The difference-in-differences (DID) research design is a key identification strategy which allows researchers to estimate causal effects under the parallel trends assumption. While the parallel trends assumption is counterfactual and cannot be tested directly, researchers often examine pre-treatment periods to check whether the time trends are parallel before treatment is administered. Recently, researchers have been cautioned against using preliminary tests which aim to detect violations of parallel trends in the pre-treatment period. In this paper, we argue that preliminary testing can -- and should -- play an important role within the DID research design. We propose a new and more substantively appropriate conditional extrapolation assumption, which requires an analyst to conduct a preliminary test to determine whether the severity of pre treatment parallel trend violations falls below an acceptable level before extrapolation to the post-treatment period is justified. This stands in contrast to prior work which can be interpreted as either setting the acceptable level to be exactly zero (in which case preliminary tests lack power) or assuming that extrapolation is always justified (in which case preliminary tests are not required). Under mild assumptions on how close the actual violation is to the acceptable level, we provide a consistent preliminary test as well confidence intervals which are valid when conditioned on the result of the test. The conditional coverage of these intervals overcomes a common critique made against the use of preliminary testing within the DID research design. To illustrate the performance of the proposed methods, we use synthetic data as well as data on recentralization of public services in Vietnam and right-to-carry laws in Virginia.

翻译：双重差分法（DID）研究设计是一种关键识别策略，使研究者能够在平行趋势假设下估计因果效应。尽管平行趋势假设具有反事实性且无法直接检验，研究者常通过考察处理前时期来检验时间趋势在处理实施前是否平行。近来，学界对旨在检测处理前时期平行趋势违反的预检验方法提出了警示。本文主张，预检验能够且应当在DID研究设计中发挥重要作用。我们提出了一个新的、更具实质适当性的条件外推假设，该假设要求分析者执行预检验，以确定处理前平行趋势违反的严重程度是否低于可接受水平，从而证明向后处理时期外推的合理性。这与先前研究形成鲜明对比——先前研究可被解读为将可接受水平设为零（此时预检验缺乏效力），或假定外推始终合理（此时无需预检验）。在对实际违反程度接近可接受水平的温和假设下，我们提出了具有一致性的预检验方法，以及在以检验结果为条件时依然有效的置信区间。这些区间的条件覆盖特性克服了针对DID研究设计中预检验使用的常见批评。为说明所提方法的性能，我们使用了合成数据以及越南公共服务再集权化与弗吉尼亚州枪支携带权法的实证数据。