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



Many researchers use unit fixed effects regression models as their default methods for causal inference with longitudinal data. We show that the ability of these models to adjust for unobserved time-invariant confounders comes at the expense of dynamic causal relationships, which are allowed to exist under an alternative selection-on-observables approach. Using the nonparametric directed acyclic graph, we highlight the two key causal identification assumptions of fixed effects models: past treatments do not directly influence current outcome, and past outcomes do not affect current treatment. Furthermore, we introduce a new nonparametric matching framework that elucidates how various fixed effects models implicitly compare treated and control observations to draw causal inference. By establishing the equivalence between matching and weighted fixed effects estimators, this framework enables a diverse set of identification strategies to adjust for unobservables provided that the treatment and outcome variables do not influence each other over time. We illustrate the proposed methodology through its application to the estimation of GATT membership effects on dyadic trade volume. The open-source software is available for implementing the proposed methodology. (Last revised, December 2017)
Longer version with two-way fixed effects.

  Software and Related Research

Kim, In Song and Kosuke Imai. ``wfe: Weighted Linear Fixed Effects Estimators for Causal Inference.'' available through The Comprehensive R Archive Network. 2011-2016.
Imai, Kosuke, In Song Kim, and Erik Wang. ``Matching Methods for Causal Inference with Time-Series Cross-Section Data..''

© Kosuke Imai
 Last modified: Fri Apr 27 21:53:34 EDT 2018