Selection into Identification in Fixed Effects Models, with Application to Head Start

Abstract

Many papers use fixed effects (FE) to identify causal impacts. We document that when treatment status only varies within some FE groups (for example, families, for family fixed effects), FE can induce nonrandom selection of groups into the identifying sample. To address this, we introduce a reweighting-on-observables estimator that can help recover the average treatment effect for policy-relevant populations. We apply these insights to reexamine the long-term effects of Head Start in the PSID and the CNLSY and find that the reweighted estimates are frequently smaller than the FE estimates. This underscores concerns with the external validity of FE estimates. The tools that we propose can strengthen the validity of this approach.