Inference with Dependent Data Using Cluster Covariance Estimators

Abstract

This paper presents an inference approach for dependent data in time series, spatial, and panel data applications. The method involves constructing and Wald statistics using a cluster covariance matrix estimator (CCE). We use an approximation that takes the number of clusters/groups as fixed and the number of observations per group to be large. The resulting limiting distributions of the t and Wald statistics are standard t and F distributions where the number of groups plays the role of sample size. Using a small number of groups is analogous to 'fixed-b' asymptotics of Kiefer and Vogelsang (2002, 2005) (KV) for heteroskedasticity and autocorrelation consistent inference. We also consider the case where the number of groups goes to infinity and obtain results similar to those for standard heteroskedasticity and autocorrelation consistent (HAC) estimators under the usual HAC asymptotics. We provide simulation evidence that demonstrates the procedure substantially outperforms conventional inference procedures.

Keywords: HAC, panel, robust, spatial

JEL Classification: C12, C21, C22, C23