QED Working Paper Number

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 too small, they can either over-reject or under-reject seriously when it is. In a previous paper, we showed that procedures based on randomization inference (RI) can work well in such cases. However, RI can be impractical when the number of possible randomizations is small. We propose a bootstrap-based alternative to randomization inference, which mitigates the discrete nature of RI P values in the few-clusters case. We also compare it to two other procedures. None of them works perfectly when the number of clusters is very small, but they can work surprisingly well.

JEL Codes
randomization inference
grouped data
clustered data
panel data
wild cluster bootstrap
kernel-smoothed P value
Working Paper