By the content of their character? Discrimination, social identity, and observed distributions of income

ABSTRACT

This paper applies information-theoretic measures to consider the systemic effects on individual incomes of complex patterns of social and economic discrimination by race, ethnicity, and gender in the U.S. It estimates non-parametric indices of joint, conditional or incremental, and mutual information between income, social identity, and observable economic characteristics obtained using large-scale cross-sectional data from that economy. The paper advances new conceptual and empirical approaches to the nature and measurement of economic discrimination and inequalities of opportunity, founded on the formal informativeness of measures of social identity on economic outcomes. Estimated values for indices of informational association also cast new light on the effects of the intersections of gender and race/ethnicity on income, perverse patterns in the effects of education across different groups, and a few notable dynamic changes in patterns of income distribution in that economy over the past 40 years.

KEYWORDS:

• Information theory
• income distributions
• discrimination

Acknowledgments

We are grateful to Duncan Foley, Sanjay Reddy, Nancy Folbre, Deepankar Basu, Peter Skott, Usama Bilal, and Jennifer Yablonski for a wide range of comments, questions, and suggestions that helped shape this article. We are also thankful to two anonymous referees for a number of useful recommendations. The usual disclaimers apply.

Notes

¹ The indices are motivated and derived in dos Santos and Wiener (2019).

² Unfortunately, this rich and uniquely large dataset does not capture any reliable measure of class background.

³ After decades of largely ignoring the issue, mainline economics has recently offered a number of important contributions documenting increasing measures of income and wealth inequality across advanced economies, see, for example, Piketty and Saez, 2006; Alvaredo et al., 2013; Piketty and Zucman, 2014; Atkinson et al., 2018.

⁴ See Quillian, Pager, Hexel, and Midtboen (2017), which reports on a large-scale meta-analysis of several such studies undertaken in the U.S. and has estimated that white job applicants enjoy on average 36 and 24 percent more callbacks than otherwise comparable black and Latino applicants, respectively. See also Daniel, 1968; Firth, 1981, 1982; Jowell & Wissoker, 1970; Kenney & Wissoker, 1994; M Bendick & Reinoso, 1994; Riach & Rich, 1987, 2002.

⁵ See the succinct summary of these contributions offered by Williams, Multhaup, and Mihaylo (2018).

⁶ Not only has the criminal justice system especially targeted types of offences “for which black and Hispanic people often are disproportionately arrested and convicted” (National Research Council, 2014, p. 91), racial disparities in the severity of sentencing have also been found as the cumulative effect of “small but systematic racial differences in case processing” (National Research Council, 2014, p. 103).

⁷ See the influential contribution by Mincer, 1974 and the synthetic review in Ashenfelter, Harmon, and Oosterbeek, 1999.

⁸ See Pager and Shepherd, 2008 and the references therein for a review of statistical approaches to the measurement of economic effects of discrimination. For contributions from scholars working on the basis of Stratification Economics, see Darity, Dietrich, & Guilkey, 2001; Goldsmith, Hamilton, & Darity, 2007; Goldsmith, Hamilton, and Jr., 2006, for instance.

⁹ Here we have a particularly strong and readily evident form of the Duhem-Quine problem.

¹⁰ Arguments for using entire income distributions in diagnostics of discrimination have been notably advanced by Del Rio, Gradin, & Canto, 2011; Dolton & Makepeace, 1985; Jenkins, 1994.

¹¹ Note that this could include additional, unobservable patterns of discrimination by socially relevant individual characteristics that may also have little to do with measures of the inherent productive potential of individuals.

¹² See also the general argument advanced in Jaynes, 2003.

¹³ For a formal proof of this observation for changes in any number of individual states, see the Appendix in dos Santos and Scharfenaker, 2019.

¹⁴ It will only do so strictly for income distributions that are monotonically decreasing on income.

¹⁵ The simplest way to see this is to note that $I\left(Y,{\mathbb{X}}_k\right)=<D_{KL}\left(f\left(Y|{\mathbb{X}}_k\right)||f\left(Y\right)\right){>}_{{\mathbb{X}}_k}$. Since the Kullback-Leibler divergence is always non-negative, the expected value in this expression is only zero when each of the divergences between $f\left(Y|{\chi }_k\right)$ and $f\left(Y\right)$ is zero. But this is known to ensure that each of those conditional distributions is equal to the marginal distribution of $Y$, almost everywhere.

¹⁶ The genetic variability across the different sets of human populations that constitute various racial and ethnic categories are very small compared to the overall genetic variability across humanity as a whole. See Witherspoon et al., 2007; Yu et al., 2002, for instance.

¹⁷ For a similarly non-parametric, entropy-based approach to the contribution of social-identity and economic characteristics to income inequality based on the above-mentioned Theil measure, see Conceiçã, Galbraith, & Bradford, 2001.

¹⁸ For different contributions and controversies, see Anderson, 1999; Dworkin, 2000; Rawls, 1971; Roemer, 1998.

¹⁹ See appendix A.1 for details on the construction of our sample, and appendix A.2 for sample sizes.

²⁰ For a robustness analysis of the binning scheme, see appendix A.3.

²¹ A large literature has investigated the contribution of the changing demand for high- vs. low-skilled labor to the increasing earnings inequality in the US. See Acemoglu and Autor, 2011; Autor, 2014; Autor, Katz, & Kearney, 2008; Card & Lemieux, 2001; Katz & Murphy, 1992; Lemieux, 2006.

²² The smaller absolute value of the incremental informativeness indices for whites reflects the fact that whites make up a majority of the sampled populations. Sometimes, as in the case of college graduates, this numerical dominance is overwhelming.

²³ As put by Martin Luther King Jr. in his 1963 speech to the March on Washington.

²⁴ See appendix A.3.