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

Published online by Cambridge University Press:  12 November 2020

Kosuke Imai Open the ORCID record for Kosuke Imai [Opens in a new window]  and
In Song Kim Open the ORCID record for In Song Kim [Opens in a new window]
Kosuke Imai
Affiliation:
Professor, Department of Government and Department of Statistics, Harvard University, 1737 Cambridge Street, Institute for Quantitative Social Science, Cambridge, MA02138, USA. E-mail: Imai@Harvard.Edu, URL: https://imai.fas.harvard.edu/
In Song Kim*
Affiliation:
Associate Professor, Department of Political Science, Massachusetts Institute of Technology, Cambridge, MA02142, USA. E-mail: insong@mit.edu, URL: http://web.mit.edu/insong/www/
*
Corresponding author In Song Kim
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Abstract

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.

Keywords

difference-in-differenceslongitudinal datamatchingunobserved confoundingweighted least squares
Type
Letter
Information
Political Analysis , Volume 29 , Issue 3 , July 2021 , pp. 405 - 415
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

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