Chapter 5. Inequality of opportunity

Cognitive ability as an opportunity and as an outcome

The PISA initiative by the OECD provides first hand data to measure inequality in one of the most important dimension of individual circumstances: cognitive ability. It now gathers the scores of samples of 15-year old students in more than 70 advanced and emerging economies in three tests: one on reading, i.e. answering questions about a short text; one on mathematics; and the third on science. This instrument has been fielded at 3-year time intervals since 2000. In addition to students’ answers to these assessment tests, the database also reports information on their family background and on the characteristics of their schools.

Considering PISA scores as circumstances implicitly supposes looking at cognitive ability at age 15 as one of the important determinants of future individual economic outcomes, earnings in particular, and acknowledging that it essentially depends on genetic factors and the family context. People cannot be held responsible for that part of their life, so that inequality of PISA scores among 15 year-olds today will be responsible for some of the inequality of opportunity they will face later in their lifetime. But PISA scores may also be seen at the outcome of the educational process and, as such, dependent on family circumstances, the efforts of the children, and the educational system itself.11 Hence the debate on how schools may correct for the inequality of opportunity arising from family background. It is however the former perspective, i.e. cognitive scores as a circumstance, that is discussed in what follows.

Much publicity is given at each new edition of PISA to mean scores by country, to the ranking of countries and how rankings change over time. From the viewpoint of measuring inequality of opportunities, however, what matters most is the statistical distribution of these scores, or their disparities across students.

Figure 5.2 plots the inequality of PISA scores in mathematics, as measured by the coefficient of variation, against the mean score in the 2012 exercise for OECD countries. Interestingly, there is a clear negative relationship between the inequality and the mean of scores (putting aside the three emerging economies, Chile, Mexico and Turkey where the coverage of the PISA survey is much lower than in advanced countries, essentially because a non-negligible proportion of 15 year-olds have already dropped out of school).12 This is presumably because better mean scores are logically obtained by improving more the lower than the upper tail of the distribution. Yet what may be more important is the substantial difference in the inequality of scores for countries in the same range of average scores. For instance, inequality is 30% higher in Belgium than in Finland or Estonia, in the upper part of the scale of mean scores; the same holds true for France compared to Denmark in the middle.

Figure 5.2. Mean and coefficient of variation of PISA mathematics scores in OECD countries, 2012

Source: OECD (2014), PISA 2012 Results: What Students Know and Can Do, https://doi.org/10.1787/9789264208780-en.

 StatLink https://doi.org/10.1787/888933839582

Cognitive ability can be considered as a dimension of economic opportunity only insofar as it is a significant determinant of an outcome like earnings or the standard of living of an individual. In this respect, it is important to stress that test scores in surveys like PISA, the OECD’s Survey of Adult Skills (PIAAC) or its predecessor (the International Adult Literacy Survey, IALS) only explain a limited part of earning differences across individuals. Murnane et al. (2000) and Levin (2012) make this point on the basis of US data. According to the former, a 1% increase in high school test scores entails a 2% increase in earnings when students are 31 years old, which is substantial.13 However, the variance of adults’ (log) earnings explained by high school test scores is small, slightly less than 5% for men (Murnane et al., 2000, p. 556). Family background is a more powerful determinant of earnings, all the more so when considering that test scores are very much dependent on the education and income of parents.

Instead of cross country comparisons as in Figure 5.2, it would be interesting to see how inequality, or more exactly the whole distribution of scores, changes over time in a given country. Data reported by the OECD in 2012 include the 90/10 inter-decile and 75/25 inter-quartile ratios for the four exercises since 2003. These measures are remarkably constant except for emerging economies where inequality goes down at the same time as mean scores go up due to the lower tail moving up. France is one of the few advanced countries where the 90/10 inter-decile ratio increased significantly over time. As France’s mean score did not change much, this would suggest that good performers do better and bad ones do worse, possibly a clear sign of an increase in inequality of that specific component of opportunities. A careful study of the evolution of the whole distribution of test scores country by country might reveal other interesting features. It is surprising that so much emphasis is being put on the evolution of the means without considering distributional features.

The same kind of analysis, based on different tests, is being performed at younger ages by a number of organisations, for instance the Progress in International Reading Literacy Study, led by the International Association for the Evaluation of Educational Achievement. However, the results have not received as much publicity, even though they are equally, if not more, relevant in the analysis of inequality of opportunity, as numerous studies have shown that differences in individual cognitive abilities appear very early in life. Pre-school tests already show high variability among children depending on their family background, and several studies have shown that these differences might have long-lasting effects, as school systems would at best compensate only part of them. Experiments with preschool programmes aimed at levelling the playing field – like the Perry programme or the Abecedarian programme in United States – have provided evidence of this (Kautz et al., 2014). As shown in recent work by Heckman,14 these preschool inequalities are due in large part both to “parenting”, i.e. the care the parents devote to their young children, and to health factors.

Other single dimensions of the inequality of opportunity

Initial inequality in non-cognitive skills is also important throughout lifetime, and may be considered as another dimension of inequality of opportunity, even though no synthetic measure is actually available, which makes comparing societies over space or over time difficult.

Health status is another dimension of childhood circumstances related to family background, and another component of human capital. In the same way that cognitive skills at age 15 influence future earnings and are heterogeneous across young people, health status at earlier ages is known to potentially influence the whole career of people and to be heterogeneous too.15 The difficulty here is to monitor inequality in health status. There is an important literature for instance on birth weights as a predictor of health status, future education achievements and adult earning levels (e.g. Currie, 2009). The same may be true of anthropometric indices at early ages, although most indices are strongly influenced by weight at birth. It is somewhat surprising that more attention is not given to the evolution of inequality in these indices and, as for educational test scores, their dependency on parental characteristics.

Another single dimension of the inequality of opportunity, different from human capital, is inherited financial capital. It is certainly possible to measure inequality of inheritance flows during a given period. Wolff (2015) does so for the United States using data from the University of Michigan’s Panel Study of Income Dynamics (PSID) and provides Gini coefficients of inheritance flows both for the whole population and among recipients. However, this is not very informative because of the heterogeneity in the age of inheritors. The extent to which inheriting the wealth of one’s parents at the age of 55, something frequent these days, may be considered as a component of inequality of opportunity is not totally clear, except if, somehow, one has been able to borrow, effectively or virtually, much earlier in life against this future wealth flow. As the credit market is highly imperfect, and the inheritance date or the amount to be inherited highly uncertain, it is not even sure it would make much sense to try to estimate something like the inequality in discounted expected inheritance flows of all 25 year-old individuals. Further, donations as well as inheritances would have to be taken into account.

Inheritance is a dimension of the inequality of opportunity whose inequality is difficult to evaluate as such, even though it is a key factor shaping inequality in economic outcomes like income or standard of living when considering cohorts beyond a certain age but they are seldom reported in surveys.

Inter-generational mobility of earnings

Much work has been devoted to the estimation of models of type (2) where the outcome $y_i$ is the (full-time) earnings of an observed individual, i, and C_i is the (log) (full-time) earnings of their parents, most often their father, observed roughly at the same age. Denoting the latter by y_-1,i, the basic specification of the model is thus:

$Log\mathrm{ }{y}_i\mathrm{ }=\mathrm{ }\gamma \mathrm{ }Log\mathrm{ }{y}_{-1,i}+\mathrm{ }a\mathrm{ }+\mathrm{ }{v}_i\mathrm{ }$ (9)16

where a is a constant and $v_i$ is a zero mean random term, standing for all unobserved earnings determinants independent of fathers’ earnings. The coefficient $\gamma$ summarises all the channels through which fathers’ earnings, and their own determinants like education, may affect sons’ earnings.

This model, reminiscent of the famous Galton (1886) analysis of the correlation of height across generations, is generally presented as belonging to the literature on inter-generational mobility, with the least square estimate $\widehat{\gamma }$ being interpreted as the inter-generational elasticity (IGE), or the degree of immobility across generation. Equivalently, in a Galtonian spirit, the coefficient $1-\widehat{\gamma }$ is interpreted as the speed of “regression towards the mean”.

This approach to inter-generational mobility is based on a parametric specification and the estimation of a specific parameter. Non-parametric specifications come under the form of mobility matrices showing the probabilities p_ij for the earnings of sons whose father’s earnings is in income bracket i to be in bracket j. We consider these two approaches in turn.

Parametric representation of inter-generational mobility

To see more clearly the relationship between IGE and inequality of opportunity, one may consider applying directly the alternative definition of inequality of opportunities provided in the preceding section of this chapter. Applying (4)-(7) to model (9) and assuming that the inequality measure M{ } is scale invariant, it can be shown that:

$I_M^{du}\left(y_{-1.}\right)=M\left\{y_{-1.}^{\widehat{\gamma }}\right\}$ and $I_M^{fg}\left(y_{-1.}\right)=M\left\{y_{.}\right\}-\mathrm{ }M\left\{\mathrm{e}\mathrm{x}\mathrm{p}\left({\widehat{v}}_{.}\right)\right\}$

where the notation ^ refers to least square estimates. In the particular case where M{ } is the variance of logarithms, VL, it turns out that the two measures in absolute terms are identical because of the additivity property of the variance:

$I_M^{du}\left(y_{-1.}\right)=I_M^{fg}\left(y_{-1.}\right)={\widehat{\gamma }}^{2}VL\left\{y_{-1.}\right\}$

while in relative terms:

${\tilde{I}}_M^{du}\left(y_{-1.}\right)={\tilde{I}}_M^{fg}\left(y_{-1.}\right)=\frac{{\widehat{\gamma }}^{2}VL\left\{y_{-1.}\right\}}{VL\left\{y_{.}\right\}}=R^2$ (10)

where $R^2$ is the measure of the explanatory power of the independent variables in regression (9) or, in the present case, the square of the correlation coefficient between the (log) earnings of parents and children.

It can be seen that there is a difference between the inter-generational mobility of earnings (IGE) and inequality of opportunity linked to father’s earnings. The former is proportional to the latter with a coefficient equal to the ratio of the inequality of children’s earnings to that of their fathers.17 In other words, it is only in a world where the inequality of earnings does not change across generations that both the inequality of opportunity, based on the variance of logarithm, and the IGE coincide.

In their study of geographical differences in inter-generational mobility in the United States, Chetty et al. (2014a) use the ranks of parents and children in the earnings distribution as a relative measure of mobility. Based on the “copula” of the joint distribution of the (log) earnings of the two generations, i.e. the joint distribution of father/children ranks in their respective earnings distribution, this measure is independent of the marginal distributions of log earnings. It turns out that the rank-rank correlation is not very different from the log-earnings correlation for reasonable small values of the latter. Through (10), it is thus possible to recover the IGE from the rank-rank correlation.

Non-parametric representation: mobility matrices

Another way of representing the inter-generational mobility of earnings is through a transition matrix representing the way a two-generation dynasty transitions from a given earnings level for fathers to another (or the same earnings) level for sons. Let there be N earning brackets denoted Y_k and denote p_ij the probability than the sons of fathers in bracket Y_i find themselves in bracket Y_j. The distribution of earnings is given by the total rows and columns of the matrix P={p_ij}, but it is also possible to break free from these distributions by defining the income brackets as the quantiles (deciles, vintiles…) of the distribution of the earnings for fathers, on the one hand, and for sons, on the other.18

Table 5.1. Inter-generational transition matrix for earnings
StatLink https://doi.org/10.1787/888933839601

Whether the transition or “mobility” matrix is defined in terms of income brackets or quantiles is not without implications for the interpretation that may be given to the comparison of two matrices. When referring to income brackets, the matrix shows “absolute” mobility, i.e. the probability that children’s earnings could be higher, or lower, than their parents’, a concern of many parents today. Conversely, defining the matrix in terms of quantiles permits to analyse “relative” mobility, irrespectively of earnings levels. The difference between the two approaches lies essentially in the fact that the latter does not take into account the change in the distribution of earnings across generations.19

There is a huge literature on how to draw mobility indicators from such a representation of the influence of parents’ earnings on children’s earnings – see Fields and Ok (1999) or the survey by Jäntti and Jenkins (2015). For instance, mobility is often measured by one minus the trace of the mobility matrix. Shorrocks (1978) suggested a “Normalised Trace” measure given by [N-trace(A)]/(N-1), where A is the matrix P with rows normalised to 1 – i.e. the N probabilities p_ij are divided by the row sum p_i. Other measures are based on the expected number of jumps from one bracket, or decile, to another.

Rather than comparing transition matrices on the basis of mobility indices, some dominance criteria have also been developed, which may lead to incomplete ordering and, thus, to cases of non-comparability between two matrices. For instance, the diagonal criterion says there is less mobility in a transition matrix than in another if all diagonal elements, rather than their sum, are smaller in the former than in the latter. Shorrocks (1978) proposed a stronger criterion, the “strong diagonal view” according to which there is more mobility in matrix A than in B if a_ij ≥ b_ij for all i≠ j.

Although related, this kind of measure based on the transition probabilities has only an indirect link with measures of inequality of opportunity in the sense that it is not expressed in terms of the distribution of outcomes, which logically should be here the distribution of children’ earnings. There are various ways in which such a link may be established:

• The Roemer inequality of opportunity formula (8) would be one way, although apparently seldom used, mostly because the transition matrix consistent with it would be conceptually different from P above. Indeed, the children’s earnings brackets should be row-dependent so as to correspond to the deciles – or other quantiles – of the distribution of earnings among children from parents in a given earnings bracket or quantile.

• An alternative would consist of associating to each row of the matrix a scalar depending on the mean earnings and its distribution within the row. In a more general context, van de Gaer (1993) suggested measuring the inequality of opportunity by the inequality of the mean earnings across “types”, i.e. fathers’ earnings here, which is actually a measure of type I^du as defined in (4). Lefranc, Pistolesi and Trannoy (2009) argued in favour of combining the mean with some inequality measure within type. More generally, one could consider the observed distribution of children’s earnings with the same father’s earnings, as being that of the ex ante random earnings of the typical child in that type. Then one would associate to each row of the transition matrix the certainty equivalent of the distribution of earnings in that row for a given level of risk aversion. This would be equivalent to associating to each row of the matrix the equivalently distributed earnings (EDE) for that row, in the sense of Atkinson (1970) and then defining inequality of opportunity as the inequality of these EDEs across rows.20

• A social welfare approach to the measurement of inter-generational mobility has been proposed by Atkinson (1981) and Atkinson and Bourguignon (1982), which differs somewhat from the inequality of opportunity analytical framework presented here. It consists of defining social welfare on father-son pairs, so that each cell of the transition matrix is given a utility U(Y_i, Y_j) and the social welfare of society is defined by the mean value of this utility, weighted by the transition probabilities, p_ij. The simplest case is when U( ) is additive in the earnings of parents and children. Atkinson and Bourguignon (1982) derived dominance criteria to compare transition matrices on that basis, depending on the properties of the function U( ).

• A similar line of thought has been pursued by Kanbur and Stiglitz (2015) who extend the preceding approach by considering a steady state of an economy consisting of infinitely lived dynasties under the assumption of constant transition matrix and earnings distribution across generations. Within that framework, they identify a social welfare based dominance criterion of one matrix over another or, in other words, of one stationary state of an economy with some inter-generational mobility feature over another stationary state with a different mobility matrix.

In the perspective of inequality of opportunity, there are problems with the last two approaches. On the one hand, the assumption of a fully stationary economy and a social welfare dominance comparison based on dynasties with an infinite number of generations seems extreme, even though the stationarity assumption is often implicit in statements about inter-generational earnings mobility. On the other hand, it is a problem that the very nature of circumstances is used to make comparisons of outcomes across groups of individuals with identical circumstances. In other words, the mobility of children with rich parents may matter less than that of poor parents. What should matter from the point of view of inequality of opportunity is how different the distribution of earnings is across parents’ earnings levels, with no particular importance being given to those levels.

In summary, there is some ambiguity about the way in which inequality of opportunity corresponding to non-parametric specifications of the inter-generational mobility of earnings can be measured. There are various ways mobility can be evaluated or transition matrices compared based on social welfare criteria. But the link with measures of inequality of opportunity of the kind that can be derived from simple parametric models of type (9) – at least under the assumption of homoscedasticity of the residual term, v – is unclear. For this reason, the rest of this section looks at the parametric case.

Data requirements

A priori, the data requirement to estimate the IGE or the parents-children earnings transition matrix seems extremely demanding. One should observe the earnings of parents, generally the father, and that of the children, generally the sons, at more or less the same age or during the same period of their lifecycle. Long panel data bases extending over 20 years and more would allow this to be done. For instance, the PSID (Panel Study of Income Dynamics) in the United States has been collecting data on the same families and their descendants for almost 50 years. The British and the German household panels also extend over 25 years and more. In some countries, register data, most often tax data, allow researchers to follow people throughout their lifetime and from one generation to the next, but only a few countries have open and anonymised register data at this stage.

However, panel data are not really necessary to estimate model (9). The availability of repeated cross-sections over long periods is sufficient. Moreover, they permit the IGE to be estimated in a consistent – i.e. asymptotically unbiased – manner, something which is not certain with panel data.

To see this, it must be noted that the observation of $Log y_{-1}$ is most likely to include measurement errors or, at least, transitory components of fathers’ earnings which are unlikely to have had any effect on their sons’ earnings. Estimating $\gamma$ in (9) with OLS and without precaution for measurement error will thus lead to the so-called attenuation bias, a bias that has been shown to be quite substantial in inter-generational mobility studies.21 The solution is to “instrument” $Log y_{-1}$ by regressing that variable on some fathers’ or parents’ characteristics at that time, Z, at the same date, say $\mathrm{ }{t}_{-1}$, and to use the predicted rather than the observed value when estimating (9) with OLS. Thus, if the parents’ characteristics Z are observed at time t in the same database as children’s earnings, and if an earlier cross-section is available at time $t_{-1},$ this allows us to estimate the log earnings of adults with characteristics Z. Running OLS on (9) using the predicted earnings of the parents at time $t_{-1}$ will yield an asymptotically unbiased estimator of the IGE. Through this so-called two-sample instrumental variable (TSIV) estimation strategy (Björklund and Jäntti, 1997) repeated cross-sections with information on respondents’ parents and covering a period long enough are sufficient to estimate the IGE.22

There are two important caveats to the preceding method. First, the instrumental variable approach just sketched is valid only to the extent that the instrument Z may be assumed to be orthogonal to the income of the children. It must be recognised, however, that this is unlikely to be the case, as most observable parents’ characteristics, like education, occupation, wealth, etc., may be thought of as influencing the economic achievements of children. Second, even if the TSIV strategy did allow the IGE to be estimated consistently with repeated cross-sections rather than with panel data, it would not permit the corresponding inequality of opportunity to be estimated as defined by (10). This is because the variance of the instrumented earnings of parents is not the same as the variance of their true earnings.

Measurement errors are also likely to affect the estimation of mobility measures, social welfare dominance tests and inequality of opportunity through the transition probability matrix methods mentioned above. In that case, both the error on fathers and sons matter. The former may be responsible for misclassifying fathers in the income scale, whereas the latter introduces noise in the transition probabilities.

Stylised facts

The best illustration of this literature on the measurement of inter-generational mobility is the well-known “Great Gatsby” curve, due to Miles Corak and popularised by Alan Krueger. It plots estimates of IGE against the level of inequality – in the contemporaneous generation – for a set of developed and developing countries. This curve is shown in Figure 5.3 below.

Figure 5.3. The Great Gatsby curve

Source: Corak, M. (2012), “Here is the source for the Great Gatsby Curve”, in the Alan Krueger speech at the Center for American Progress on January 12, https://milescorak.com/2012/01/12/here-is-the-source-for-the-great-gatsby-curve-in-the-alan-krueger-speech-at-the-center-for-american-progress/.

Along the vertical scale of the chart, one observes a rather wide dispersion of the estimated IGE, from 0.2 for Nordic countries – Sweden being a little above that level – to 0.5 in the United States and 0.6 in Latin American countries. If it is assumed that the inequality of earnings is similar among parents and children, then (10) suggests that a consistent measure of inequality of opportunity is the square of the IGE, or the R² of the regression of the log of sons’ earnings over the log of fathers’. Then it can be seen that inequality of opportunity corresponding to the fathers’ earnings alone is extremely low in Nordic countries, amounting to less than 4% of the variance of log earnings, while it is more substantial in the United States, amounting to 25% of sons’ earnings inequality. Yet, this would still leave considerable room for mobility if it were the case that no other circumstance, orthogonal to parents’ earnings, constrained children’s earnings, which seems unlikely.

The plot also shows a strong correlation between earnings immobility (i.e. IGE) or inequality of opportunity, and the degree of inequality, as measured by the Gini coefficient of household disposable income, at a point in time. Several explanations have been given for the negative correlation shown in Figure 5.3. The most frequent one relies on some convexity in the relationship between parents’ income and their investment in the human capital of their children, or possibly some unequal access to quality schooling depending on parents’ income. If rich parents invest a higher proportion of their own income in the education of their children, or if only the children of parents above some level of income have access to good quality schools, then more income inequality among parents should generate less inter-generational mobility.

The preceding argument is equivalent to assuming some non-linearity in the basic model (9) or, more exactly, that the IGE may depend on the level of income. If the IGE increases with income, as just suggested, then the linear approximation (9) would indeed yield an OLS estimate of the IGE that increases with the degree of income inequality.23

That the IGE may vary with the level of income is shown in the case of the United States by Landersø and Heckman (2016), p. 22, as can be seen in Figure 5.4 below.24

Figure 5.4. Non-linear inter-generational elasticity in the United States

Parents observed in 1987 and children 36-38 in 2011

Source: Landersø, R. and J.J. Heckman (2016), “The Scandinavian fantasy: The sources of intergenerational mobility in Denmark and the US”, Centre for the economics of human development, University of Chicago.

Another, more mechanical, explanation of the negative slope of the Great Gatsby curve is based on (10) above. If one compares two countries where income inequality was the same in the older generation, then it is the case that, with the same correlation coefficient (R²) between the earnings of the two generations, the IGE will be higher in the country with the highest inequality today. For instance, Landersø and Heckman (2016, p.17) show that the IGE in Denmark would be much bigger than what it is if the distribution of children’s earnings was identical to the US distribution. This again illustrates the difference between the concept of immobility as described by IGE and that of inequality of opportunity related to parents’ earnings. Yet it is unlikely that Figure 5.3 would be fundamentally different if the IGE were replaced by the inequality of opportunity as defined in (10).25

Other explanations of the upward sloping Gatsby curve are available that go from mobility to inequality rather than the opposite. For instance, Berman (2016) stresses that if the distribution of the residual term, v, is constant, model (9) leads to a steady-state distribution of earnings whose inequality is given by: $VL\left(y\right)= \frac{Var\left(v\right)}{1-{\gamma }^2}$. Thus, inequality of income increases with IGE. As a matter of fact, it should be noted that this property does not hold only at a steady state. Among two societies with the same distribution of earnings in one generation, inequality will be higher, all things being equal, in the society where parents transmit more of their earning capacity to their children. Formally, (9) implies that:

$VL\left(y\right)={\gamma }^{2}VL\left(y_{-1}\right)+Var\left(v\right)$

which is increasing in $\gamma$.

One might ask whether this positive relationship between inequality and inter-generational immobility may also hold inter-temporally. Interestingly enough, Aaronsson and Mazumder (2008) show that trends in wage inequality between 1940 and 2000 in the United States coincide with trends in IGE, with a compression in the first part of the period and increasing disparities in the later part.26 However not enough data are available to test that hypothesis on a cross-country basis.

The same type of analysis may be undertaken with other economic outcomes. However to keep with the spirit of model (9) it is important to make sure that the same variable can be observed for both parents and children. For instance, having parents’ earnings on the right hand side of the equation and income per capita (or per adult equivalent) on the left hand side is interesting, but the interpretation is not anymore in terms of inter-generational transmission of earning potential, as income per capita also depends on family size, marriage and labour supply. There is also an issue with the period of observation of the right-hand variable. Presumably, one would expect parents’ income to influence the life-time earnings of children. This may not be reflected when observing children during a short period at some stage of their life.

Chetty et al. (2014a) address this issue when analysing the spatial heterogeneity of inter-generational income mobility in the United States, as they indeed use lifetime pre-tax family income as income variables in both generations as drawn from administrative tax data. They find considerable spatial variation of income mobility across “commuting zones”: “the probability that a child reaches the top quintile of the national income distribution starting from a family in the bottom quintile is 4.4% in Charlotte (North Carolina) but 12.9% in San Jose (California)”.

Taking advantage of the length of register data, Chetty et al. (2014b) also study the time evolution of inter-generational mobility, in effect the rank correlation between fathers’ and sons’ earnings. They find no significant change across birth cohorts born between 1971 and 1982. This is line with the results found earlier by Lee and Solon (2009) for the US using the PSID panel dataset for cohorts born between 1952 and 1975. Both results diverge somewhat from Aaronsson and Mazumder (2008). Non-consensual results are also found in other countries, as shown by the critiques by Goldthrope (2012) to the finding by Blanden et al. (2011) that mobility would have fallen in the United Kingdom.

Another interesting concept, closer to the sociological view on mobility, has recently been studied by Chetty et al. (2017). “Absolute mobility”, is defined as the proportion of 30-year old children whose real income is higher than their parents’ when they were 30. Combining register data since 1970 with assumptions on rank correlation together with cross-sectional data for the period before, absolute mobility has declined continuously from the 1940 to the 1965 birth cohort – i.e. the baby boomers. It then stabilised but fell again soon because of the financial crisis – i.e. for cohorts born in the late 1970s.

Somewhat surprisingly, much less work has been done on the inter-generational transmission of wealth inequality and on the key role of inheritance in the inequality of opportunity. This is in part due to the availability of data. Typical household surveys generally do not include data on wealth. When they do, they do not necessarily include data on parents, or they are not repeated over a period long enough to apply the TSIV methodology. As for panel data, some waves of PSID do include wealth questionnaires. They have been used by Charles and Hust (2003) to estimate an IGE for wealth. Unfortunately, no information is available that would allow to correct for measurement error bias. The British and German household panels do include data on wealth but the number of observations is too small to estimate IGE for wealth at mid-life, an age at which the wealth concept becomes relevant for both parents and children. One could also think of using estate statistics, but these actually lack relevance as their link to inequality of opportunity is through the heirs, whose wealth is not observed.

In Nordic countries, several recent studies of inter-generational wealth dynamics have relied on administrative data. Boserup, Kopczuk and Kreiner (2014) provide estimates of the wealth IGE at mid-life in Denmark, and Adermon, Lindahl and Waldenström (2015) do the same for Sweden. Both studies cover more than two generations. In both countries, the wealth IGE estimates are comparable and of limited size (around 0.3), a value comparable to the earnings IGE in Sweden but twice as large in Denmark.

Generalised inter-generational mobility analysis and inequality of observed opportunities

Parental income is only one of the circumstances affecting the economic outcome of an individual, even though it may be correlated with other circumstances. To provide a more complete picture, fathers’ earnings, y_-1 in equation (9) can be replaced or complemented by a vector of variables referring to the parental characteristics of an individual in the current generation. Labour force or household surveys often give information on the parents of respondents (education, occupation, residence, age when respondent was 10). Rather than using the TSIV approach to estimate parental earnings or income based on these characteristics, one may simply measure the related inequality of opportunity by the share of the inequality of income or earnings in the current generation that is accounted for by parents’ characteristics, including the determinants of their own earnings.

Formally, model (9) is replaced by:

$Log\mathrm{ }{y}_i\mathrm{ }=\beta \mathrm{ }{Z}_i+\mathrm{ }{v}_i\mathrm{ }$ (11)

where $y_i$ is a particular economic outcome; $Z_i$ a vector of variables that include all observed parental characteristics and some other characteristics beyond individual control, like gender; and $v_i$ all the unobserved determinants of the economic outcome that are orthogonal to $Z_i$. In agreement with the definition (7), the R² statistics of that regression may be interpreted as the inequality of opportunities associated with individual characteristics in $Z_i$ when measuring the inequality of outcomes with the variance of logarithms. Some authors prefer using other measures of inequality.27

In comparison with model (9), model (11) may be considered as a model of “generalised” mobility in the sense that more parental characteristics are taken into account that do not necessarily include the outcome being explained in the current generation. It can also be noted that this model is identical to the model used in the inter-generational mobility analysis of earnings when instrumenting the earnings of the parent by a set of characteristics available in the data base – i.e. the TSIV approach. Model (11) would then correspond to the “reduced” form of the earnings mobility model, necessarily less restrictive than the structural form (9).

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 is in some sense the equivalent of the Great Gatsby curve, with the IGE being replaced by the inequality of observed opportunities.29 This generalisation 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 observed in Figure 5.3.

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 https://doi.org/10.1787/888933839620

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 labour earnings for the EU countries and the United States30, 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 standardising generalised mobility analyses of the type described above – to make them comparable across countries, over time and across cohorts – might be easier to implement than standardising 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 non-parametric 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 labour 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 account for all observed and unobserved family background characteristics as well as presumably for other circumstances which 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 with 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 generalised 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 labour market? Also, to what extent do the differentials shown in Figure 5.6 reflect differences in labour force participation rates, 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 labour 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) labour 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

Percentage gap between median earnings of men and women, full-time workers

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

 StatLink https://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 non-linear through interactions between gender and the other components of Z, namely:

$Log\mathrm{ }{y}_i\mathrm{ }=\mathrm{\beta }{Z}_i+\mathrm{ }\delta \mathrm{ }{Z}_i\mathrm{*}{G}_i+\mathrm{ }{v}_i\mathrm{ }$ (12)

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

$Log\mathrm{ }{y}_i^g\mathrm{ }={\beta }_g\mathrm{ }{Z}_i^g+\mathrm{ }{v}_i^g\mathrm{ },\mathrm{ }\mathrm{ }\mathrm{ }g=M,\mathrm{ }F\mathrm{ }$(13)

Based on the estimates of the two sets of coefficients ${\beta }_g$, 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 ${\widehat{\beta }}_F$ and ${\widehat{\beta }}_M$. 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:

$Log\mathrm{ }{\stackrel{-}{y}}^F-Log\mathrm{ }{\stackrel{-}{y}}^M={(n}_F{\widehat{\beta }}_F+n_M{\widehat{\beta }}_M)\left({\stackrel{-}{Z}}^F-{\stackrel{-}{Z}}^M\right)+\mathrm{ }\left({\widehat{\beta }}_F-{\widehat{\beta }}_M\right).(n_F{\stackrel{-}{Z}}^F+n_M{\stackrel{-}{Z}}^M)$ (14)33

where the notation $\stackrel{-}{ }$ refers to means, and $n_F$ and $n_M$ 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 stylised 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 Oaxaca-Blinder 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 labour market discrimination has not changed in the average country.

From a policy point of view, the Oaxaca-Blinder 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 Oaxaca-Blinder decomposition shows that both education and job experience are rewarded differently for male and female workers. Then, the inequality of opportunity arising from labour 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.

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”, The Journal of Economic Surveys, Vol. 19(3), pp. 479-511.

Having said this, the issue remains of the fundamental ambiguity of the distinction between efforts and circumstances. Are interruptions to job, labour force participation and career caused by child rearing only the responsibility of women? Wasn’t it society as a whole that constrained women’s labour 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.