Disparity analysis: a tale of two approaches

Zhou X., Pan G.

How does higher education shape the Black-White earnings gap? It may help close the gap if Black youth benefit more from attending and completing college than do White youth. On the other hand, Black college-goers are less likely to complete college relative to White students, and this disparity in degree completion helps reproduce racial inequality. In this study, we use a novel causal decomposition and a debiased machine learning method to isolate, quantify, and explain the equalizing and stratifying roles of college. Analyzing data from the NLSY97, we find that a bachelor’s degree has a strong equalizing effect on earnings among men (albeit not among women); yet, at the population level, this equalizing effect is partly offset by unequal likelihoods of bachelor’s completion between Black and White students. Moreover, a bachelor’s degree narrows the male Black-White earnings gap not by reducing the influence of class background and pre-college academic ability, but by lessening the “unexplained” penalty of being Black in the labor market. To illuminate the policy implications of our findings, we estimate counterfactual earnings gaps under a series of stylized educational interventions. We find that interventions that both boost rates of college attendance and bachelor’s completion and close racial disparities in these transitions can substantially reduce the Black-White earnings gap.

Park S., Kang S., Lee C., Ma S.

Abstract A key objective of decomposition analysis is to identify a factor (the “mediator”) contributing to disparities in an outcome between social groups. In decomposition analysis, a scholarly interest often centers on estimating how much the disparity (e.g., health disparities between Black women and White men) would be reduced/remain if we set the mediator (e.g., education) distribution of one social group equal to another. However, causally identifying disparity reduction and remaining depends on the no omitted mediator–outcome confounding assumption, which is not empirically testable. Therefore, we propose a set of sensitivity analyses to assess the robustness of disparity reduction to possible unobserved confounding. We derived general bias formulas for disparity reduction, which can be used beyond a particular statistical model and do not require any functional assumptions. Moreover, the same bias formulas apply with unobserved confounding measured before and after the group status. On the basis of the formulas, we provide sensitivity analysis techniques based on regression coefficients and R 2 {R}^{2} values by extending the existing approaches. The R 2 {R}^{2} -based sensitivity analysis offers a straightforward interpretation of sensitivity parameters and a standard way to report the robustness of research findings. Although we introduce sensitivity analysis techniques in the context of decomposition analysis, they can be utilized in any mediation setting based on interventional indirect effects when the exposure is randomized (or conditionally ignorable given covariates).

Voss K., Hout M., George K.

Abstract Fewer than half of America’s college students complete their bachelor’s degrees. To many, cost seems to be the crucial barrier. Sociologists of education have long argued, though, that inequalities start before costs matter. Entrenched “sort and sieve” processes apportion outcomes to family background. The whole system of grading, testing, and selecting some students while rejecting others makes a degree much more likely for students from higher status families—and that system was in place long before states limited appropriations and tuition skyrocketed. Analyzing longitudinal data from three cohorts of high school students, we find only small changes in the college graduation rate as of 1988, 1998, and 2010. Second, baseline socioeconomic and racial disparities in college completion were just as high in 1988 as in 2010. Third, mediation analysis shows that half of the socioeconomic disparities work through pre-college factors such as grades and curriculum choices. The other half reflect higher graduation rates at selective colleges. Fourth, the only notable change concerned community colleges; the potential disadvantage of starting at one declined after the 1980s. Our analysis affirms sociologists’ focus on persistent aspects of academic sorting, not recent changes, as the root of inequality of opportunity in American higher education.

Lundberg I.

Disparities across race, gender, and class are important targets of descriptive research. But rather than only describe disparities, research would ideally inform interventions to close those gaps. The gap-closing estimand quantifies how much a gap (e.g., incomes by race) would close if we intervened to equalize a treatment (e.g., access to college). Drawing on causal decomposition analyses, this type of research question yields several benefits. First, gap-closing estimands place categories like race in a causal framework without making them play the role of the treatment (which is philosophically fraught for non-manipulable variables). Second, gap-closing estimands empower researchers to study disparities using new statistical and machine learning estimators designed for causal effects. Third, gap-closing estimands can directly inform policy: if we sampled from the population and actually changed treatment assignments, how much could we close gaps in outcomes? I provide open-source software (the R package gapclosing) to support these methods.

Park S., Qin X., Lee C.

In the field of disparities research, there has been growing interest in developing a counterfactual-based decomposition analysis to identify underlying mediating mechanisms that help reduce disparities in populations. Despite rapid development in the area, most prior studies have been limited to regression-based methods, undermining the possibility of addressing complex models with multiple mediators and/or heterogeneous effects. We propose a novel estimation method that effectively addresses complex models. Moreover, we develop a sensitivity analysis for possible violations of an identification assumption. The proposed method and sensitivity analysis are demonstrated with data from the Midlife Development in the US study to investigate the degree to which disparities in cardiovascular health at the intersection of race and gender would be reduced if the distributions of education and perceived discrimination were the same across intersectional groups.

Zhou X.

Causal mediation analysis concerns the pathways through which a treatment affects an outcome. While most of the mediation literature focuses on settings with a single mediator, a flourishing line of research has examined settings involving multiple mediators, under which path-specific effects (PSEs) are often of interest. We consider estimation of PSEs when the treatment effect operates through K(≥ 1) causally ordered, possibly multivariate mediators. In this setting, the PSEs for many causal paths are not nonparametrically identified, and we focus on a set of PSEs that are identified under Pearl's nonparametric structural equation model. These PSEs are defined as contrasts between the expectations of 2 K + 1 potential outcomes and identified via what we call the generalized mediation functional (GMF). We introduce an array of regression-imputation, weighting and ‘hybrid’ estimators, and, in particular, two K + 2-robust and locally semiparametric efficient estimators for the GMF. The latter estimators are well suited to the use of data-adaptive methods for estimating their nuisance functions. We establish the rate conditions required of the nuisance functions for semiparametric efficiency. We also discuss how our framework applies to several estimands that may be of particular interest in empirical applications. The proposed estimators are illustrated with a simulation study and an empirical example.

Lundberg I., Johnson R., Stewart B.M.

We make only one point in this article. Every quantitative study must be able to answer the question: what is your estimand? The estimand is the target quantity—the purpose of the statistical analysis. Much attention is already placed on how to do estimation; a similar degree of care should be given to defining the thing we are estimating. We advocate that authors state the central quantity of each analysis—the theoretical estimand—in precise terms that exist outside of any statistical model. In our framework, researchers do three things: (1) set a theoretical estimand, clearly connecting this quantity to theory; (2) link to an empirical estimand, which is informative about the theoretical estimand under some identification assumptions; and (3) learn from data. Adding precise estimands to research practice expands the space of theoretical questions, clarifies how evidence can speak to those questions, and unlocks new tools for estimation. By grounding all three steps in a precise statement of the target quantity, our framework connects statistical evidence to theory.

Jackson J.W.

Causal decomposition analyses can help build the evidence base for interventions that address health disparities (inequities). They ask how disparities in outcomes may change under hypothetical intervention. Through study design and assumptions, they can rule out alternate explanations such as confounding, selection bias, and measurement error, thereby identifying potential targets for intervention. Unfortunately, the literature on causal decomposition analysis and related methods have largely ignored equity concerns that actual interventionists would respect, limiting their relevance and practical value. This article addresses these concerns by explicitly considering what covariates the outcome disparity and hypothetical intervention adjust for (so-called allowable covariates) and the equity value judgments these choices convey, drawing from the bioethics, biostatistics, epidemiology, and health services research literatures. From this discussion, we generalize decomposition estimands and formulae to incorporate allowable covariate sets (and thereby reflect equity choices) while still allowing for adjustment of non-allowable covariates needed to satisfy causal assumptions. For these general formulae, we provide weighting-based estimators based on adaptations of ratio-of-mediator-probability and inverse-odds-ratio weighting. We discuss when these estimators reduce to already used estimators under certain equity value judgments, and a novel adaptation under other judgments.

Nguyen T.Q., Schmid I., Stuart E.A.

The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements-effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this article is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference between the causal inference and traditional approaches to mediation analysis and making a case for the need for explicit causal thinking and the causal inference approach in mediation analysis. It then explains in as-plain-as-possible language existing effect types, paying special attention to motivating these effects with different types of research questions, and using concrete examples for illustration. This presentation differentiates 2 perspectives (or purposes of analysis): the explanatory perspective (aiming to explain the total effect) and the interventional perspective (asking questions about hypothetical interventions on the exposure and mediator, or hypothetically modified exposures). For the latter perspective, the article proposes tapping into a general class of interventional effects that contains as special cases most of the usual effect types-interventional direct and indirect effects, controlled direct effects and also a generalized interventional direct effect type, as well as the total effect and overall effect. This general class allows flexible effect definitions which better match many research questions than the standard interventional direct and indirect effects. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Storer A., Schneider D., Harknett K.

Precarious work in the United States is defined by economic and temporal dimensions. A large literature documents the extent of low wages and limited fringe benefits, but research has only recently examined the prevalence and consequences of unstable and unpredictable work schedules. Yet practices such as on-call shifts, last minute cancellations, and insufficient work hours are common in the retail and food-service sectors. Little research has examined racial/ethnic inequality in this temporal dimension of job quality, yet precarious scheduling practices may be a significant, if mostly hidden, site for racial/ethnic inequality, because scheduling practices differ significantly between firms and because front-line managers have substantial discretion in scheduling. We draw on innovative matched employer-employee data from The Shift Project to estimate racial/ethnic gaps in these temporal dimensions of job quality and to examine the contribution of firm-level sorting and intra-organizational dynamics to these gaps. We find significant racial/ethnic gaps in exposure to precarious scheduling that disadvantage non-white workers. We provide novel evidence that both firm segregation and racial discordance between workers and managers play significant roles in explaining racial/ethnic gaps in job quality. Notably, we find that racial/ethnic gaps are larger for women than for men.

Jeffrey W.

Although most students graduate from high school and enroll in college the following fall, rates of entry into higher education and completion of a bachelor's degree continue to be stratified by race and class. Because of the potential returns that accrue to individuals and society overall when students complete their 4-year degree, these disparate trends should motivate more policy-relevant research in this area. In this review, I show how a longitudinal perspective of the path to a BA degree helps to reconcile competing theories of college completion by race and class across disciplinary boundaries. Both human capital theory and status attainment theory largely examine college completion as the long-term process of BA attainment, although they differ in their focal stages and mechanisms. In contrast, the theory of categorical inequality, as applied in this review, focuses on the years in higher education and describes the ways in which colleges and universities as organizations create, legitimate, and reinforce categorical distinctions in postsecondary schooling and how these processes independently shape college completion inequality. As public interest grows in holding colleges accountable for their graduation rates, more research is needed on how the formal and informal organizational policies and practices of colleges produce inequality.

Smith-Doerr L., Alegria S., Husbands Fealing K., Fitzpatrick D., Tomaskovic-Devey D.

This study advances understanding of gender pay gaps by examining organizational variation. The gender pay gap literature supplies mechanisms but does not attend to organizational variation; the ge...

An W., N. Glynn A.

The Blinder–Oaxaca decomposition (BOD) is a popular method for studying the contributions of explanatory factors to social inequality. The results have often been given causal interpretations. While recent work and this article both show that some types of BOD are equivalent to a counterfactual-based treatment effect/selection bias decomposition, this equivalence does not hold in general. Given this lack of general equivalence, in this article based on the counterfactual framework, we propose a method of treatment effect deviation (TED) to study social inequality. Essentially, the TED assesses to what extent the omission of particular covariates (i.e., selection bias in the omitted variables) can alter the estimated treatment effect. The TED has a better causal interpretation and can be estimated nonparametrically (and hence is more robust to model misspecification errors). Therefore, the TED may serve as an alternative to or may be used in tandem with the BOD. We illustrate the new method through two case studies. In the first case study, we show that the TED provides a more credible estimate of the treatment effect on the treated than does the BOD. However, both the TED and the BOD highlight the importance of accounting for prior earning in estimating the training effect. In the second case study, the results of the two methods differ notably, but both agree that normative factors play a significant role in generating the rural–urban disparity in social policy preference in China.

Zhou X.

Intergenerational mobility is higher among college graduates than among people with lower levels of education. In light of this finding, researchers have characterized a college degree as a great equalizer leveling the playing field, and proposed that expanding higher education would promote mobility. This line of reasoning rests on the implicit assumption that the relatively high mobility observed among college graduates reflects a causal effect of college completion on intergenerational mobility, an assumption that has rarely been rigorously evaluated. This article bridges this gap. Using a novel reweighting technique, I estimate the degree of intergenerational income mobility among college graduates purged of selection processes that may drive up observed mobility in this subpopulation. Analyzing data from the National Longitudinal Survey of Youth 1979, I find that once selection processes are adjusted for, intergenerational income mobility among college graduates is very close to that among non-graduates. This finding suggests that expanding the pool of college graduates per se is unlikely to boost intergenerational income mobility in the United States. To promote mobility, public investments in higher education (e.g., federal and state student aid programs) should be targeted at low-income youth.

Ciocca Eller C., DiPrete T.A.

Bachelor’s degree (BA) completion is lower among black students than among white students. In this study, we use data from the Education Longitudinal Study of 2002 and the Integrated Postsecondary Education Data System, together with regression-based analytical techniques, to identify the primary sources of the BA completion gap. We find that black students’ lower academic and socioeconomic resources are the biggest drivers of the gap. However, we also find that black students are more likely to enroll in four-year colleges than are white students, given pre-college resources. We describe this dynamic as “paradoxical persistence” because it challenges Boudon’s well-known assertion that the secondary effect of educational decision-making should reinforce the primary effect of resource discrepancies. Instead, our results indicate that black students’ paradoxical persistence widens the race gap in BA completion while also narrowing the race gap in BA attainment, or the proportion of high school graduates to receive a BA. This narrowing effect on the BA attainment gap is as large or larger than the narrowing effect of black students’ “overmatch” to high-quality colleges, facilitated in part by affirmative action. Paradoxical persistence refocuses attention on black students’ individual agency as an important source of existing educational gains.