The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently in the absence of treatment, namely if the parallel trends assumption is violated. We propose a general identification strategy that leverages two groups of control units whose outcomes relative to the treated units exhibit a negative correlation, and achieves partial identification of the average treatment effect for the treated. The identified set is of a union bounds form that involves the minimum and maximum operators, which makes the canonical bootstrap generally inconsistent and naive methods overly conservative. By utilizing the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct uniformly valid confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we establish the method's theoretical properties. We develop a simple falsification test and sensitivity analysis. We apply the proposed strategy for bracketing to study whether minimum wage laws affect employment levels.
翻译:然而,如果治疗和控制单位的结果在没有治疗的情况下变化不同,即如果平行趋势假设被违反,那么根据不同的计算方法将产生偏差。我们提议一项一般性的识别战略,利用两组控制单位,其结果与所治疗单位的对比显示负相关,并部分确定所治疗单位的平均治疗效果。确定的一套是涉及最低操作员和最大操作员的结合界限,使罐装靴普遍不一致和天真的方法过于保守。我们利用靴子分布的方向不一致,开发一种新颖的靴子捕捉方法,以在所查明的套装套合形式时,为已确定的固定利息和参数建立统一有效的信任间隔,并确立该方法的理论属性。我们开发了一种简单的伪造测试和敏感性分析。我们采用了一个涉及最低操作员和最大操作员的联盟界限形式,这使得罐装靴子装置普遍不连贯和天真的方法过于保守。我们采用拟议的战略来研究最低限度工资等级是否影响工资等级。