Generalized linear mixed models or multilevel regression models have become increasingly popular. Several methods have been proposed for estimating such models. However,to date there is no single method that can be assumed to work well in all circumstances in terms of both parameter recovery and...

The cluster robust variance estimator (CRVE) relies on the number of clusters being large. The precise meaning of 'large' is ambiguous, but a shorthand 'rule of 42' has emerged in the literature. We show that this rule depends crucially on the assumption of equal-sized clusters. Monte Carlo...

Many empirical projects are well suited to incorporating a linear difference-in-differences research design. While estimation is straightforward, reliable inference can be a challenge. Past research has not only demonstrated that estimated standard errors are biased dramatically downwards in...

Inference using difference-in-differences with clustered data requires care. Previous research has shown that t tests based on a cluster-robust variance estimator (CRVE) severely over-reject when there are few treated clusters, that different variants of the wild cluster bootstrap can...

Inference based on cluster-robust standard errors is known to fail when the number of clusters is small, and the wild cluster bootstrap fails dramatically when the number of treated clusters is very small. We propose a family of new procedures called the sub- cluster wild bootstrap. In the case...

Clustered covariances or clustered standard errors are very widely used to account for correlated or clustered data, especially in economics, political sciences, or other social sciences. They are employed to adjust the inference following estimation of a standard least-squares regression or...

We study a cluster-robust variance estimator (CRVE) for regression models with clustering in two dimensions that was proposed in Cameron, Gelbach, and Miller (2011). We prove that this CRVE is consistent and yields valid inferences under precisely stated assumptions about moments and cluster...

Inference for estimates of treatment effects with clustered data requires great care when treatment is assigned at the group level. This is true for both pure treatment models and difference-in-differences regressions. Even when the number of clusters is quite large, cluster-robust standard...

When there are few treated clusters in a pure treatment or difference-in-differences setting, t tests based on a cluster-robust variance estimator (CRVE) can severely over-reject. Although procedures based on the wild cluster bootstrap often work well when the number of treated clusters is not...

Political science data often contain grouped observations, which produces unobserved "cluster effects" in statistical models. Typical solutions include (1) ignoring the impact on coefficients and only adjusting the standard errors of generalized linear models (GLM) or (2) addressing clustering...