论文标题
合成控制方法的渐近特性
Asymptotic Properties of the Synthetic Control Method
论文作者
论文摘要
本文为合成控制方法（SCM）的渐近特性提供了新的见解。我们表明，合成控制（SC）的重量会收敛到有限的重量，当预处理周期数达到无穷大时，将平方平方的预测风险最小化，我们还量化了收敛速度。在观察SCM和模型平均之间的联系时，我们进一步建立了在不完善的预处理下的SC估计器的渐近优化性，从某种意义上说，它在所有可能的治疗效应估计器中达到了最低的平方预测误差，这些估计值基于控制单元的平均值，例如匹配，违反的可能性权重和差异差异和差异。无论控制单元的数量是固定的还是发散的，渐近最佳性能都保持不变。因此，我们的结果为SCM提供了广泛应用的理由。理论结果通过模拟进行验证。
This paper provides new insights into the asymptotic properties of the synthetic control method (SCM). We show that the synthetic control (SC) weight converges to a limiting weight that minimizes the mean squared prediction risk of the treatment-effect estimator when the number of pretreatment periods goes to infinity, and we also quantify the rate of convergence. Observing the link between the SCM and model averaging, we further establish the asymptotic optimality of the SC estimator under imperfect pretreatment fit, in the sense that it achieves the lowest possible squared prediction error among all possible treatment effect estimators that are based on an average of control units, such as matching, inverse probability weighting and difference-in-differences. The asymptotic optimality holds regardless of whether the number of control units is fixed or divergent. Thus, our results provide justifications for the SCM in a wide range of applications. The theoretical results are verified via simulations.
