When Should You Adjust Standard Errors for Clustering?
提出一个包含抽样和实验设计的新框架，解释为何在某些情况下（如按州而非性别）调整聚类标准误，并指出当样本中聚类数占总体比例较大时，传统标准误可能严重偏大，进而提出修正的方差估计量。
Abstract Clustered standard errors, with clusters defined by factors such as geography, are widespread in empirical research in economics and many other disciplines. Formally, clustered standard errors adjust for the correlations induced by sampling the outcome variable from a data-generating process with unobserved cluster-level components. However, the standard econometric framework for clustering leaves important questions unanswered: (i) Why do we adjust standard errors for clustering in some ways but not others, for example, by state but not by gender, and in observational studies but not in completely randomized experiments? (ii) Is the clustered variance estimator valid if we observe a large fraction of the clusters in the population? (iii) In what settings does the choice of whether and how to cluster make a difference? We address these and other questions using a novel framework for clustered inference on average treatment effects. In addition to the common sampling component, the new framework incorporates a design component that accounts for the variability induced on the estimator by the treatment assignment mechanism. We show that, when the number of clusters in the sample is a nonnegligible fraction of the number of clusters in the population, conventional clustered standard errors can be severely inflated, and propose new variance estimators that correct for this bias.