Since LaLonde's (1986) seminal paper, there has been ongoing interest in estimating treatment effects using pre- and post-intervention data. Scholars have traditionally used experimental benchmarks to evaluate the accuracy of alternative econometric methods, including Matching, Difference-in-Differences (DID), and their hybrid forms (e.g., Heckman et al., 1998b; Dehejia and Wahba, 2002; Smith and Todd, 2005). We revisit these methodologies in the evaluation of job training and educational programs using four datasets (LaLonde, 1986; Heckman et al., 1998a; Smith and Todd, 2005; Chetty et al., 2014a; Athey et al., 2020), and show that the inequality relationship, Matching $\leq$ Hybrid $\leq$ DID, appears as a consistent norm, rather than a mere coincidence. We provide a formal theoretical justification for this puzzling phenomenon under plausible conditions such as negative selection, by generalizing the classical bracketing (Angrist and Pischke, 2009, Section 5). Consequently, when treatments are expected to be non-negative, DID tends to provide optimistic estimates, while Matching offers more conservative ones.

翻译：自LaLonde（1986）的开创性论文发表以来，利用干预前后数据估计处理效应的研究一直备受关注。学者们传统上采用实验基准来评估各种替代计量经济学方法的准确性，包括匹配法、双重差分法及其混合形式（例如Heckman等，1998b；Dehejia与Wahba，2002；Smith与Todd，2005）。本文使用四个数据集（LaLonde，1986；Heckman等，1998a；Smith与Todd，2005；Chetty等，2014a；Athey等，2020）重新审视这些方法在职业培训与教育项目评估中的应用，并证明不等式关系“匹配法 ≤ 混合法 ≤ 双重差分法”呈现为一种稳健的规律，而非偶然现象。我们在负向选择等合理条件下，通过推广经典的边界约束理论（Angrist与Pischke，2009，第5节），为这一令人困惑的现象提供了正式的理论解释。因此，当处理效应预期为非负时，双重差分法倾向于给出乐观的估计，而匹配法则提供更为保守的估计。