Covariate balancing estimation and model selection for difference-in-differences approach
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双重差分方法的协变量平衡估计与模型选择
- 研究问题
- 如何增强半参数双重差分中处理组平均效应估计对倾向得分误设的稳健性，并建立与其目标损失相匹配的模型选择准则？
- 方法与思路
- 作者在倾向得分逆加权中加入协变量平衡，通过设计矩条件获得双重稳健性，并推导目标风险的渐近偏差修正选择准则。
- 材料陈述的贡献
- 摘要称新估计具双重稳健性，模型选择惩罚不同于常见 AIC 型形式；数值实验报告更稳健的效应估计及更低的目标风险。
- 阅读关注点
- 应核对双重稳健性对应的两类模型、DID 识别条件、平衡矩构造，以及选择准则的风险定义、惩罚推导和比较方案。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或被期刊接收；摘要未详述识别与模型条件，实证结果差异本身不能证明新方法更准确。
原文摘要
Remarkable progress has been made in difference-in-differences (DID) approaches to causal inference that estimate the average effect of a treatment on the treated (ATT). Of these, the semiparametric DID (SDID) approach incorporates a propensity score analysis into the DID setup. Supposing that the ATT is a function of covariates, we estimate it by weighting the inverse of the propensity score. In this study, as one way to make the estimation robust to the propensity score modeling, we incorporate covariate balancing. Then, by attentively constructing the moment conditions used in the covariate balancing, we show that the proposed estimator is doubly robust. In addition to the estimation, we also address model selection. In practice, covariate selection is an essential task in statistical analysis, but even in the basic setting of the SDID approach, there are no reasonable information criteria. Here, we derive a model selection criterion as an asymptotically bias-corrected estimator of risk based on the loss function used in the SDID estimation. We show that a penalty term can be derived that is considerably different from almost twice the number of parameters that often appears in AIC-type information criteria. Numerical experiments show that the proposed method estimates the ATT more robustly compared with the method using propensity scores given by maximum likelihood estimation, and that the proposed criterion clearly reduces the risk targeted in the SDID approach in comparison with the intuitive generalization of the existing information criterion. In addition, real data analysis confirms that there is a large difference between the results of the proposed method and those of the existing method.