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When applied to single personal traits, the preceding type of analysis is equivalent to measuring what is called “horizontal inequality” in the inequality literature, typically inequality of earnings or other income variable across gender, race, migrant status, or other individual characteristics. Combined with other individual circumstances that may depend themselves on individual traits, the measurement of these dimensions of inequality of opportunity allows for a detailed analysis of the observed discrimination that society exerts on individuals through the traits being studied.

  The empirical literature on inequality of opportunity relies on various types of measures. When focusing on single scalar dimensions of the inequality of opportunity, it is not clear that the various measures available for economic outcomes—which are implicitly based on value judgments—are relevant. For instance, is the Gini coefficient adequate to represent the inequality of health status or cognitive ability? The variance, the coefficient of variation or quantile ratios may be sufficient to describe the spread of the distribution. Things are different when the observed dimensions of inequality of opportunity are measured in the outcome space, or by their contribution to the inequality of outcomes. In that case, a distinction must be made between parametric and nonparametric approaches.

  A parametric specification of the relationship between outcomes and individual characteristics allows us to figure out what the inequality would be if only outcome differences due to individual characteristics were taken into account; or, alternatively, what difference ignoring them would make with respect to the overall inequality of outcomes. Then the resulting “virtual” outcome inequality can be evaluated by the usual measures of outcome inequality, including the Gini coefficient, the variance of logarithms, and the Atkinson measures. Based on the familiar log-linear relationship between economic outcomes and individual characteristics, this approach often leads to quite simple measures of the observed dimensions of the inequality of opportunity: the R2 correlation coefficient when outcome inequality is measured with the variance of logarithms; the between-group component of decomposable inequality measures when the observed combinations of individual characteristics are used to define types of individuals; or the mean income gap in the case of a single individual trait like gender. Of course, as many measures of inequality of opportunity can be defined as there are measures of inequality of outcomes.

  Things are different with nonparametric specifications that fully take into account the difference in the distribution of outcomes conditional on individual type. This includes the case where types correspond to the level of parental income as the dimension of the inequality of opportunity being studied, and where the inter-generational mobility of outcomes is described through a transition matrix; in these cases, comparing distributions requires comparing those matrices. Some interesting comparison criteria have been proposed that generally rely on strong assumptions about the way the social welfare of a society characterized by a given transition matrix is evaluated. At this stage, it cannot be said there is a consensus about these criteria.

  The case where the overall inequality of outcomes is shown to result from different outcome distributions across various types of people, defined by a set of characteristics assumed to be outside their control, is the most general and realistic specification on which to ground the measurement of the observed dimensions of inequality of opportunity. It is equivalent to the parametric specification when the distribution of the effects of unobserved determinants of outcomes depends on the individual characteristics under study, i.e., heteroscedasticity in the core specification. Most measures used in the literature ignore this aspect of the measurement problem. For instance, the adjusted gender earnings gap ignores the fact that not only the mean but also the distribution of earnings expressed as a proportion of the mean differs across gender. The inequality measure drawn from Roemer (1998) would allow to remedy this.

  Conclusions

  Until now, concern about inequality focused mostly on inequality in key outcomes like earnings, gross or disposable income, standard of living, or wealth. Monitoring inequality of outcomes, or inequality ex post, is crucial to monitor social progress and redistribution instruments. Ideally, however, one would also want to monitor ex ante inequality, or inequality of opportunity, as it is a key determinant of ex post inequality. As argued throughout this chapter, however, there is something illusory in such an objective. The best that can be done is to monitor the observed dimensions of inequality of opportunity, or equivalently some determinants of inequality of outcomes that can be considered not to be the result of individual decisions or economic behaviors. Of course, such monitoring is of utmost importance for policy as it permits the sources of change in the distribution of the outcome considered to be identified and to adopt corrective policies if deemed necessary. These sources of change comprise the distribution in the population of individual characteristics like individual traits, family background including parental income or wealth, cognitive and noncognitive abilities, and all assets people can rely on to generate economic outcomes. They also include the way in which the economic sphere rewards the efforts of people with different traits or background, i.e., procedural inequality.

  While some observed dimensions of the inequality of opportunity have received much attention in the recent economic literature, it is fair to say that their measurement still belongs to the realm of research. Unlike the inequality of disposable income or earnings regularly monitored through Gini coefficients or other inequality measures, few statistics related to inequality of opportunity are regularly produced by statistical institutes and publicly debated. For instance, we are ignorant in most countries about whether inter-generational mobility, one among many possible indicators of inequality of opportunity, has increased, remained the same, or decreased in the last decades. Progress has been made in monitoring mean educational achievements in many countries, most notably under the PISA initiative, but no systematic reporting or discussion takes place on the evolution of their dispersion. If the mean earnings gap across gender is reported regularly in most advanced economies, the same cannot always be said of the adjusted earnings gap or the gap across ethnic groups or between natives and first- and second-generation migrants. Yet, in most countries, data to evaluate these indicators on a regular basis either are available or could be made available at little cost.

  Building off the analysis in this chapter, we list below the data required to improve the situation and monitor the observable dimensions of the inequality of opportunity in a systematic way rather than relying on the work done irregularly by researchers. We also list the statistics that should be published on a regular basis for a monitoring of inequality that would go beyond the Gini coefficient or other usual inequality measures of equivalized disposable income or earnings.

  Data Requirements

  Knowledge of the role that family background plays in determining inequality of earnings or income is essential for understanding the causes of inequality and possible changes in them. From that point of view, the ideal data by far are long-term panels such as the PSID in the United States, which has been running since 1968 and covers 5,000 families and all their descendants. With such long panels, one may observe many of the circumstances that surrounded the childhood and the adolescence of the younger cohorts of the panel, including parental income and wealth. Other long panels include the British Household Panel Study (BHPS) and the German Socio-Economic Panel. In Europe, the EU-SILC comprises longitudinal data but these are generally much shorter and do not follow descendants, so that family economic conditions during the youth of respondents are not observable.36

  An alternative to long panels is the linkage of administrative data. Matching the tax returns of parents 30 years ago to that of their 40-year-old children today allows for the direct observation of income mobility. In some cases, it is even possible to link family characteristics other than income, thus allowing for more complete studies of the inter-generational sources of inequal
ity. As established above, such data permitted detailed studies of the inter-generational transmission of wealth in Nordic countries and of the spatial heterogeneity of inter-generational mobility in the United States—as in Chetty et al. (2014a). Unfortunately, data such as these are still extremely scarce, even though steps could be taken by administrations to make them more systematically available in the future.

  It is not because long panels are not always available that it is impossible to monitor the role of family background in generating inequality in economic outcomes. Repeated standard cross-sectional household or labor force surveys with recall information on the family characteristics of the respondents already allow for monitoring the impact of family background on the inequality of earnings, income, or standard of living. What is needed is to make sure that such information is available at regular time intervals and under the same, and possibly the most complete, format. It should not be too difficult to establish international norms in this area. Possible biases arising from the imperfect observation of top incomes in these data sources should not be ignored, and measures to prevent such biases should be seriously considered.

  Some of the studies reviewed in this chapter show the use that could be made of such information (Figure 5.5). Note also that in a given cross-section, it is possible to conduct the analysis at the cohort level. The way the earnings of the 40- to 50-year-old depend at a given point of time on their family background is not the same as for the 30- to 40-year-old or the 50- to 60-year-old. With repeated cross-sections, it would then become possible to distinguish the cohort and the age effect. Finally, note that if the repeated cross-sections cover a long enough period, which is now the case in many advanced countries, then it is possible to use family background variables as instruments to estimate the earnings or income of parents, thus allowing for some monitoring of inter-generational income mobility, as in the study by Aaronsson and Mazumder (2008) mentioned earlier.

  In the field of the inequality of wealth, cross-sectional data are scarcer, although several countries are now following the example of the Survey of Consumer Finances in the United States and its practice of oversampling the top of the distribution, where most wealth is concentrated. These surveys are extremely useful and one may only hope they will become more frequent. In particular, it would be interesting to investigate in more depth how it would be possible to monitor the role of bequests in generating wealth and income inequality, especially at a time where inheritance flows tend to grow faster than income, as suggested by Piketty (2014).

  Horizontal inequality across gender and other personal traits can be followed through standard household or labor-force surveys. Here, the problem is not so much the availability of data as the use being made of them and the depth of the analysis conducted. As shown above, there is much to be learned from going beyond pure differences in earnings means. At a time where migration has become such an important issue in so many countries, data for monitoring the differences that natives and migrants face in the labor market should also be made available.

  Students’ skills surveys at various stages in childhood and adolescence, such as those assessed by PISA, are extremely helpful for detecting changes in a dimension of inequality of opportunity that is likely to entail changes in the inequality of outcomes later in life. PISA is a mine of information, although it was suggested above that more emphasis should be put on the inequality of test scores—on top of their differences across family backgrounds. Also, developing PISA-type instruments to measure inequality in cognitive abilities at younger age levels, including pre-school, is essential. For primary school, the data seem to exist, and it is perhaps only a matter of analyzing them in more detail, and certainly publicizing them better.

  Priority Statistics

  These data could and probably will generate many different types of statistics, related to various specific dimensions of the inequality of opportunity. It is important to define those that are likely to be the most useful in assessing social and economic progress, the most amenable to stimulating discussion among researchers, policy-makers, and civil society, and the most likely to be available in a timely manner in a reasonably large number of countries.

  The lack of knowledge today in many countries of whether inter-generational mobility is increasing or decreasing is symptomatic of the data deficit and, until now, of the lack of interest by policy-makers and statisticians in monitoring key sources of outcome inequality beyond inequality itself as measured by the usual inequality indices. Yet the social demand for such information is mounting.

  Three basic statistics should receive priority attention and should be harmonized as much as possible across countries and over time within countries:

  • Inequality of economic outcomes (earnings, income) arising from parental background and its share in total inequality of outcome. Variance of logarithms of outcomes among various types of individuals and the R2 statistics of family background variables (at least education, occupation, and age of the parents at respondent’s birth) in explaining outcomes are the simplest examples of such statistics. Statistical institutes could seek to publish these statistics at 5-year intervals, possibly distinguishing across 5-year cohorts. Reflection should start about the key family background variables that could be systematically included in the analysis so as to develop international and inter-temporal comparability.

  • Variance analysis of scores in PISA and analogous surveys at earlier ages, including pre-school, and the share of it explained by parental/social background, or the gaps in scores between students from different families. The 3-year periodicity of PISA seems adequate.

  • Gender inequality in earnings, unadjusted and adjusted for differences in education, age, job experience, occupation, etc. Mentioning gender differences explicitly in basic coefficients like the return to education or to job experience, or simply showing both the unadjusted and the adjusted gaps as in Figure 5.7 would be helpful. This could be done easily for gender, although this again requires defining standards to allow for comparability. Depending on the country, the same type of analysis should also be performed for race, religion, or migrant status.

  Concerning the nature of the statistics to be released, the simplest option would be to rely on the parametric approach emphasized in this chapter and on the measures it leads to, as they are easily understood. But extending them to the nonparametric case, where the observed dimensions of the inequality of opportunity are represented in matrix form of individual types by outcome level, would also be desirable.

  Annex: The Difficulty of Empirically Disentangling the Role of Opportunity and Effort in the Determination of Earnings

  Consider a database with information on individual earnings, circumstances, and efforts and a linear model where (log) earnings of individual i, Log yi, depends on the circumstances, Ci, and efforts, Ei, of the same person, both vectors being split into observed (Ci1, Ei1) and unobserved (Ci2, Ei2) components:

  where ui summarizes all the other determinants of earnings, including luck and measurement error, and where a, b, and c are parameters, or vectors of parameters.

  While a specification with interactions between circumstances and efforts would be more general, the points made below would be equally relevant with a more complete model—but a bit more intricate from a notational point of view.

  Rearranging the terms in the preceding equation leads to:

  Where, without loss of generality, the residual terms, Ei, may be assumed to have zero expected value for each observation in the sample.

  The objective is to estimate the two sets of coefficients b1 and c1 so as to disentangle the role of observed circumstances and efforts in observed earnings. To do so with standard Ordinary Least Squares would require the residual, ε, to be independent of the explanatory variables C1 and E1. This is problematic, however. Indeed, it is to be expected that the efforts expended by people to increase their earnings depend on the circumstances they face. This can be formalized as:
<
br />   where θi1 and θi2 stand for other determinants of efforts, presumably independent of circumstances, but possibly mutually correlated. Substituting (3)-(4) into (2), it appears that εi is correlated to observed circumstances Ci1 and observed efforts Ei1 through unobserved circumstances and efforts, even when both are assumed to be orthogonal to their observed counterparts.

  It follows that equation (2) cannot be estimated without a bias, and that disentangling the role of efforts and circumstances in the determination of earnings is generally impossible.37

  This may not prevent estimating the total effect of observed circumstances on earnings. Substituting (3) and (4) in (2), gives:

  with:

  For the residual term, ωi, in (5), to be independent of the observed circumstance variables in C1 it must be assumed that the unobserved circumstances and efforts E2 and C2 are orthogonal to observed circumstances. If this is not the case, this means that the coefficient γ in (5) accounts not only for the effects of observed circumstances, both directly and through efforts, but also for that part of unobserved circumstances and efforts correlated to observed circumstances.

  Practically, parametric empirical analyses of inequality of opportunity are based on a model of type (5). This lessens the relevance of some of the theoretical measures of inequality of opportunity proposed in the literature, and justifies focusing on measures that can be derived from the reduced form (5) as shown in the main text.

  Notes

  1. This paragraph briefly summarizes an important literature in economics and in moral philosophy, which started with Rawls (1971) and whose major contributions are from Dworkin (1981), Arneson (1989), Cohen (1989), Roemer (1998), and Fleurbaey and Maniquet (2011).

  2. This conclusion somewhat resembles Sen’s emphasis on the “equality of capabilities” rather than “equality of functionings,” at least when capabilities are defined as the set of functionings accessible to an individual (Sen, 1980, 1985). Interpreting functionings as a vector of outcomes, Sen’s “capability equality” concept, similar to the concept of “equality of access to advantage” in Cohen (1989), would consist of equalizing the determinants of the set of accessible functionings, which are conceptually very similar to “circumstances” in the “equality of opportunity” framework. The only difference is that equalization in that case would be through equalizing those circumstances rather than compensation in the space of outcomes.