On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data

The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ab...

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Bibliographic Details
Published in:Political analysis Vol. 29; no. 3; pp. 405 - 415
Main Authors: Imai, Kosuke, Kim, In Song
Format: Journal Article
Language:English
Published: New York, USA Cambridge University Press 01.07.2021
Subjects:
Applied research
Causal models
Causality
Inference
Justification
Letter
Letters
Longitudinal studies
Panel data
Time periods
difference-in-differences
unobserved confounding
weighted least squares
longitudinal data
matching
ISSN:1047-1987, 1476-4989
Online Access:Get full text
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Summary:The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ability of the 2FE model to simultaneously adjust for these two types of unobserved confounders critically relies upon the assumption of linear additive effects. Another common justification for the use of the 2FE estimator is based on its equivalence to the difference-in-differences estimator under the simplest setting with two groups and two time periods. We show that this equivalence does not hold under more general settings commonly encountered in applied research. Instead, we prove that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights. These analytical results imply that in contrast to the popular belief, the 2FE estimator does not represent a design-based, nonparametric estimation strategy for causal inference. Instead, its validity fundamentally rests on the modeling assumptions.
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ISSN:1047-1987
1476-4989
DOI:10.1017/pan.2020.33