Distributional Counterfactual Analysis in High-Dimensional Setup
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高维设定下的分布反事实分析
- 研究问题
- 当面板中仅有一个或少数处理单位、潜在对照很多时，如何恢复整个反事实分布，并推断干预后的逐期处理效应？
- 方法与思路
- 作者使用干预前数据进行 l1 惩罚条件分位数回归，推导分位数上一致的非渐近界，并构造效应区间与尖锐零假设检验。
- 材料陈述的贡献
- 摘要称，误差界显式关联时间长度、对照数量、β 混合和尾部衰减，并提出临界值可模拟的近枢轴检验。
- 阅读关注点
- 应核对反事实识别、稀疏性和时间稳定性条件，以及分位数一致界、覆盖率界与近枢轴零分布各自的适用范围。
- 阅读边界
- 所给来源为 arXiv 预印本，同行评审未经核实；摘要未列完整条件，零分布涉及干预后期数及其“大小”的表述需核对。
原文摘要
In the context of treatment effect estimation, this paper proposes a new methodology to recover the counterfactual distribution when there is a single (or a few) treated unit and possibly a high-dimensional number of potential controls observed in a panel structure. The methodology accommodates, albeit does not require, the number of units to be larger than the number of time periods (high-dimensional setup). As opposed to modeling only the conditional mean, we propose to model the entire conditional quantile function (CQF) without intervention and estimate it using the pre-intervention period by a l1-penalized regression. We derive non-asymptotic bounds for the estimated CQF valid uniformly over the quantiles. The bounds are explicit in terms of the number of time periods, the number of control units, the weak dependence coefficient (beta-mixing), and the tail decay of the random variables. The results allow practitioners to re-construct the entire counterfactual distribution. Moreover, we bound the probability coverage of this estimated CQF, which can be used to construct valid confidence intervals for the (possibly random) treatment effect for every post-intervention period. We also propose a new hypothesis test for the sharp null of no-effect based on the Lp norm of deviation of the estimated CQF to the population one. Interestingly, the null distribution is quasi-pivotal in the sense that it only depends on the estimated CQF, Lp norm, and the number of post-intervention periods, but not on the size of the post-intervention period. For that reason, critical values can then be easily simulated. We illustrate the methodology by revisiting the empirical study in Acemoglu, Johnson, Kermani, Kwak and Mitton (2016).