When Should We Use Linear Fixed Effects Regression Models for Causal Inference with Longitudinal Data?

 

  Abstract

Many social scientists use linear fixed effects regression models for causal inference with longitudinal data to account for unobserved time-invariant confounders. We show that these models require two additional causal assumptions, which are not necessary under an alternative selection-on-observables approach. Specifically, the models assume that past treatments do not directly influence current outcome, and past outcomes do not directly affect current treatment. The assumed absence of causal relationships between past outcomes and current treatment may also invalidate some applications of before-and-after and difference-in-differences designs. Furthermore, we propose a new matching framework to further understand and improve one-way and two-way fixed effects regression estimators by relaxing the linearity assumption. Our analysis highlights a key trade-off --- the ability of fixed effects regression models to adjust for unobserved time-invariant confounders comes at the expense of dynamic causal relationships between treatment and outcome. The open-source software is available for implementing the proposed methodology. (Last revised, July 2016)

  Software

Kim, In Song and Kosuke Imai. ``wfe: Weighted Linear Fixed Effects Estimators for Causal Inference.'' available through The Comprehensive R Archive Network. 2011-2016.

© Kosuke Imai
 Last modified: Thu Jul 28 09:14:33 EDT 2016