A Penalized Synthetic Control Estimator for Disaggregated Data
A Penalized Synthetic Control Estimator for Disaggregated Data
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DOI：
10.1080/01621459.2021.1971535
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发表时间：
2021-11-03
影响因子：
3.7
通讯作者：
L'Hour, Jeremy
中科院分区：
文献类型：
--
作者：
Abadie, Alberto;L'Hour, Jeremy
综合控制方法通常用于实证研究，以估计治疗或干预对总体结果的影响。一个综合控制估计器比较处理单元的结果与未处理单元的加权平均值的结果，未处理单元的加权平均值最类似于干预前处理单元的特征。当分类数据可用时，为每个处理单元构建单独的合成控制可能有助于避免插值偏差。然而，找到一个合成控制，最好地再现处理单元的特性的问题可能没有一个唯一的解决方案。当数据包括许多处理和未处理的单位时，解决方案的多样性是一个特别艰巨的挑战。为了解决这一挑战，我们提出了一个合成控制估计，惩罚成对的差异之间的特性的处理单元和特性的单位，有助于他们的合成控制。惩罚参数权衡相对于合成控制中的每个单元的特性的成对匹配差异和相对于作为整体的合成控制单元的特性的匹配差异。我们研究了这个估计的性质，并提出了数据驱动的惩罚参数的选择。
Synthetic control methods are commonly applied in empirical research to estimate the effects of treatments or interventions on aggregate outcomes. A synthetic control estimator compares the outcome of a treated unit to the outcome of a weighted average of untreated units that best resembles the characteristics of the treated unit before the intervention. When disaggregated data are available, constructing separate synthetic controls for each treated unit may help avoid interpolation biases. However, the problem of finding a synthetic control that best reproduces the characteristics of a treated unit may not have a unique solution. Multiplicity of solutions is a particularly daunting challenge when the data include many treated and untreated units. To address this challenge, we propose a synthetic control estimator that penalizes the pairwise discrepancies between the characteristics of the treated units and the characteristics of the units that contribute to their synthetic controls. The penalization parameter trades off pairwise matching discrepancies with respect to the characteristics of each unit in the synthetic control against matching discrepancies with respect to the characteristics of the synthetic control unit as a whole. We study the properties of this estimator and propose data-driven choices of the penalization parameter.