Estimation precision and robust inference in archival research

OLS estimates of linear regression models become imprecise when distributional assumptions about the regression errors are not strictly met. Such situations frequently arise in applied research due to the heavy-tailed distributions of dependent variables. Using simulated data and replication settings, we show how robust regression estimation can produce more policy-relevant inferences by increasing the precision of estimates, improving test power, and tightening confidence intervals. We provide guidance to researchers on when and how to apply robust estimation as alternative to OLS and how to combine robust regression estimators with fixed effects and clustered standard errors. Given the non-random nature of observations typically downweighted by robust regression estimators, we also illustrate the importance of inspecting the robust regression weights and discuss how these weights can provide useful insights about heterogeneity in treatment effects or relations of interest.