Reworking Wild Bootstrap Based Inference for Clustered Errors

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 models possessing a group clustered design, but has also suggested a number of bootstrap-based improvements to the inference procedure. In this paper, I first demonstrate using Monte Carlo experiments, that these bootstrap-based procedures and traditional cluster-robust standard errors perform poorly in situations with fewer than eleven clusters - a setting faced in many empirical applications. With few clusters, the wild cluster bootstrap-t procedure results in p-values that are not point identified. I subsequently introduce two easy-to-implement alternative procedures that involve the wild bootstrap. Further Monte Carlo simulations provide evidence that the use of a 6-point distribution with the wild bootstrap can improve the reliability of inference.