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仅有一个集群接受处理时的推断

Inference with a Single Treated Cluster
Review of Economic Studies · 2025 · Andreas Hagemann

中文摘要

本文提出一种通用方法,用于在集群数量有限、集群具有异质性且仅有一个集群接受处理的研究设计中,对标量参数进行推断。这种情形在双重差分估计中十分常见,但本文提出的检验适用范围更广。本文证明,在各集群内观测数较大而集群数固定的渐近框架下,该检验能够控制检验水平并具有检验功效。该检验将加权的、近似服从高斯分布的参数估计量与重排程序相结合,以获得临界值。大多数实证研究相关情形所需的权重已在文中列成表格。临界值的计算简单,无需模拟或重抽样。对于某些集群的变异性远大于其他集群的情形,重排检验具有高度稳健性。文中提供了示例和一项实证应用。

Abstract

Abstract I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation, but the test developed here applies more broadly. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed. The test combines weighted, approximately Gaussian parameter estimates with a rearrangement procedure to obtain its critical values. The weights needed for most empirically relevant situations are tabulated in the paper. Calculation of the critical values is computationally simple and does not require simulation or resampling. The rearrangement test is highly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.
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