Matrix Completion Methods for Causal Panel Data Models
因果面板数据模型的矩阵补全方法AI 解读 ↓
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因果面板数据模型的矩阵补全方法
- 研究问题
- 面板中部分单位在部分时期接受处理时，如何利用未处理观测补全反事实结果，并据此估计处理的因果效应？
- 方法与思路
- 作者利用未处理结果矩阵的已观测元素，通过核范数正则化补全处理单元的反事实结果，并允许缺失模式具有时间依赖。
- 材料陈述的贡献
- 摘要称，方法连接矩阵补全、交互固定效应、无混杂性与合成控制，并在基于真实数据的模拟中优于所比较方法。
- 阅读关注点
- 应核对反事实识别条件、矩阵复杂度限制、处理时序与缺失依赖的处理，以及统一目标函数和模拟比较的具体设定。
- 阅读边界
- 所据为 arXiv 预印本，同行评审与期刊接收未核实；摘要未给出识别条件和模拟数值，所述优势不能外推至所有面板。
原文摘要
In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix, corresponding to treated units/periods. This leads to a matrix that well-approximates the original (incomplete) matrix, but has lower complexity according to the nuclear norm for matrices. We generalize results from the matrix completion literature by allowing the patterns of missing data to have a time series dependency structure that is common in social science applications. We present novel insights concerning the connections between the matrix completion literature, the literature on interactive fixed effects models and the literatures on program evaluation under unconfoundedness and synthetic control methods. We show that all these estimators can be viewed as focusing on the same objective function. They differ solely in the way they deal with identification, in some cases solely through regularization (our proposed nuclear norm matrix completion estimator) and in other cases primarily through imposing hard restrictions (the unconfoundedness and synthetic control approaches). The proposed method outperforms unconfoundedness-based or synthetic control estimators in simulations based on real data.