Triply Robust Panel Estimators

This paper studies estimation of causal effects in a panel data setting. We introduce a new estimator, the Triply Robust Panel (TROP) estimator, that combines (Formula presented.) a flexible model for the potential outcomes based on a low-rank factor structure on top of a two-way-fixed effect specification, with (Formula presented.) unit weights intended to upweight units similar to the treated units and (Formula presented.) time weights intended to upweight time periods close to the treated time periods. We study the performance of the estimator in a set of simulations designed to closely match several commonly studied real data sets. We find that there is substantial variation in the performance of the estimators across the settings considered. The proposed estimator outperforms Two-Way-Fixed-Effect (TWFE) or Difference-In-Differences (DID), Synthetic Control (SC), Matrix Completion (MC) and Synthetic-Difference-In-Differences (SDID) estimators. We investigate what features of the data generating process lead to this superior performance and assess the relative importance of the three components of the proposed estimator. We have two recommendations. Our preferred strategy is that researchers use simulations closely matched to the data they are interested in, along the lines discussed in this paper, to investigate which estimators work well in their particular setting. A simpler approach is to use more robust estimators such as SDID or the new TROP estimator, which we find to substantially outperform TWFE/DID estimators in many empirically relevant settings.