Difference-in-differences (DiD) is a popular method to evaluate causal effects of real-world policy interventions. To identify the average treatment effect on the treated, DiD relies on the parallel trends (PT) assumption, which states that the time trends for the average of treatment-free potential outcomes are parallel across the treated and control groups. A well-known limitation of the PT assumption is its lack of generalization to causal effects for discrete outcomes and to nonlinear effect measures. In this paper, we consider Universal Difference-in-Differences (UDiD) based on an alternative assumption to PT for identifying treatment effects for the treated on any scale of potential interest, and outcomes of an arbitrary nature. Specifically, we introduce the odds ratio equi-confounding (OREC) assumption, which states that the generalized odds ratios relating the treatment-free potential outcome and treatment are equivalent across time periods. Under the OREC assumption, we establish nonparametric identification for any potential treatment effect on the treated in view. Moreover, we develop a consistent, asymptotically linear, and semiparametric efficient estimator for any given treatment effect on the treated of interest which leverages recent learning theory. We illustrate UDiD with simulations and two real-world applications in labor economics and traffic safety evaluation.
翻译:差异差异(DID)是评价现实世界政策干预的因果关系的流行方法。为了确定对治疗对象的平均治疗效果,DID依赖平行趋势的假设(PT),该假设指出,在接受治疗和控制的群体中,无治疗潜在结果平均结果的时间趋势是平行的。PT假设的一个众所周知的限制是,它缺乏对离散结果和非线性效果措施的因果关系的概括性影响。在本文中,我们认为普遍差异差异(UDID)是基于一种替代假设,即确定治疗对象在任何范围的潜在利益治疗的治疗效果和任意性质的结果。具体地说,我们采用不治疗潜在结果的平均时间趋势(OREC)假设,该假设表明与无治疗潜在结果和治疗相关的普遍差异比率在一段时间内是相等的。根据OREC的假设,我们对所治疗对象的任何潜在治疗效果是任何可能的治疗效果。此外,我们开发了一种一致的、即时线性、半数的高效交通评估工具,用以说明对最新劳动力理论和现实性理论中的任何影响。