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Cluster standard error (Liang and Zeger, 1986) is widely used by empiricalresearchers to account for cluster dependence in linear model. It is well knownthat this standard error is biased. We show that the bias does not vanish underhigh dimensional asymptotics by revisiting Chesher and Jewitt (1987)'sapproach. An alternative leave-cluster-out crossfit (LCOC) estimator that isunbiased, consistent and robust to cluster dependence is provided under highdimensional setting introduced by Cattaneo, Jansson and Newey (2018). SinceLCOC estimator nests the leave-one-out crossfit estimator of Kline, Saggio andSolvsten (2019), the two papers are unified. Monte Carlo comparisons areprovided to give insights on its finite sample properties. The LCOC estimatoris then applied to Angrist and Lavy's (2009) study of the effects of highschool achievement award and Donohue III and Levitt's (2001) study of theimpact of abortion on crime.

Robust Inference in High Dimensional Linear Model with Cluster Dependence