In this paper, we generalize methods in the Difference in Differences (DiD) literature by showing that both additive and multiplicative standard and coarse Structural Nested Mean Models (Robins, 1994, 1997, 1998, 2000, 2004; Lok and Degruttola, 2012; Vansteelandt and Joffe, 2014) are identified under parallel trends assumptions. Our methodology enables adjustment for time-varying covariates, identification of effect heterogeneity as a function of time-varying covariates, identification of additional causal contrasts (such as effects of a `blip' of treatment at a single time point followed by no further treatment and controlled direct effects), and estimation of treatment effects under a general class of treatment patterns (e.g. we do not restrict to the `staggered adoption' setting, and treatments can be multidimensional with any mix of categorical and continuous components). We stress that these extensions come essentially for free, as our parallel trends assumption is not stronger than other parallel trends assumptions in the DiD literature. We also provide a method for sensitivity analysis to violations of our parallel trends assumption. However, in contrast to much of the DiD literature, we only consider panel data, not repeated cross sectional data. We also explain how to estimate optimal treatment regimes via optimal regime Structural Nested Mean Models under parallel trends assumptions plus an assumption that there is no effect modification by unobserved confounders. Finally, we illustrate our methods with real data applications estimating effects of bank deregulation on housing prices and effects of floods on flood insurance take-up.

翻译：在本文中,我们概括了差异差异(DID)文献中的方法,表明在平行趋势假设下确定“差异(Robins,1994年、1997年、1998年、2000年、2004年、Lok和Degruttola,2012年;Vansteelandt和Joffe,2014年),我们的方法可以调整时间变化的共变,确定影响差异差异(DID)文献中的差异,找出额外的因果对比(例如,在一个单一时间点上“重复”治疗的影响,然后没有进一步的治疗和控制的直接效果),以及在一般治疗模式下对治疗效果的估计(例如,我们不限制“错采用”设置,而治疗可以是多层面的,任何明确和连续的组成部分组合)。我们强调,这些扩展基本上免费,因为我们的平行趋势假设并不比DID文献中的其他平行趋势假设更强。我们还提供一种方法,用以对违反我们平行趋势假设的情况进行敏感性分析。然而,我们与“反复采用”采用“错位”的假设相比,我们只是用“模型”的假设来解释“反复使用“反复使用”的模型和“结构”的假设。