Difference-in-differences (DiD) is a popular method to evaluate treatment effects of real-world policy interventions. Several approaches have previously developed under alternative identifying assumptions in settings where pre- and post-treatment outcome measurements are available. However, these approaches suffer from several limitations, either (i) they only apply to continuous outcomes and the average treatment effect on the treated, or (ii) they depend on the scale of outcome, or (iii) they assume the absence of unmeasured confounding given pre-treatment covariate and outcome measurements, or (iv) they lack semiparametric efficiency theory. In this paper, we develop a new framework for causal identification and inference in DiD settings that satisfies (i)-(iv), making it universally applicable, unlike existing DiD methods. Key to our framework is an odds ratio equi-confounding (OREC) assumption, which states that the generalized odds ratio relating treatment and treatment-free potential outcome is stable across pre- and post-treatment periods. Under the OREC assumption, we establish nonparametric identification for any potential treatment effect on the treated in view, which in principle would be identifiable under the stronger assumption of no unmeasured confounding. Moreover, we develop a consistent, asymptotically linear, and semiparametric efficient estimator of treatment effects on the treated by leveraging recent learning theory. We illustrate our framework with extensive simulation studies and two well-established real-world applications in labor economics and traffic safety evaluation.

翻译：双重差分法是一种评估现实世界政策干预处理效应的流行方法。在可获得处理前后结果测量的场景中，已有多种基于不同识别假设的方法被提出。然而，这些方法存在若干局限性，具体表现为：(i) 仅适用于连续型结果变量及处理组的平均处理效应；(ii) 依赖于结果变量的尺度；(iii) 假设在给定处理前协变量和结果测量后不存在未测量混杂；或 (iv) 缺乏半参数效率理论。本文针对双重差分框架提出一种新的因果识别与推断方法，同时满足条件(i)-(iv)，从而使其具有普适性——这是现有双重差分方法所不具备的。该框架的核心在于比值比等混杂假设：该假设表明，处理与未处理潜在结果之间的广义比值比在处理前和处理后时期保持稳定。在该假设下，我们建立了任何目标处理组处理效应的非参数识别——这些效应从原理上当存在更强的无未测量混杂假设时即可被识别。此外，通过借鉴最新学习理论，我们构建了一致、渐近线性且半参数有效的处理组处理效应估计量。最后通过大量模拟研究及劳动经济学与交通安全评估两个经典现实应用验证了该框架的有效性。