For Good Measure Read online

  3. The debate in the sociological literature about the idea that people raised in a low socio-economic status environment may inherit low preferences for work effort illustrates that point. See a summary of that discussion in Piketty (1998).

  4. A rigorous econometric analysis of this issue is provided in the annex at the end of this chapter.

  5. The notation used for this equation is different from the one used in the annex at the end of this chapter.

  6. Schooling being considered as a “circumstance,” mostly determined by parental background.

  7. Both sources of inequality are analyzed in detail below.

  8. Thus, without loss of generality, ve can be set to zero, its sample mean value, when (2) is estimated by Ordinary Least Squares.

  9. With enough observations for each type, the two means differ by a factor that depends on the inequality of unobserved outcome determinants within the type.

  10. Roemer justifies comparing outcomes across types for given quantiles by considering that individuals of different types (but in the same quantile of their own outcome distribution) expend the same efforts. The above formula does not appear in Roemer (1998) but it ensues logically from the specification of his objective function in the design of policies to minimize inequality of opportunities. Note also that Mint{qt(π)} in (8) could be replaced by any standard outcome inequality measure across types.

  11. This dependency of PISA scores on family background has been studied in detail by the OECD (2016) in an analysis where cognitive ability is precisely taken as an outcome rather than a circumstance.

  12. Ferreira and Gignoux (2011a) analyze carefully this source of bias in a cross-country comparison.

  13. The standard deviation in test scores being 7, this means that test scores at the end of high school may be responsible for earnings differentials of close to 30%.

  14. See for instance the survey by Conti and Heckman (2012).

  15. An interesting paper shows, for instance, the influence of in utero factors on adult earnings: see Almond, Mazumder, and Van Ewijk (2015).

  16. Parameter notations differ from those used above or in the annex at the end of this chapter.

  17. Note that this is true only for the variance of logarithm as an inequality measure.

  18. When brackets are deciles (or other quantiles) of the distribution of earnings of parents for rows and of sons for columns, the transition matrix is bi-stochastic, with the sum of columns and rows being equal to 0.1 in the case of decile (and of 0.05 in the case of vintile, etc.). This mobility matrix is a representation of the copula of the joint distribution of father/children earnings defined above.

  19. Sociologists, who are used to working with socio-economic classes rather than earnings or income, tend to emphasize “absolute” mobility, i.e., moving from one rung of the social ladder to another. Economists traditionally tend to work with “relative” mobility—although see the analysis of absolute earnings mobility in Chetty et al. (2017).

  20. Note that this approach would also apply to the case where the parametric outcome model (2) is heteroskedastic, as discussed above.

  21. See, for instance, Jäntti and Jenkins (2015, pp. 899–905) for examples drawn from the US literature.

  22. Björklund and Jäntti (1997) apply this technique to compare mobility in Sweden and in the United States, whereas Aaronson and Mazumder (2008) do so to compare earnings mobility in the United States over time.

  23. The argument is as follows: Let γ in (9) depend linearly on [need eq.], for observation i, e.g., with γ1 > 0. Taking the means on both sides of (9), the average IGE for the whole population is then given by: where n is the size of the sample and ȳ−1 the mean of parents’ income. For a given mean parent income, the mean IGE in the sample thus increases with the variance, or more generally with the inequality of parents’ income. Note however that the Gatsby curve refers to the inequality of household income at the time children’s earnings are observed.

  24. See also Chetty et al. (2014a), Figure 1b.

  25. It is indeed unlikely that the change in inequality across generations could compensate for the differences in IGE.

  26. Aaronsson and Mazumder (2008) use the TSIV method sketched above with US census data.

  27. For instance, Bourguignon, Ferreira, and Menendez (2007) use the relative version of (7) with the Gini coefficient for the inequality measure M{ } and the mean of Z for the reference circumstance Ce in (6). Brunori, Ferreira, and Peragine (2013) use the mean logarithmic deviation.

  28. The mean logarithmic deviation (MLD) in a sample of individuals with economic outcome yi is simply the difference between the log of the mean of the y’s and the mean of the log y’s. For some countries in Figure 5.5, a semi-parametric model is used, based on “types” of individuals, as defined by specific combinations of characteristics Z, rather than by these characteristics themselves.

  29. It is the case that the relative inequality of observed opportunities based on the mean logarithmic deviation is close to the R2 of the regression of outcomes on observed opportunities. From (9), this implies that the square root of that measure is comparable to the IGE.

  30. This uniformity in the European case comes from being based on a common data source, the EU-SILC, which is roughly uniform across EU members. See Checchi, Peragine, and Serlenga (2010).

  31. Such an analysis by cohorts is performed in Bourguignon, Ferreira, and Menendez (2007).

  32. Essentially, homoscedasticity in a model of type (11).

  33. Other expressions of the Blinder-Oaxaca decomposition use the β coefficients of one group in the first term and the mean characteristics of the other in the second rather than means over the two groups. The problem is that the decomposition then depends on what group is chosen for β. The formulation used here is path independent.

  34. Additional difficulties would appear if, instead of focusing on wages, gender inequality focused on income, or more exactly household income (per capita or equivalized), as labor supply, marriage, assortative mating, and fertility would become important issues, on top of the fact that the distribution of income within the household is not directly observed (on these issues, see Meurs and Ponthieux, 2015).

  35. For instance, through principal component analysis of answers to questions on noncognitive ability in PISA.

  36. In connection with EU-SILC, it should be noted that shorter panels may still be helpful in analyzing the inequality arising from involuntary shocks experienced by individuals in their recent past, which may be the main source of inequality of opportunity appearing during adult life. In particular, such data should help to evaluate the hysteresis of such events and the role of social policies in neutralizing their long-run effects.

  37. Bourguignon, Ferreira, and Menendez (2007, 2013) tried to find bounds on the b1 and c1 coefficients, but they proved to be too large to be of any use in identifying the inequality of opportunity conditional on efforts.

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  6.

  Distributional National Accounts

  Facundo Alvaredo, Lucas Chancel, Thomas Piketty, Emmanuel Saez, and Gabriel Zucman

  This chapter summarizes the concepts, methods, and goals of the WID.world project, the World Inequality Database, along with some first results from this source. WID.world builds on the experience of the World Top Incomes Database (WTID) to construct time series on the concentration of income at the very top of the distribution in more than 30 countries, to include wealth distribution and developing as well as developed countries. The ultimate goal of WID.world is to provide annual estimates of the distribution of income and wealth using concepts consistent with macro-economic accounts, i.e., to construct distributional national accounts (DINA). WID.world also aims to produce synthetic micro-files providing online information on income and wealth (i.e., individual-level data that do not result from direct observation but rather through estimates that reproduce the observed distribution of the underlying data). The long-run aim of the WID.world project is to release income and wealth synthetic DINA micro-files for all countries on an annual basis.