Estimating Variances for Causal Panel Data Estimators

This paper studies variance estimators in panel data settings. There has been a recent surge in research on panel data models with a number of new estimators proposed. However, there has been less attention paid to the quantification of the precision of these estimators. Of the variance estimators that have been proposed, their relative merits are not well understood. In this paper we develop a common framework for comparing some of the proposed variance estimators for generic point estimators. We reinterpret three commonly used approaches as targeting different conditional variances under an exchangeability assumption. We find that the estimators we consider are all valid on average, but that their performance in terms of power differs substantially depending on the heteroskedasticity structure of the data. Building on these insights, we propose a new variance estimator that flexibly accounts for heteroskedasticity in both the unit and time dimensions, and delivers superior statistical power in realistic panel data settings.