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  Figure 5.5 illustrates this approach to inequality of opportunity, drawing on a paper by Brunori, Ferreira, and Peragine (2013) that puts together estimates of some observed dimensions of inequality of opportunity in selected countries as reported in several papers, including Checchi, Peragine, and Serlenga (2010) and Ferreira and Gignoux (2011b). The inequality of opportunities measure used in these papers is the one defined in (5), with the mean logarithmic deviation as a measure of inequality.28 The figure shows the relative inequality of observed opportunities (vertical axis) against the total inequality of outcomes (horizontal axis).

  Figure 5.5. Inequality of Outcomes and Share Due to Observed Dimensions of Inequality of Opportunity, Selected Countries Around 2005

  Source: Based on Brunori, P., F. Ferreira, and V. Peragine (2013), “Inequality of opportunity, income inequality and economic mobility: Some international comparisons,” IZA Discussion Paper, No. 7155. StatLink 2 http://dx.doi.org/10.1787/888933839620.

  Figure 5.5 is in some sense the equivalent of the Great Gatsby curve, with the IGE being replaced by the inequality of observed opportunities.29 This generalization of the Great Gatsby curve, which consists of replacing parental earnings by observed parents’ characteristics and individual traits, leads to a relationship between inequality of observed opportunities and inequality of outcomes that is still positive. However, that relationship disappears when restricting the sample to advanced countries, unlike what is observed in Figure 5.3.

  This difference must be taken with very much precaution, though. On the one hand, countries are not the same. On the other hand, both the outcome variables and the observed circumstances Z in Brunori, Ferreira, and Peragine (2013) may not be the same across countries. The economic outcome, y, refers to labor earnings for the EU countries and the United States,30 household income per capita in Latin American countries, household earnings per capita in India, and household gross income per capita in South Africa. An important lesson to be drawn from these exercises is the need to use uniform definitions of variables. This is not always possible across countries, but is absolutely necessary for comparing the same country over time.

  Another important caveat is that the inequality of observed opportunities reported in Figure 5.5 is estimated on the whole population rather than on specific age cohorts as in studies of inter-generational earnings mobility. In other words, the implicit assumption is that this inequality is uniform across age groups, or cohorts, in national populations. This is far from granted. The way an economic outcome depends on individual and parental circumstances may change over the life cycle, and may change across cohorts. Cohorts are definitely the most relevant statistical reference. What policy-makers and analysts are interested in is whether younger cohorts are less dependent on their family background than older cohorts, presumably at the same age.31

  Improving and standardizing generalized mobility analyses of the type described above—to make them comparable across countries, over time, and across cohorts—might be easier to implement than standardizing inter-generational earnings mobility studies. It should permit key determinants of the inequality of outcomes to be monitored effectively—be it earnings, income, or subjective well-being—and to identify forces behind the evolution of the inequality, or possibly behind its stability. Done in a systematic way, such analyses should be most helpful for policy-making in the field of inequality.

  It should also be noted that the same nonparametric matrix specification used for inter-generational mobility analysis can be used here. The matrix P in Table 5.1 would differ simply by the definition of the rows. Instead of referring to the earnings of parents, they would refer to types of individuals in the current generation, the types being defined by the most frequent combinations of individual characteristics, Z. This would not be a mobility matrix or a copula anymore but simply a matrix comparing the distribution of a given economic outcome across individuals with different social and family background or individual traits. The corresponding inequality of opportunity could be measured using the Roemer-like measure (8) above or some of the suggestions made when discussing the measure of inter-generational mobility.

  Sibling Studies

  Other approaches have been used in the literature to identifying what part of the inequality of outcomes has its roots in family background in the strict sense, rather than in the mixed bag of characteristics, Z, that can be found in household surveys. In this context, the idea of using differences or similarities among siblings or twins is particularly attractive.

  If the economic outcome being studied is labor earnings, the square of the correlation coefficient of earnings between siblings is a direct measure of the share of the inequality of outcomes that comes from a common family context. This requires some assumptions on the underlying earnings model.32 If these assumptions are found to be reasonable, then this correlation coefficient logically accounts for all observed and unobserved family background characteristics as well as presumably for other circumstances that were common to siblings in their childhood or adolescence. Because of this, it is expected that the share of outcome inequality explained in this way be higher than that of other estimations based on observed circumstances, even though siblings may not share all the family background factors susceptible to affect their earnings later in life. At first sight, however, orders of magnitude seem comparable to what is obtained in inter-generational earnings mobility studies—in the few countries where both estimates are available. For instance, the correlation coefficient between brothers’ earnings is 0.23 in Denmark (Jäntti et al., 2002) and 0.49 in the United States (Mazumder, 2008). The former value is somewhat above what is shown in Figure 5.4, whereas the latter is roughly the same.

  Sibling analysis of this type may well be able to capture a bigger part of the overall effect of family circumstances on outcome inequality but, contrary to the type of study described in the preceding sub-section, it does not say much about the channels behind this effect. Also, this type of analysis cannot be performed on the basis of standard household surveys, which are the most commonly used source for measuring outcome inequality.

  Outcome Inequality Related to Gender or Other Personal Traits

  The characteristics Z considered in the generalized inter-generational mobility approach may be of different kinds. They may be personal traits like gender, ethnicity, or migrant status, family background characteristics, or more generally the assets people may have received from their family, including schooling. The analysis of the inequality of observed opportunities discussed above did not make any distinction between these various components of Z. Yet the inequality associated with them may be subject to different value judgments and may have different policy implications in terms of the inequality of outcomes.

  Gender is a case in point. If gender were the only component of the Z variables in the general model (11), then the associated decomposition of inequality would boil down to singling out the relative difference in the mean outcome across genders. This is the first step in the literature on gender earnings inequality, and more generally on “horizontal inequality,” i.e., inequality in the mean outcomes of people with different personal traits (for example race, migrant status, or place of residence). Figure 5.6 on gender earnings inequality is typical of that literature. It shows how the male-female earnings differential fell substantially over the last decades in the OECD countries where it was the highest, but remains sizable, at around or above 15%, in a majority of countries.

  At the same time, this figure raises questions that are directly related to the distinction between circumstance and effort in the inequality of opportunity literature. To what extent is the observed earnings differential due to different occupational and career choices made by male and female workers, or to features completely outside their own control, like education or, most importantly, employer discrimination in the labor market? Also, to what extent do the differentials shown in Figure 5.6 reflect differences in labor force participation rat
es, themselves related to wage determinants like age or job experience? The answer to these questions is of great importance for policy, in particular to identify the role of labor market discrimination and the possible remedies to other sources of earnings inequality. For instance, concluding from Figure 5.6 that gender earnings discrimination has gone down by 15 to 20 percentage points in countries where it was around 45% 40 years ago would not be correct if the composition of the female (or male) labor force had changed over time or if the proportion of better paid women increased.

  Figure 5.6. Gender Wage Gap in Selected OECD Countries, 1975–2015

  Source: OECD (2018), OECD Earnings: Gross earnings: decile ratios (database), https://doi.org/10.1787/lfs-data-en. StatLink 2 http://dx.doi.org/10.1787/888933839639.

  Part of the answer to the questions mentioned above is obtained by adding other personal traits and circumstances to gender as regressors in model (11). For instance, if schooling is introduced as an additional circumstance variable, the coefficient of the gender component would then reflect the male-female difference in earnings once the effect of male-female differences in schooling on the earnings differential had been accounted for. In a more general model, the gender coefficient would measure the gender earnings gap that comes in addition to gender differences in all observed earnings determinants. This coefficient is generally referred to as the “adjusted” gender earnings gap.

  It is possible to go further by making the model nonlinear through interactions between gender and the other components of Z, namely:

  where Gi is a dummy variable that stands for the gender of person i and the δ coefficients measure the earnings differential associated with the individual characteristics in Zi. Alternatively, model (12) can be estimated separately for male and female workers:

  On the basis of the estimates of the two sets of coefficients ßg, the gender earnings gap may be decomposed into gender differences in the earnings determinants and differences in the return to these determinants, i.e., between the estimated coefficients and . For instance, women may be paid at a lower rate than men because they have less education, which was true for some time and still is for older cohorts, but they may also be paid less than men for any additional year of schooling, which might be considered as pure discrimination.

  Formally, this so-called Blinder-Oaxaca decomposition is:

  where the notation ¯ refers to means, and nF and nM are the weight of female and male workers respectively in the population sample. The first term corresponds to the contribution of differences in individual characteristics between men and women, i.e., the difference between the earnings gap and the adjusted earnings gap defined above. The second term stands for the true discrimination, i.e., the fact that the same characteristics are not rewarded in the same way among men and women. Actually, it is precisely the adjusted earnings gap defined earlier, the interest of (14) being that this adjusted gap can be decomposed into the contributions of the various components of Z. In the context of gender inequality, this adjusted gap may be considered as a measure of procedural inequality, i.e., the way the same characteristics are not rewarded in the same way for two groups of individuals.

  Figure 5.7 illustrates this decomposition and at the same time exhibits quite a remarkable stylized fact. The figure is drawn from a meta-analysis of gender wage discrimination and shows the mean gender earnings gap and the adjusted earnings gap in a set of 263 papers covering a large number of countries at different points of time. The figure reports the means of all studies reporting estimates for a given year, year by year. A remarkable pattern emerges. Over time, the mean gender wage gap has declined substantially, as shown in Figure 5.6 for selected countries. At the same time the mean adjusted gap, or the second term in the Blinder-Oaxaca equation above, remains more or less constant on average. In other words, on average across countries, the main reason why the gender earnings gap declined is because the gender differences in wage determinants like education or job experience have declined, not because the returns to these determinants have become less unequal. Assuming the studies in this meta-analysis are fully comparable, this would mean that the inequality of opportunity related to labor market discrimination has not changed in the average country.

  Figure 5.7. Gender Earnings Gap and Adjusted Earnings Gap in a Meta-analysis of the Literature

  Source: Weichselbaumer, D. and R. Winter-Ebmer (2005), “A Meta-analysis of the international gender wage gap,” Journal of Economic Surveys, Vol. 19(3), pp. 479–511.

  From a policy point of view, the Blinder-Oaxaca equation is of obvious interest since it shows the orientation to be chosen in order to reduce gender inequality, and therefore total earnings inequality. From a perspective of inequality of opportunity, however, it also raises an interesting issue, which is that focusing exclusively on circumstances as the source of inequality may not always be justified. The way efforts are rewarded by the economic system, depending on individual circumstances or personal traits, matters too.

  As an example, consider the standard Mincer equation that explains the log of earnings or wages as a function of the number of years of schooling and job experience. A priori, it seems reasonable to consider years of schooling as a circumstance forced upon an individual by parents or family context, whereas job experience would more logically reflect decisions made by a person in adult life. But now, assume that the Blinder-Oaxaca decomposition shows that both education and job experience are rewarded differently for male and female workers. Then, the inequality of opportunity arising from labor market discrimination would actually depend on the inequality of circumstances—i.e., education—but also on efforts through the interaction between efforts and gender. In other words, the fact that a woman must make more effort to earn as much as a man with the same intrinsic productivity should be part of the inequality of observed opportunities.

  Having said this, there remains the issue of the fundamental ambiguity of the distinction between efforts and circumstances. Are interruptions to job, labor force participation, and career caused by child rearing only the responsibility of women? Wasn’t it society as a whole that constrained women’s labor force participation and progressively relaxed that constraint under various economic and sociological pressures? These are difficult questions, which at the same time reveal the ambiguity of the very concept of gender-related inequality of opportunity and the measurement of it.34 Under these conditions, it might be better to ignore the distinction between circumstances and effort and to make sure that we measure correctly the effect on the overall inequality of earnings of different personal characteristics, including job experience or part-time work, across gender, as well as the effect of differentiated rewards to these characteristics by the economic system.

  To conclude these remarks on the measurement of the inequality of opportunity related to gender, the fact that the earnings gap or adjusted earnings gap refers exclusively to averaging operations within the two samples of male and female workers must be stressed. The fact that the spread of earnings rates around the mean may be quite different in the two groups should also be taken into account. In relation to model (11), this is equivalent to allowing for the variance of the residual term, v, to depend itself on gender, i.e., heteroscedasticity. This is a good case for using the Roemer measure defined in (8), or to follow the suggestion made above to replace the mean earnings by some function of the mean and the variance.

  Overview of Practical Issues

  Measuring inequality of opportunity, seen as the inequality of outcomes due to all factors completely outside individual control, seems unrealistic. The best that can be done is to measure the contribution to inequality of outcomes of some factors that seem beyond individual responsibility. In that sense, it is only possible to measure some dimensions of the inequality of opportunity. Yet even the distinction between circumstances outside individual control and voluntary individual decisions in the determination of economic outcomes is often ambiguous. Indeed, some dimensions of
inequality of opportunity depend on these individual decisions, as is the case with discrimination within the labor market.

  It is possible to measure directly some dimensions of inequality of opportunity, independently of their impact on economic outcomes. This is true, for instance, of cognitive ability, in adolescence or pre-school, potentially of noncognitive ability if some quantitative index is available,35 or of health status. Note also that these individual characteristics may be considered as circumstances contributing to the inequality of individual outcomes like earnings or standard of living, but also as an outcome whose inequality may be explained by family-related characteristics. Most often, however, measuring the observable dimensions of the inequality of opportunity goes through the measurement of their impact on the inequality of economic outcomes.

  The most obvious example of the measure of single dimensions of inequality of opportunity is the sizable literature on the inter-generational mobility of earnings, or other economic or socio-economic outcomes. The observed dimension of inequality of opportunity is the earnings of parents, and it is measured by its contribution to the inequality of children’s earnings. This can be generalized to other observed family characteristics that may or may not include parental income or earnings, as well as personal traits like gender or ethnicity. Data requirements for this kind of analysis are much less demanding than what is needed for measuring the inter-generational mobility of earnings. Representative household surveys with recall information on the family background of respondents are the basic input. Of course, monitoring the corresponding dimensions of the inequality of opportunity over time or making comparisons across countries requires some uniformity of the information available in these surveys.