We study several methods of constructing confidence sets for the coefficient of the single right-hand-side endogenous variable in a linear equation with weak instruments. Two of these are based on conditional likelihood ratio (CLR) tests, and the others are based on inverting <italic>t</italic> statistics or the...

Confidence intervals based on cluster-robust covariance matrices can be constructed in many ways. In addition to conventional intervals obtained by inverting Wald (t) tests, the paper studies intervals obtained by inverting LM tests, studentized bootstrap intervals based on the wild cluster...

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...

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...

Inference using large datasets is not nearly as straightforward as conventional econometric theory suggests when the disturbances are clustered, even with very small intra-cluster correlations. The information contained in such a dataset grows much more slowly with the sample size than it would...

Confidence intervals based on cluster-robust covariance matrices can be constructed in many ways. In addition to conventional intervals obtained by inverting Wald (t) tests, the paper studies intervals obtained by inverting LM tests, studentized bootstrap intervals based on the wild cluster...