To understand the patterns and trends of various forms of inequality, quantitative social science research has typically relied on statistical models linking the conditional mean of an outcome of interest to a range of explanatory factors. A prime example of this approach is the widely used Kitagawa-Oaxaca-Blinder (KOB) method. By fitting two linear models separately for an advantaged group and a disadvantaged group, the KOB method decomposes the between-group outcome disparity into two parts, a part explained by group differences in a set of background characteristics and an unexplained part often dubbed “residual inequality.” In this paper, we explicate and contrast two distinct approaches to studying group disparities, which we term the descriptive approach, as epitomized by the KOB method and its variants, and the prescriptive approach, which focuses on how a disparity of interest would change under a hypothetical in- tervention to one or more manipulable treatments. For the descriptive approach, we propose a generalized KOB decomposition that considers multiple (sets of) explanatory variables sequen- tially. For the prescriptive approach, we introduce a variety of stylized interventions, such as lottery-type and affirmative-action-type interventions that close between-group gaps in treat- ment. We illustrate the two approaches to disparity analysis by assessing the Black-White gap in college completion, how it is statistically explained by racial differences in demographic and socioeconomic background, family structure, ability and behavior, and college selectivity, and the extent to which it would be reduced under hypothetical reallocations of college-goers from different racial/economic backgrounds into different tiers of college --- reallocations that could be targeted by race- or class-conscious admissions policies.
Zhou, Xiang, and Aleksei Opacic. Marginal Interventional Effects
[Abstract]
Conventional causal estimands, such as the average treatment effect (ATE), reflect how the mean outcome in a population or subpopulation would change if all units received treatment versus control. Real-world policy changes, however, are often incremental, changing the treatment status for only a small segment of the population who are at or near “the margin of participation.” To capture this notion, two parallel lines of inquiry have developed in economics and in statistics and epidemiology that define, identify, and estimate what we call interventional effects. In this article, we bridge these two strands of literature by defining interventional effect (IE) as the per capita effect of a treatment intervention on an outcome of interest, and marginal interventional effect (MIE) as its limit when the size of the intervention approaches zero. The IE and MIE can be viewed as the unconditional counterparts of the policy-relevant treatment effect (PRTE) and marginal PRTE (MPRTE) proposed in the economics literature. However, different from PRTE and MPRTE, IE and MIE are defined without reference to a latent index model, and, as we show, can be identified either under unconfoundedness or through the use of instrumental variables. For both scenarios, we show that MIEs are typically identified without the strong positivity assumption required of the ATE, highlight several “stylized interventions” that may be of particular interest in policy analysis, discuss several parametric and semiparametric estimation strategies, and illustrate the proposed methods with an empirical example.
Working papers
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Opacic, Aleksei. Mothers and Mobility: a Re-examination of (Trends in) Intergenerational Mobility in the UK
[Abstract]
Existing research on intergenerational class mobility typically uses either fathers’ occupation, or the occupation of the ‘class dominant’ parent, as an indicator of ‘class origin’, ignoring heterogeneity in mothers’ and fathers’ class effects on children’s mobility outcomes. Such an elision therefore misses how class reproduction may be shaped by gender in important ways. In this paper, I bring new empirical evidence to the role of mothers in intergenerational mobility in Britain for birth cohorts born in the latter half of the 20th century. I find a significant independent effect of mothers’ class on individuals’ class destinations, and evidence that fathers’ and mothers’ class positions show a stronger effect on same-gender children. Further, mothers and fathers’ class effects do not show similar trends across cohorts; while fathers’ effects have weakened for women but stayed constant for men, mothers’ effects have weakened for both men and women. My findings highlight the importance of taking a gender-sensitive approach to the study of intergenerational mobility patterns and trends.
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Opacic, Aleksei. An Interventional Approach to Primary and Secondary Class Effects on Intergenerational Mobility
[Abstract]
The theoretical distinction introduced by sociologists of education between primary and secondary class effects on educational outcomes helps researchers disentangle
mechanisms underpinning class-based educational inequalities. Research capitalizing on these concepts has, however, been inattentive to the multiple pathways that characterize attainment inequalities, net of demonstrated ability, and further reveals little about the contribution of such effects to intergenerational persistence more broadly. In this paper, I provide a new approach for conceptualizing primary and secondary effects within a causal framework. I propose two novel types of ‘secondary’ intervention on educational outcomes which map onto two distinct forms of policy intervention designed to break the link between social origin and education. My proposed approach engages with one of the primary contributions of the original theory - namely, the distillation of one mechanism underpinning class educational inequalities particularly amenable to policy intervention - while integrating this framework within the broader research agenda of education’s role in intergenerational mobility. Second, I demonstrate how researchers can quantify the impact of these educational interventions on mobility using observational data. I illustrate my approach by showing the utility of distinguishing between these two types of intervention in understanding the sources of intergenerational income persistence using the NLSY97 cohort.
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Opacic, Aleksei and Xiang Zhou. Path-Specific Effects Under Monotonic Mediation
[Abstract]
Identification and estimation of causal mechanisms is an area that has seen rapid innovation in recent years across the social sciences. Yet, to date, mediation analysis has been implicitly concerned exclusively with settings where levels of the mediator are accessible to all individuals, irrespective of their treatment status. Thus, conventional approaches are ill-equipped for studying many demographic events, actions and milestones that are characterized by a setup in which each “transition” can be considered “monotonic” in nature. In this article, we introduce a general framework for tracing causal mediation effects in the context of multiple monotonic mediators. Our framework considers the effect of any given demographic transition as operating indirectly, via subsequent transitions, and directly, net of these transitions. We demonstrate that the average treatment effect (ATE) of a transition can be additively decomposed into mutually exclusive components that capture these direct and indirect effects. Our proposed decomposition has a number of special properties which distinguish it from conventional decompositions of the ATE via multiple sequential mediators, properties which facilitate less restrictive identification assumptions as well as identification of all of the causal paths in the decomposition. We propose both parametric and semiparametric methods for estimating our decomposition, and illustrate the proposed framework using two empirical examples drawn from the education and sociology literature.