In studies of discrimination, researchers often seek to estimate a causal effect of race or gender on outcomes. For example, in the criminal justice context, one might ask whether arrested individuals would have been subsequently charged or convicted had they been a different race. It has long been known that such counterfactual questions face measurement challenges related to omitted-variable bias, and conceptual challenges related to the definition of causal estimands for largely immutable characteristics. Another concern, which has been the subject of recent debates, is post-treatment bias: many studies of discrimination condition on apparently intermediate outcomes, like being arrested, that themselves may be the product of discrimination, potentially corrupting statistical estimates. There is, however, reason to be optimistic. By carefully defining the estimand -- and by considering the precise timing of events -- we show that a primary causal quantity of interest in discrimination studies can be estimated under an ignorability condition that may hold approximately in some observational settings. We illustrate these ideas by analyzing both simulated data and the charging decisions of a prosecutor's office in a large county in the United States.

翻译：在对歧视的研究中,研究人员往往试图估计种族或性别对结果的因果关系。例如,在刑事司法方面,人们可能会问,如果被捕者是不同的种族,他们后来是否会受到指控或定罪。人们早就知道,这种反事实问题面临着与省略可变的偏见有关的计量挑战,以及与因果估计值定义有关的概念挑战,因为在很大程度上是不可改变的特征。最近辩论的另一个问题是后期偏见:许多关于明显中间结果的歧视状况的研究,如被捕,可能是歧视的产物,有可能腐蚀统计估计。然而,有理由感到乐观。通过仔细界定估计数字 -- -- 并考虑到事件的准确时间 -- -- 我们表明,对歧视研究兴趣的主要因果数量可以估计,但这种忽略条件在某些观察环境中可能大致存在。我们通过分析模拟数据和美国大县检察官办公室的起诉决定来说明这些想法。