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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: [email protected], 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: [email protected], 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

References

Abadie, A., Diamond, A., and Hainmueller, J.. 2010. “Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program.” Journal of the American Statistical Association 105(490):493–505.CrossRefGoogle Scholar
Abraham, S., and Sun, L.. 2018. “Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects.” Technical report, Department of Economics, Massachusetts Institute of Technology.CrossRefGoogle Scholar
Angrist, J. D., and Pischke, J.-S.. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Aronow, P. M., and Samii, C.. 2015. “Does Regression Produce Representative Estimates of Causal Effects?” American Journal of Political Science 60(1):250–267.CrossRefGoogle Scholar
Athey, S., and Imbens, G.. 2018. “Design-Based Analysis in Difference-in-Differences Settings with Staggered Adoption.” Technical report, Stanford Graduate School of Business. https://arxiv.org/abs/1808.05293.Google Scholar
Ben-Michael, E., Feller, A., and Rothstein, J.. 2019. “Synthetic Controls and Weighted Event Studies with Staggered Adoption.” Technical report, arXiv:1912.03290.Google Scholar
Bertrand, M., Duflo, E., and Mullainathan, S.. 2004. “How Much Should We Trust Differences-in-Differences Estimates?” Quarterly Journal of Economics 119(1):249–275.CrossRefGoogle Scholar
Bilinski, A., and Hatfield, L. A.. 2018. “Seeking Evidence of Absence: Reconsidering Tests of Model Assumptions.” Preprint, arXiv:1805.03273.Google Scholar
Borusyak, K., and Jaravel, X.. 2017. “Revisiting Event Study Designs, with an Application to the Estimation of the Marginal Propensity to Consume.” Technical report, Department of Economics, Harvard University.CrossRefGoogle Scholar
Chaisemartin, C. D., and D’Haultfœuille, X.. 2018. “Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects.” Technical report, Department of Economics, University of California, Santa Barbara. https://arxiv.org/abs/1803.08807.Google Scholar
Goodman-Bacon, A. 2018. “Difference-in-Differences with Variation in Treatment Timing.” Working Paper 25018, National Bureau of Economic Research.CrossRefGoogle Scholar
Humphreys, M. 2009. “Bounds on Least Squares Estimates of Causal Effects in the Presence of Heterogeneous Assignment Probabilities.” Technical report, Department of Political Science, Columbia University. http://www.columbia.edu/~mh2245/papers1/monotonicity7.pdf.Google Scholar
Imai, K., and Kim, I. S.. 2011. “On the Use of Linear Fixed Effects Regression Models for Causal Inference.” Technical report, Princeton University.Google Scholar
Imai, K., and Kim, I. S.. 2019. “When should we use linear unit fixed effects regression models for causal inference with longitudinal data?” American Journal of Political Science 63(2):467–490.CrossRefGoogle Scholar
Imai, K., Kim, I. S., and Wang, E.. 2018. “Matching Methods for Time-Series Cross-Sectional Data.” Working Paper. https://imai.fas.harvard.edu/research/tscs.html Google Scholar
Kahn-Lang, A., and Lang, K.. 2019. “The Promise and Pitfalls of Differences-in-Differences: Reflections on 16 and Pregnant and Other Applications.” Journal of Business & Economic Statistics 38:613–620.CrossRefGoogle Scholar
Rambachan, A., and Roth, J.. 2019. An Honest Approach to Parallel Trends.” Working Paper. https://scholar.harvard.edu/jroth/publications/Roth_JMP_Honest_Parallel_Trends.Google Scholar
Solon, G., Haider, S. J., and Wooldridge, J. M.. 2015. “What are we weighting for?” Journal of Human Resources 50(2):301–316.CrossRefGoogle Scholar
Xu, Y. 2017. “Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models.” Political Analysis 25(1):57–76.CrossRefGoogle Scholar
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