SMEP: Bootstrap for Inference

SMEP: Bootstrap for Inference

There are too many variations on bootstrap.

Here is a list of choices for Wald tests with cluster-robust standard errors after OLS

{begin reformated citation Cameron, Gelbach Miller 2008}

Choices that need to be made when bootstrapping include the following:

• what observational units to sample (individual observations or clusters);
• what objects to sample in generating bootstrap sample (y, X) pairs, residuals drawn from the sample residuals, or residuals based on transformations of sample residuals);
• what statistics to calculate in each bootstrap replication;
• how to use the resulting bootstrap distribution of the statistics; and
• whether to impose the null hypothesis in generating the bootstrap samples.

Some combinations of these choices provide asymptotic refinement; others do not. Some choices in principle provide valid tests, but in fact perform poorly with few clusters and commonly occurring empirical settings.

{end citation}

The wild bootstrap (with -1, 1) is the best choice for Wald tests with robust (sandwich) standard errors according to several articles.