Fast cluster bootstrap methods for linear regression models

Efficient computational algorithms for bootstrapping linear regression models with clustered data are discussed. For OLS regression, a new algorithm is provided for the pairs cluster bootstrap, and two algorithms for the wild cluster bootstrap are compared. One of these is a new way to express an existing algorithm, and the other is new. For IV regression, an algorithm is provided for the wild restricted efficient cluster (WREC) bootstrap, which up to now has been computationally burdensome for large samples. These algorithms are remarkably fast because all computations are based on matrices and vectors that contain sums over the observations within each cluster, which have to be computed just once before the bootstrap loop begins. Monte Carlo experiments are used to study the finite\tkk-sample properties of bootstrap Wald tests for OLS regression and of WREC bootstrap tests for IV regression.