标题： 当干扰参数可能部分识别时的稳健推断及其在合成控制中的应用 显示英文标题

标题： Robust Inference when Nuisance Parameters may be Partially Identified with Applications to Synthetic Controls

摘要： 在使用合成控制估计量进行处理组平均处理效应的推断时，控制权重向量是一个干扰参数，通常受到约束、高维，并且即使处理组平均处理效应是点识别的，也可能仅部分识别。 这三种干扰参数的特性在使用标准方法时可能导致感兴趣参数估计量的渐近正态性失效。 我提供了一种新方法，即使存在所有这三个复杂情况，也能使感兴趣参数的估计量具有渐近正态性。 这是通过首先使用正则化惩罚估计干扰参数以实现某种形式的识别，然后使用相对于干扰参数正交化的矩条件来估计感兴趣参数来实现的。 我提出了该估计量的高层充分条件，并在一个涉及合成控制的示例中验证了这些条件。 显示英文摘要

摘要： 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 which 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 standard methods. I provide a new method yielding asymptotic normality for an estimate of the parameter of interest, even when all three of these complications are present. This is accomplished by first estimating the nuisance parameter using a regularization penalty to achieve a form of identification, and then estimating the parameter of interest using moment conditions that have been orthogonalized with respect to the nuisance parameter. I present high-level sufficient conditions for the estimator and verify these conditions in an example involving Synthetic Controls.