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A Gini approach to inequality of opportunity: evidence from the PSID

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Abstract

Given (pragmatic) partial ordering criteria for the comparison of individuals in terms of both circumstances and responsible choices, a Gini-based approach is proposed for the measurement of opportunity inequality and its (relative) contribution to outcome inequality. An application to US income distributions from 1999 to 2009 is also discussed. Given six circumstance variables (gender, health, economic condition of parents in the early years, ethnicity, IQ score in the early years and unemployment rate in the place of origin), opportunity inequality is found to account for between 15.0 and 16.6 % of outcome inequality from 1999 to 2009 with a U-shaped pattern over time, supporting existing evidence on the inequality implications of financial crises.

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Notes

  1. Evidently, opportunity egalitarianism strongly relies on the identification of both circumstances and responsible choices, which is not straightforward: even effort—the icon of responsible choices for economists—is somehow and partially influenced by circumstances, such as family education and social environment (Rawls 1971).

  2. Niehues and Peichl (2013) implement the same methodology proposed by Ferreira and Gignoux (2011) for the estimation of the “lower-bounded IOp” while introducing a parametric estimate of the “upper-bounded IOp” accounting for the unobservability of the full set of circumstances. Here, IOp in Germany and USA are found, respectively, to represent 28–62 % and 16–36 % of inequality of outcomes.

  3. For major details on the stochastic dominance approach to IOp, see Lefranc et al. (2008).

  4. Due to the partial observability of the full set of circumstances, a similar outcome, with upper and lower bounds for IOp, is achieved in Niehues and Peichl (2013).

  5. The two principles can be differently defined and supported depending on the ex-ante or the ex-post perspective. On this topic, see Fleurbaey and Peragine (2009).

  6. For instance, following Sugden (2004), one may reasonably exclude compensation for some unfair opportunity outcome inequalities, whereas, as will be clearer later on, one may ask for compensation with respect to ambiguous (i.e., “non-fair” and “non-unfair”) outcome disparities.

  7. An additional but less used criterion is the principle of utilitarian reward. In the latter, compensation for outcome disparities due to unequal circumstances is recommended if and only if it allows a maximization of the sum of individual outcomes, i.e., compensation is not ethically desirable itself (zero inequality aversion).

  8. Let \(\{x_1,x_2,y_1,y_2\}\) be the outcomes of four individuals where (i) \((x_1,x_2)\) and \((y_1,y_2)\) share the same opportunity set with \(x\) preferred to \(y\), and (ii) \((x_1,y_1)\) and \((x_2,y_2)\) share the same set of responsible choices with \(x_2\) and \(y_2\) being more deserving than \(x_1\) and \(y_1\), respectively. Given \(\{x_1,x_2,y_1,y_2\}=\{4,9,1,7\}\), if the redistributive policy is defined as a series of non re-ranking (between the donor and the recipient) rich-to-poor outcome transfers among equally responsible individuals, then by virtue of the principle of natural reward, maximum equality of opportunity is achieved if \(\{3,8,2,8\}\) is obtained. However, by virtue of strict egalitarianism of opportunity, maximum equality of opportunity is obtained if \(\{2.5,8,2.5,8\}\) is achieved.

  9. Alternatively, the need for a third component may be motivated by the distinction between native- and context-specific circumstances or, compatible with the Mincerian tradition, between (pure) circumstances and (resultant) luck (e.g., Ferreira and Gignoux 2011) or between observed and unobserved circumstances (Ramos and Van de gaer 2012).

  10. On the different methodological implications of the two approaches, see Ooghe et al. 2007.

  11. Alternatively, y may be regarded as general or domain satisfaction in the subjective/objective well-being approach (e.g., Campbell 1976).

  12. For instance, given two increasingly ordered subgroup income vectors, \(x:=\{x_1,x_2\}\) and \(y:=\{y_1,y_2,y_3\}\), then \(x_2\succ _e x_1, y_3\succ _e y_2\succ _e y_1, y_3\succ _e x_1\) and \(x_2\succ _e y_1\), while the couples \((x_1,y_1), (x_1,y_2), (x_2,y_2)\) and \((x_2,y_3)\) identify the set of non-responsibility comparable income units.

  13. Evidently, the latter orderings should be defined a priori on the base of existing evidence.

  14. Evidently, the set of partially unfair outcome gaps from Definition (2.1) coincides with the setof partially fair outcome gaps from Definition (2.2).

  15. A similar ethical value judgment (equality of luck) has been proposed in Vallentyne (2002). Intuitively, the primary idea behind strict equality of opportunity is reminiscent of other ethical value judgments such as the reasonable doubt rule, by which it is said, “it is better that ten guilty persons escape, than that one innocent suffer” (Blackstone 1765–1769).

  16. Replication invariance holds when the k-fold replication of the population fully replicates each income unit with respect to all characteristics (responsibility type, circumstance and outcome). Obviously, if responsibility types are redefined after the k-fold replication, then this would not be a replication of the initial population.

  17. Panel Study of Income Dynamics public use dataset. Produced and distributed by the Institute for Social Research, Survey Research Center, University of Michigan, Ann Arbor, MI (2009).

  18. Income data refer to the previous chronological year (e.g., 1999 income records refer to 1998).

  19. As transfer, taxable and labor incomes are not available in the 2001 wave, the latter have been replaced with the corresponding values obtained by averaging the 1999 and 2003 responses for each individual.

  20. To account for the Federal Income Tax, brackets and tax rates from 1998 to 2008 have been considered.

  21. The introduction of a proxy for cognitive abilities (IQ test) within the set of circumstance variables is not straightforward from a philosophical point of view because a trade-off may occur between different social and ethical objectives: that is, as observed in Lefranc et al. (2008), the “above notion of equality of opportunity may contradict other ethical principles such as self-ownership and freedom.”

  22. Mostly, the definition of binary variables is expected to reflect the discriminating power of each circumstance variable, that is, the shares of the advantaged/disadvantaged income units. If the definition of the binary circumstance variable implies a fifty-fifty chance of being advantaged/disadvantaged, then the discriminating power is maximum. On the contrary, the discriminating power is minimum whenever all income units are advantaged or disadvantaged. This aspect is not irrelevant for measurement purposes because the number of between-group (CD and non-CD) pairwise income gaps is strictly increasing with the discriminating power.

  23. This partition is supported by empirical evidence on average disposable incomes for each group. For instance, in the 1999 wave, the average disposable incomes for “American,” “national origin” and “religious” are, respectively, 27.796 USD, 28.265 USD and 30.811 USD. Meanwhile, the average disposable incomes for “hyphenated American,” “non-specific Hispanic identify,” “racial” and “other” are, respectively, 19.457 USD, 21.248 USD, 22.907 USD and 18.417 USD.

  24. For the 1968 wave, the PSID database reports information on Ammons’ Quick Test (Mednick 1965). For the 1972 wave, instead, a standard IQ word test has been used.

  25. To define each of the subgroups, both the PSID family and the PSID individual data files have been used. Specifically, longitudinal sample weights have been extracted from the individual data files from the 1999 to the 2009 waves. Income information, gender, health status, ethnicity and the economic condition of parents in the early years have been extracted from the family data file for 1999, 2001, 2003, 2005, 2007 and 2009. IQ test records and the unemployment rate in the place of origin are obtained from the family data file for the 1968 and the 1972 waves. The latter variables have been associated with the corresponding income units from the 1999 to the 2009 waves using control variables (family identifier, person number and age of individual).

  26. In addition, available IQ scores mostly refers to head income units because, even if the result is assigned to each member of the family, the head income unit was expected to administer the test both in the 1968 and in the 1972 waves.

  27. Zero values have been replaced for rental income, dividends, trust funds, interest and property taxes (104–184 substitutions in each wave). Average values are used for health status, unemployment rate and economic condition of parents (19–24 substitutions in each wave). Finally, “other” has been assigned to non-respondents with respect to ethnicity (12–21 substitutions in each wave).

  28. It is worth observing that the income units observed in one wave are not necessarily respondents in the other waves. In particular, both ethnicity and the economic condition of parents for 1999 and 2001 have not been brought forward for the same heads and wives. In addition, a new codification of ethnicity responses was introduced in 2001. These changes are likely to be the primary source of the abrupt change in subgroup composition when comparing the 1999/2001 wave with the others.

  29. The very large range with respect to the economic condition of parents is due to the 1999 wave. The shares from 1999 to 2009 are, respectively, 3, 4, 23, 24, 15 and 15 %: that is, an unbalanced subgroup partition occurs for the 1999 wave only. See previous footnote for an explanation.

  30. Evidently, the population of singles is not the same as the population of head income units, but the latter definitely accentuates the share of singles.

  31. It is worth observing that, as a rank-based definition of effort is implemented, such a remarkable size for the IOp interval cannot be ascribed to the impact of circumstances on individual voluntary decisions.

  32. The contribution of circumstances has been assumed to be upper bounded by the size of the entire outcome gap.

  33. Or, equivalently, by subtracting the sole contribution of responsible choices from \(G^\mathrm{Max}_\mathrm{EO}\).

  34. It is worth observing that this procedure is informative but not path independent because the contribution of each circumstance is inevitably influenced by the circumstance-based partition of the population, that is, by the other circumstance variables. As a result, the total IOp cannot be obtained as an aggregation of the contribution of single circumstances.

  35. Note that these results may be partly driven by the age profile of the population (pre-1972 cohorts).

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  1. Dipartimento di Scienze Economiche e Statistiche (DISES), Centro di Economia del Lavoro e di Politica Economica (CELPE), Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Antonio Abatemarco

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Appendix

Appendix

See Tables 4, 5 and 6.

Table 4 Subgroup composition and average disposable income (thousand dollars)
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Table 5 Groups of subgroups’ average disposable incomes (thousand dollars)
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Table 6 Correlation matrices
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Abatemarco, A. A Gini approach to inequality of opportunity: evidence from the PSID. Empir Econ 49, 1497–1519 (2015). https://doi.org/10.1007/s00181-015-0918-y

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