Asymptotic theory and wild bootstrap inference with clustered errors

By Antoine A. Djogbenou, James G. MacKinnon, Morten Ørregaard Nielsen. Journal of Econometrics, 2019

116 citations recorded by the source corpus.

We study inference based on cluster-robust variance estimators for regression models with clustered errors, focusing on the wild cluster bootstrap. We state conditions under which asymptotic and bootstrap tests and confidence intervals are asymptotically valid. These conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity. We also derive Edgeworth expansions for the asymptotic and bootstrap test statistics. Simulation experiments illustrate the theoretical results and suggest that alternative variants of the wild cluster bootstrap may perform quite differently. The Edgeworth expansions explain the overrejection of asymptotic tests and shed light on the choice of auxiliary distribution and whether to use restricted or unrestricted estimates in the bootstrap data-generating process.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/18dc0ba43568f736ea01727efdc5f35525c9f09a

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Citations in the corpus

Asymptotic theory for clustered samples (2019, unknown): “The conditions (11)-(12) may be stronger than necessary when within-cluster dependence is weak, but are necessary under strong within-cluster dependence.”
Towards Safe Policy Improvement for Non-Stationary MDPs (2020, unknown): “[23] and show in the following theorem that the CI for ρ(π, k + δ) obtained using pseudo-samples from wild bootstrap is consistent.”
Wild Bootstrap and Asymptotic Inference With Multiway Clustering (2019, unknown): “For example, in the context of heteroscedasticity and autocorrelation robust testing, Gonçalves and Vogelsang (2011) show theoretically that the iid bootstrap is more accurate than the standard normal approximation, even when data are serially correlated, as long as the test statistic is calculated…”
Cluster-robust inference: A guide to empirical practice (2022, methodology): “Djogbenou et al. (2019) also proves the asymptotic validity of two variants of the ordinary wild bootstrap, restricted (WR) and unrestricted (WU), for the model (1).”
The Wild Bootstrap with a “Small” Number of “Large” Clusters (2019, background): “Given that in this application 2 1 − q ≤ 2 − 18 , theorem 3 and the beneﬁts of studentizing as the number of clusters diverges to inﬁnity (Djogbenou et al., 2019) suggest that test based on the studentized wild bootstrap p -values are preferable to those based on unstudentized wild bootstrap p…”