuals can be taken as morally responsible for them.2 The opposite stream of the literature rejects this distinction between circumstances and efforts on the basis of preferences being themselves partly transmitted to individuals by their families or the social group they belong to. If so, most outcome determinants may be understood as circumstances, and the correction of inequality should entirely focus on the distribution of final outcomes.

  At this stage, incentives must be taken into account. In the case where all determinants of outcome, including the taste for hard work, are considered as circumstances, compensating for all of them would lead to equalizing outcomes irrespective of individual actions and initiatives, thus eliminating work, entrepreneurship, or innovation incentives. In the case where only some income determinants are taken to be circumstances, compensating for differences in them and leaving uncorrected the inequality arising from individual decisions may not always be possible or efficient. In the case of labor market discrimination, for instance, we may know that women or children of immigrants are discriminated against on average, but it would be difficult, and certainly controversial, to establish this discrimination at the individual level. Even if it were possible, compensating through lump-sum payments those who are discriminated against would reinforce the market distortion created by discrimination, as people would get the same wage as before but would possibly expend less effort due to the lump-sum transfer. This is a clear case where inequality of opportunity is responsible for both inefficiency and inequality of outcomes, and where the only efficient corrective policy is to eliminate the market imperfection responsible for the inequality of opportunity in the first place.

  Ambiguity and Observability Issues in Defining Opportunities

  The framework shown in Figure 5.1, and the idea that inequality of opportunity could be compensated by transfers in the outcome space, has three fundamental weaknesses for practical application, in addition to the preceding inefficiency argument. First, there is a fundamental ambiguity about what can be defined as circumstances and individual decisions resulting from preferences supposedly independent of circumstances. Second, even if the distinction between circumstances and efforts were unambiguous, there is a problem with the fact that many circumstances and many efforts are not observable. Third, the relationship between opportunities and outcomes is actually two-way. If, at a point of time, inequality of opportunity is affecting inequality of outcomes when Figure 5.1 is read from left to right, the dotted array (8) in Figure 5.1 stands for the fact that inequality of outcome, possibly due to the free decisions of economic agents, may dynamically affect future inequality of opportunity. Taken together, these weaknesses justify focusing on the inequality of outcomes, while at the same time taking into account the sources of the inequality related to specific observable circumstances. These points are developed below.

  The first critique of the distinction between circumstances outside individual control and individual decisions reflecting independent personal preferences is precisely that it is difficult to hold that preferences are under individual control, as if they were freely chosen by people. An in-depth critique of that assumption has been made by Arneson (1989). Somebody’s taste for work, for thrift, or for entrepreneurship must come from somewhere, possibly from family background.3 If so, the distinction between the inequality in outcomes due to circumstances and due to individual decisions becomes fuzzy and practically nonoperational.

  The fact that many circumstances are not observed is another reason why the distinction between circumstances and efforts may have limited empirical relevance, at least as long as one is not ready to make several restrictive assumptions. Many circumstances that shape people’s professional and family trajectory are not observable. Yet they may affect individual decisions as well as outcomes. For instance, parents may transmit to their children values or talents that will make them decide to go to graduate school and at the same time will help them in their career. If those values and talents are not observed, however, how could we disentangle in observed outcomes what is actually due to observed efforts—i.e., graduate school—and what is due to unobserved circumstances? It is only when it can be assumed that efforts do not depend on unobserved circumstances that also affect outcomes that such identification is possible. If this is not the case, the contribution of efforts to outcomes cannot be properly identified, which makes again the distinction between circumstances and efforts somewhat artificial.4

  Another weakness of the distinction between inequality of opportunity and inequality of outcomes illustrated by Figure 5.1 is that, if outcomes are determined by circumstances and individual decisions, then outcomes at one point of time may determine future circumstances. As a matter of fact, the whole framework is set in static terms, when it should actually be dynamic. Outcomes of one generation or at one point of time are likely to affect circumstances in the next generation or at a future point of time, for instance, through accumulating or running down wealth or human capital, taken as a circumstance. Under these conditions, ignoring that part of the inequality of outcomes that comes from individual decisions implies ignoring a future source of inequality in the space of circumstances. It may also be noted that, in such a dynamic framework, the measurement of the inequality of outcomes raises some issues. If the unit of time is a generation, how should outcomes be defined? Certainly not by their value at a point of time. Within a dynamic intra-generational analysis, isn’t it the case that many “individual decisions” quickly become circumstances, so that again the distinction between circumstances and efforts yields limited insights?

  Summing up, the focus put by some moral philosophers and normative economists on inequality of opportunity rather than on inequality of outcomes may be perfectly justified in theory. Practically, however, the distinction that has to be made between factors that are under individual responsibility (efforts) and those that are not (circumstances) is most often blurred, in part because of observability issues. Even when relying only on observed circumstances and efforts, disentangling which part of inequality of outcome is due to one or the other is difficult upon admitting that observed and unobserved circumstances may affect both outcomes and efforts. Actually, the only solid empirical evidence that can be relied upon is the way outcomes depend on observed circumstances, i.e., essentially some personal traits and family-related characteristics.

  Measuring Inequality of Observed Opportunities

  Data on specific outcomes, some circumstances and, possibly, some types of efforts are available in household surveys or from
administrative sources. On the basis of that data, it is possible to estimate the relationship between specific outcomes, circumstances, and efforts.

  Before getting into the measurement of inequality of opportunity, or rather some dimensions of it, within these databases, it is worth formalizing that relationship and the arguments in the preceding section. Assume that a survey sample of the population is available with information on individual or household economic characteristics and background. Denote by yi the outcome of interest for an individual i in the sample; denote his/her observed circumstances by Ci; and his/her efforts by Ei. We can represent the way in which circumstances and efforts determine outcome by the relationship:

  where f( ) is some function to be specified below and ui stands for the role of unobserved circumstances and efforts as well as temporary shocks or measurement errors on the observed outcome. In empirical work, that relationship is often assumed to be log-linear:

  where a and b are vectors of parameters. Such a specification of the function f( ) is very restrictive, as one would expect some interaction between circumstances and efforts in determining outcome. Yet it is simple and quite sufficient for our purpose.

  The argument in the preceding section and in the annex at the end of this chapter suggests that Ei is correlated to the observed circumstances, Ci, and the unobserved circumstances, Ui. Because of the latter, it is thus not possible to get unbiased estimates of a and b. Under these conditions, the only empirical relationship that can be reliably estimated is a reduced-form model where the outcome depends only on observed circumstances:

  where α is a set of coefficients that describe the effect of observed circumstances on the outcome directly or indirectly through their correlation with efforts (observed or not observed), and vi stands for all outcome determinants different from observed circumstances. It should be noted, however, that for α to be estimated without bias, it is necessary to assume that all these unobserved outcome determinants are independent of the observed circumstances, Ci. Otherwise, the estimated α coefficients will also include the effects of all unobserved outcome determinants that are correlated in one way or another with Ci.

  Estimating models of type (2) through Ordinary Least Squares (OLS) is a trivial exercise that has been performed under a variety of specifications for the outcome variable, yi, and the explanatory variables, Ci. Perhaps the most familiar specification is the famous Mincer equation that includes the earnings rate of employed people as the outcome variable, and schooling6 and personal traits as explanatory variables.

  There is a burgeoning literature on the measurement of inequality of opportunity based on models of type (1) or (2). Using model (1), it essentially consists of comparing the actual inequality in outcomes to the inequality that would be observed if all individuals in the data sample were facing the same circumstances, or were all expending a given level of effort. This literature is exhaustively summarized in Ramos and Van de Gaer (2012) and Brunori (2016). We take here a simpler approach based on the fact that efforts are either not observed or endogenous—i.e., correlated with unobserved outcome determinants—so that model (2) is the only solid basis to measure the inequality of opportunities described by the variables in Ci.

  It can be noted that, in some cases, it is possible to measure the inequality of single components of C irrespectively of outcomes and model (2). For instance, parental income or cognitive ability may be components of C, the inequality of which can be observed in some databases.7 The higher the inequality of a component of C, the more unequal the distribution of outcomes, provided that the corresponding coefficient in α is strictly positive.

  The inequality of the distribution of C may also be expressed in terms of the inequality of outcomes. When the latter is measured by the variance of logarithms and when there is a single component in C, model (2) implies that:

  Thus, the inequality of that single component of C can also be expressed as what could be the inequality of outcomes if other determinants of outcomes were neutralized, i.e., in the case where they were the same for all individuals. If the inequality of outcomes is measured by the variance of logarithms (VL), the inequality of C, I VL (C), could in that case be written as:

  and

  when there is more than one component in C.

  This definition can be generalized to any measure of outcome inequality M{ }—i.e., Gini, Theil, mean logarithmic deviation—and to any number of components in C in two ways.

  First, define the “virtual” outcome, for every individual i, as what would be the outcome of that individual if all the outcome determinants other than the opportunities in C were equal to some exogenous value, ve, common to all, i.e.:

  Then compute the measure of inequality M{ } on the distribution of in the whole sample. An absolute measure of the inequality of opportunities in C is then given by , where stands for the whole distribution of in the sample. Fleurbaey and Schokkaert (2012) labeled this measure the “direct unfairness” (du) of the inequality of opportunity associated with C:

  Thus, measures the inequality of opportunities in C by considering their impact on the inequality of outcome, irrespective of all other outcome determinants. Of course, a measure of inequality of opportunities in C can be defined for each measure M{ } of outcome inequality. As most outcome inequality measures M{ } are scale invariant, the arbitrary value of ve does not actually matter.8

  Second, one may use the “dual” of the preceding definition of inequality of opportunities in the following sense. Instead of equalizing the outcome determinants other than C, one may define a virtual income resulting from the equalization of the opportunities in C across all individuals in the sample. Let Ce be the common value of opportunities and the corresponding virtual income:

  Then another absolute measure of inequality of opportunities in C may be defined for any outcome inequality measure M{ } as the difference between the actual inequality of outcome and that which would result from equalizing circumstances among all individuals in the sample. Fleurbaey and Schokkaert (2012) proposed to label this the “fairness gap” (fg) measure of inequality of opportunity associated with C:

  As before, this measure is independent of the arbitrary value, Ce, taken for opportunities when the outcome inequality measure is scale invariant.

  Both measures of inequality of opportunities may also be defined in “relative” terms by expressing them as a proportion of the actual inequality of the outcome being studied, M{y.}. They will be denoted respectively and .

  The preceding notations may seem complicated. Their interpretation is extremely simple and intuitive when applied to actual data, as illustrated by the following remarks.

  1. Consider equation (2) as a standard regression equation of outcomes on a set of observed opportunities, with the unobserved outcome determinants, v, as the residuals of the regression. Then, if the inequality measure of outcome M{ } is the variance of logarithms, then both the direct unfairness (5) and the fairness gap measures (7) are equal to the variance of the logarithm of outcome explained by the opportunities C, and the corresponding relative measure is simply the familiar R2 statistic associated with regression (2).

  2. Consider now the individual “types” defined by combinations of the variables in C with a minimum number of observations. For instance, with only gender in C, there would be two types. With gender and two possible values for the education of the parents, there would be four types: men from low-education parents, women from high-education parents, etc. It turns out then that the direct unfairness inequality of opportunity (5) is very close to the familiar between group inequality of outcomes when groups are defined by types, except that the inequality is defined on the mean of the logarithm of outcomes rather than on the outcome means.9

  3. The preceding expressions to evaluate the inequality of observed opportunities refer to the linear case, where the opportunities being considered have independent effects on the outcome of interest. Of course, it is also possible to take into account i
nteractions between opportunities as, for instance, between gender and education in explaining the inequality of earnings.

  4. When considering types, the above formulas seem to leave little room for the inequality of outcomes within types. This is not completely true since the outcome inequality between types corresponding to (5) is not the same as the inequality between the types’ mean outcomes, the difference depending on the distribution of outcomes within types. An approach that takes more explicitly into account outcome inequality within types is the inequality of opportunity measure that can be derived from the principles set in Roemer (1998):

  where q1(π) is the outcome of the quantile of order π in the outcome distribution for type t, (π) is the (weighted) mean of those quantiles across types, and y−1,i is the overall mean outcome. In other words, inequality of the opportunities defined by types is the mean across quantiles of a Rawlsian type of inequality measure across types for each quantile.10

  The preceding inequality measure corresponds to the case where the residual term, v, in (2) is heteroskedastic with a distribution, and hence a variance, that depends on the observed circumstance variables, C, or differs across types. This is perfectly consistent with the usual assumptions that the residual term v has zero expected value and is orthogonal to C. With heteroskedasticity, however, defining the inequality of opportunity through (5) or (7) is not possible anymore. The definition of the virtual income in (4) ignores the dependency of the residual term on C, and the equalizing of circumstances in (6) should require modifying the vi. term, so that its distribution does not depend on C anymore or, equivalently, is the same across types.