Inference in time series models using smoothed-clustered standard errors

Abstract

This paper proposes a long run variance estimator for conducting inference in time series regression models that combines the nonparametric approach with a cluster approach. The basic idea is to divide the time periods into non-overlapping clusters. The long run variance estimator is constructed by first aggregating within clusters and then kernel smoothing across clusters or applying the nonparametric series method to the clusters with Type II discrete cosine transform. We develop an asymptotic theory for test statistics based on these “smoothed-clustered” long run variance estimators. We derive asymptotic results holding the number of clusters fixed and also treating the number of clusters as increasing with the sample size. For the kernel smoothing approach, these two asymptotic limits are different whereas for the cosine series approach, the two limits are the same. When clustering before kernel smoothing, we find that the “fixed-number-of-clusters” asymptotic approximation works well whether the number of clusters is small or large. Finite sample simulations suggest that the naive i.i.d. bootstrap mimics the fixed-number-of-clusters critical values. The simulations also suggest that clustering before kernel smoothing can reduce over-rejections caused by strong serial correlation at a cost of power. When there is a natural way of clustering, clustering can reduce over-rejection problems and achieve small gains in power for the kernel approach. In contrast, the cosine series approach does not benefit from clustering.