发表机构
Graduate School of Economics, Keio University; Faculty of Economics, Keio University; RIKEN Center for Advanced Intelligence Project（庆应义塾大学经济学研究科; 庆应义塾大学经济学院; 理化学研究所先进智能项目中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种在双重差分中考虑数据驱动对照组选择的选择性推断方法，允许估计协方差，建立条件覆盖和边际覆盖，并适用于交错采用等复杂情形。
AI 中文摘要
在双重差分（DiD）中，研究者可能利用处理前趋势来选择对照组，使得平行趋势假设在该组中看似合理，目的是估计处理组平均处理效应（ATT）。我们早前的论文、Nakano 和 Hoshino (2016) 以及本文共同首次提供了明确考虑这种对照选择的 ATT 选择性推断方法。我们将已知协方差的精确高斯过程推广到允许协方差矩阵从用于对照选择和 DiD 估计的同一个体层面数据中估计。我们使用该估计来计算方差、条件方向、残差和截断集。在区域和时期数量固定的情况下，我们建立了选择事件的均匀条件覆盖，其概率远离零，并在没有该限制的情况下建立了所选目标边际覆盖。我们允许区域样本量不等、异质协方差、总体拟合中的并列情况以及趋于零的区域样本份额。我们建立了插入式与已知协方差区间端点之间的渐近等价性，并推导了区间长度的速率。对于交错采用，对照池可能因队列和时期而异，对照可能尚未被处理，观测可能被重复使用，处理效应可能是异质的。我们还构建了基于选择路径并集的条件推断，这些并集使报告的参数保持不变，同时为有限多个事件时间效应提供同时置信带。在平行趋势和其他识别条件下，覆盖结果适用于 ATT。我们给出了个体面板和独立重复横截面的充分抽样条件。
英文摘要
In difference-in-differences (DiD), researchers may use pre-treatment trends to select a control group for which the parallel-trends assumption appears plausible, with the aim of estimating the average treatment effect on the treated (ATT). Our earlier paper,Nakano and Hoshino (2016), and the present paper jointly provide the first selective-inference approach to the ATT that explicitly accounts for this control selection. We generalize our exact Gaussian procedure with known covariance to allow the covariance matrix to be estimated from the same individual-level data used for control selection and DiD estimation. We use this estimate to compute the variance, conditioning direction, residual, and truncation set. With fixed numbers of regions and periods, we establish uniform conditional coverage for selection events with probabilities bounded away from zero, and marginal coverage of the selected target without that restriction. We allow unequal regional sample sizes, heterogeneous covariances, ties in population fit, and regional sample shares that converge to zero. We establish asymptotic equivalence between the plug-in and known-covariance interval endpoints and derive rates for interval length. For staggered adoption, the control pools may differ across cohorts and periods, controls may be not yet treated, observations may be reused, and treatment effects may be heterogeneous. We also construct inference conditional on unions of selection paths that leave the reported parameter unchanged, together with simultaneous confidence bands for finitely many event-time effects. Under parallel trends and the other identifying conditions, the coverage results apply to the ATT. We give sufficient sampling conditions for individual panels and independent repeated cross-sections.
