A Negative Correlation Strategy for Bracketing in Difference-in-Differences

• 成果类型: Article
• 署名作者: Ye, Ting; Keele, Luke; Hasegawa, Raiden; Small, Dylan S.
• 署名单位: University of Washington; University of Washington Seattle; University of Pennsylvania; Alphabet Inc.; Google Incorporated
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2252576
• 发表日期: 2024
• 页码: 2256-2268
• 关键词: partial identification; confidence-intervals; sensitivity-analysis; moment inequalities; inference

摘要

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 using the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we theoretically establish the asymptotic validity of the proposed method. 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. Supplementary materials for this article are available online.