A General Synthetic Control Framework of Estimation and Inference

在过去十年中，综合控制估计器在经济学和社会科学的实证研究中被广泛应用，作为评估公共政策和其他干预措施或利益事件影响的工具。对于受感兴趣的干预影响的每个单元（例如，城市，州或地区），合成控制是选择未受影响单元的组合，以类似于干预前处理单元的特征。综合控制用于估计受影响单位在没有感兴趣的干预的情况下所达到的结果，为研究人员评估政策影响提供了一个基准。综合控制方法最初是针对一个或少量的总单位受到利益政策影响的情况而开发的。然而，应用文献在这一领域的贡献已经超过了方法论。特别是，许多当前的应用程序侧重于具有大量受影响单元的设置。因此，需要额外的方法学研究来指导该方法的实证实施。这项研究将为实证研究人员提供一个强大的、通用的框架，用于综合控制的估计和推理，以及实现它的免费软件。当分解数据可用时，为每个处理单元构建单独的合成控制有助于避免插值偏差。然而，寻找一种最能再现处理单元特性的综合控制方法可能没有唯一的解决方案，而在有许多处理单元的情况下，解决方案的多样性是一个特别艰巨的挑战。本研究将为估计和推理提供一个广义的综合控制框架。该框架建立在合成控制的基础上，并引入了一个惩罚参数，该参数将合成控制中每个单元的特性的成对匹配差异与合成控制单元的整体特性的匹配差异进行权衡。可以证明，只要惩罚参数为正，广义综合控制估计量是唯一且稀疏的。研究人员提出了惩罚参数的数据驱动选择，以及在许多处理单元设置中合成控制的推理方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Over the past decade, synthetic control estimators have found wide applicability in empirical research in economics and the social sciences as tools to evaluate the effects of public policies and other interventions or events of interests. For each unit (e.g., city, state, or region) affected by the intervention of interest, a synthetic control is a combination on unaffected units chosen to resemble the characteristics of the treated units before the intervention. Synthetic controls are used to estimate the outcomes that affected units would have attained in the absence of the intervention of interest, providing a benchmark against which researchers can evaluate policy impacts. The synthetic control method was originally developed for cases with one or a small number of aggregate units affected by the policy of interest. However, the applied literature has surpassed the methodological contributions in this area. In particular, many current applications focus on settings with a large number of affected units. As a result, additional methodological research is needed to guide the empirical implementation of the method. This research will provide empirical researchers with a robust and general framework for estimation and inference with synthetic controls as well as freely available software with which to implement it.When disaggregated data are available, constructing separate synthetic controls for each treated unit helps 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, and multiplicity of solutions is a particularly daunting challenge in settings with many treated units. This research will provide a generalized synthetic control framework for estimation and inference. The framework builds on synthetic controls and introduces a penalization parameter that 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. It can be shown that, as long as the penalization parameter is positive, the generalized synthetic control estimator is unique and sparse. The investigators propose data driven choices for the penalization parameter, as well as inferential methods for synthetic controls in settings with many treated units.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.