Robust Inference in High Dimensional Linear Model with Cluster Dependence

TL;DR

This paper introduces an unbiased, consistent, and robust estimator for high-dimensional linear models with cluster dependence, addressing bias issues in traditional cluster standard errors and unifying previous methods.

Contribution

It proposes the leave-cluster-out crossfit (LCOC) estimator that corrects bias in high-dimensional settings and unifies existing approaches, with demonstrated finite sample performance.

Findings

LCOC estimator is unbiased and consistent under high-dimensional asymptotics.

Monte Carlo simulations show favorable finite sample properties.

Application to empirical studies illustrates practical usefulness.

Abstract

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