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

AJPS Author Summary of “When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?” by Kosuke Imailn and Song Kim

This paper investigates the causal assumptions of unit fixed effects regression models, which many researchers use as their default methods for the analysis of longitudinal data.  Most importantly, 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 permitted under an alternative selection-on-observables approach. Using the nonparametric directed acyclic graph, we highlight two key causal identification assumptions of unit fixed effects models: past treatments do not directly influence a current outcome, and past outcomes do not affect current treatment. Furthermore, we introduce a new nonparametric matching framework that elucidates how various unit fixed effects models implicitly compare treated and control observations to draw causal inference. By establishing the equivalence between matching and weighted unit fixed effects estimators, this framework enables a diverse set of identification strategies to adjust for unobservables in the absence of dynamic causal relationships between treatment and outcome variables. We illustrate the proposed methodology through its application to the estimation of GATT membership effects on dyadic trade volume.  The open-source software package, wfe: Weighted Linear Fixed Effects Regression Models for Causal Inference, is available at the Comprehensive R Archive Network (CRAN) for implementing the proposed methodology.

While this article examines regression models with unit fixed effects, our related paper proposes a new matching method for causal inference with time-series cross sectional data and show how this method relates to the regression models with both unit and time fixed effects.  The proposed matching method can be implemented through an open-source R package, PanelMatch: Matching Methods for Causal Inference with Time-Series Cross-Sectional Data.

About the Authors: Kosuke Imai is Professor of Government and of Statistics at Harvard University and also an affiliate of the Institute for Quantitative Social Science . Song Kim is Associate Professor of Political Science and a Faculty Affiliate of the Institute for Data, Systems, and Society (IDSS) at Massachusetts Institute of Technology. Their research “When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data? (https://doi.org/10.1111/ajps.12417 )” is now available in Early View and will appear in a forthcoming issue of the American Journal of Political Science.