Reworking wild bootstrap-based inference for clustered errors

Cluster-robust inference is increasingly common in empirical research. With few clusters, inference is often conducted using the wild cluster bootstrap. With conventional bootstrap weights the set of valid $P$-values can create ambiguities in inference. I consider several modifications to the bootstrap procedure to resolve these ambiguities. Monte Carlo simulations provide evidence that both a new 6-point bootstrap weight distribution and a kernel density estimation approach improve the reliability of inference. A brief empirical example highlights the implications of these findings.