Trajectory Balancing: A General Reweighting Approach to Causal Inference With Time-Series Cross-Sectional Data
Trajectory Balancing: A General Reweighting Approach to Causal Inference With Time-Series Cross-Sectional Data
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轨迹平衡：利用时间序列横截面数据进行因果推理的通用重新加权方法
DOI：
10.2139/ssrn.3214231
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Yiqing Xu
中科院分区：
文献类型：
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作者：
C. Hazlett;Yiqing Xu
我们介绍了轨迹平衡，一般的重新加权的因果推理与时间序列横截面（TSCS）数据的方法。我们专注于其中一个或多个单元在给定时间暴露于治疗的设置，而一组控制单元在整个感兴趣的时间窗口内保持未治疗。首先，我们表明，许多常用的TSCS方法意味着一个假设，即一个单位的非治疗的潜在结果在治疗后的时期是线性的，该单位的治疗前的结果，以及时不变的协变量。在此假设下，我们引入了均值平衡法，该方法对控制单元进行重新加权，使得治疗前结局和协变量的平均值在治疗组和（重新加权）对照组之间近似相等。其次，我们放松了线性假设，并提出了核平衡方法，寻求一个近似的平衡基于核的特征扩展的预处理结果和协变量。该方法继承了综合控制模型和潜在因子模型中处理时变混杂因素的特性，但具有以下优点：（1）与现有方法相比，提高了可行性和稳定性，减少了用户的自由裁量权;（2）适应于短和长的预处理时间段，处理单元多或少;以及（3）在治疗前结果的高阶“轨迹”上实现平衡，而不是在每个时间段的简单平均值。我们用模拟和两个实证例子来说明这种方法。
We introduce trajectory balancing, a general reweighting approach to causal inference with time-series cross-sectional (TSCS) data. We focus on settings in which one or more units is exposed to treatment at a given time, while a set of control units remain untreated throughout a time window of interest. First, we show that many commonly used TSCS methods imply an assumption that a unit's non-treatment potential outcomes in the post-treatment period are linear in that unit's pre-treatment outcomes as well as time-invariant covariates. Under this assumption, we introduce the mean balancing method that reweights the control units such that the averages of the pre-treatment outcomes and covariates are approximately equal between the treatment and (reweighted) control groups. Second, we relax the linearity assumption and propose the kernel balancing method that seeks an approximate balance on a kernel-based feature expansion of the pre-treatment outcomes and covariates. The resulting approach inherits the property of handling time-vary confounders as in synthetic control and latent factor models, but has the advantages of: (1) improving feasibility and stability with reduced user discretion compared to existing approaches; (2) accommodating both short and long pre-treatment time periods with many or few treated units; and (3) achieving balance on the high-order "trajectory" of pre-treatment outcomes rather than their simple average at each time period. We illustrate this method with simulations and two empirical examples.