Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis
平衡、回归、双重差分与合成控制方法的综合AI 解读 ↓
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平衡、回归、双重差分与合成控制方法的综合AI 解读 ↓
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In a seminal paper Abadie, Diamond, and Hainmueller [2010] (ADH), see also Abadie and Gardeazabal [2003], Abadie et al. [2014], develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units. The method constructs a set of weights such that selected covariates and pre-treatment outcomes of the treated unit are approximately matched by a weighted average of control units (the synthetic control). The weights are restricted to be nonnegative and sum to one, which is important because it allows the procedure to obtain unique weights even when the number of lagged outcomes is modest relative to the number of control units, a common setting in applications. In the current paper we propose a generalization that allows the weights to be negative, and their sum to differ from one, and that allows for a permanent additive difference between the treated unit and the controls, similar to difference-in-difference procedures. The weights directly minimize the distance between the lagged outcomes for the treated and the control units, using regularization methods to deal with a potentially large number of possible control units.
交错处理采纳下结合双重差分调整的风险集传输合成控制
In staggered treatment-adoption designs, later-treated units are valid controls for an earlier-treated cohort only until their own treatment begins, so the admissible donor set contracts with event time. Fixing the donor pool at the longest horizon discards temporarily eligible donors, whereas re-estimating synthetic-control weights independently at each horizon can make the counterfactual unstable as donor composition changes. We propose Risk-Set Transported Synthetic…
以最小桥函数控制面板数据中的未观测混杂:从双向固定效应到因子模型
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences…
交错双重差分中的部分同质性
In staggered difference-in-differences (DiD) designs, units enter treatment at different calendar times, so the treatment effect is not a single number but a set of Cohort-Average Treatment effects on the Treated (CATTs), one per cohort-time cell. Estimating every CATT as its own parameter, as the standard fully flexible estimator does, is unbiased but inefficient when some of these effects are in fact equal, whereas pooling them all into a single two-way fixed effects…
合成控制中的谱截断
Synthetic control (SC) matches a treated unit's pre-treatment trajectory to a weighted combination of donor units. We study Spectral SC, which instead matches the treated unit in coordinates defined by the leading temporal singular vectors of the donor panel, and a hybrid estimator that places separately tunable weight on retained and discarded directions, nesting raw-path SC and truncated Spectral SC as endpoints. We prove that the family reduces exactly to raw-path SC at…
通过 Riesz 表示构建现代因果面板估计量的贝叶斯稳健性值
We develop a sensitivity-analysis workflow for causal panel estimators, covering synthetic difference-in-differences, matrix completion, fixed-effect imputation, and group-time average treatment effects. The workflow combines Riesz-representation omitted-variable-bias bounds with partial-$R^2$ robustness values and separates two reporting routes. Route A gives a direct sensitivity profile for additive or projected confounding summarized by outcome-side and Riesz-side partial…
正交化合成控制
When conducting inference for the average treatment effect on the treated with a Synthetic Control Estimator, the vector of control weights is a nuisance parameter that is often constrained, high-dimensional, and may be only partially identified even when the average treatment effect on the treated is point-identified. All three of these features of a nuisance parameter can lead to failure of asymptotic normality for the estimate of the parameter of interest when using…