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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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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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.
AbstractList	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. 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 theweighted 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. 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.
Author	Kim, In Song Imai, Kosuke
Author_xml	– sequence: 1 givenname: Kosuke orcidid: 0000-0002-2748-1022 surname: Imai fullname: Imai, Kosuke email: Imai@Harvard.Edu organization: 1Professor, Department of Government and Department of Statistics, Harvard University, 1737 Cambridge Street, Institute for Quantitative Social Science, Cambridge, MA 02138, USA. E-mail: Imai@Harvard.Edu, URL: https://imai.fas.harvard.edu/ – sequence: 2 givenname: In Song orcidid: 0000-0002-5774-1585 surname: Kim fullname: Kim, In Song email: insong@mit.edu organization: 2Associate Professor, Department of Political Science, Massachusetts Institute of Technology, Cambridge, MA 02142, USA. E-mail: insong@mit.edu, URL: http://web.mit.edu/insong/www/
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Copyright	The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology The Author(s) 2020
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References_xml	– volume: 38 start-page: 613 year: 2019 end-page: 620 article-title: The Promise and Pitfalls of Differences-in-Differences: Reflections on 16 and Pregnant and Other Applications publication-title: Journal of Business & Economic Statistics – volume: 25 start-page: 57 issue: 1 year: 2017 end-page: 76 article-title: Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models publication-title: Political Analysis – volume: 60 start-page: 250 issue: 1 year: 2015 end-page: 267 article-title: Does Regression Produce Representative Estimates of Causal Effects? publication-title: American Journal of Political Science – volume: 50 start-page: 301 issue: 2 year: 2015 end-page: 316 article-title: What are we weighting for? publication-title: Journal of Human Resources – volume: 105 start-page: 493 issue: 490 year: 2010 end-page: 505 article-title: Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program publication-title: Journal of the American Statistical Association – volume: 119 start-page: 249 issue: 1 year: 2004 end-page: 275 article-title: How Much Should We Trust Differences-in-Differences Estimates? publication-title: Quarterly Journal of Economics – volume: 63 start-page: 467 issue: 2 year: 2019 end-page: 490 article-title: When should we use linear unit fixed effects regression models for causal inference with longitudinal data? publication-title: American Journal of Political Science – ident: S1047198720000339_r3 doi: 10.1515/9781400829828 – ident: S1047198720000339_r5 doi: 10.3386/w24963 – ident: S1047198720000339_r11 doi: 10.3386/w25018 – ident: S1047198720000339_r10 doi: 10.3386/w25904 – ident: S1047198720000339_r14 doi: 10.1111/ajps.12417 – ident: S1047198720000339_r9 doi: 10.2139/ssrn.2826228 – ident: S1047198720000339_r1 doi: 10.1198/jasa.2009.ap08746 – ident: S1047198720000339_r18 doi: 10.3368/jhr.50.2.301 – ident: S1047198720000339_r6 – ident: S1047198720000339_r8 – ident: S1047198720000339_r15 – ident: S1047198720000339_r2 doi: 10.2139/ssrn.3158747 – ident: S1047198720000339_r7 doi: 10.1162/003355304772839588 – ident: S1047198720000339_r19 doi: 10.1017/pan.2016.2 – ident: S1047198720000339_r17 – ident: S1047198720000339_r4 doi: 10.1111/ajps.12185 – ident: S1047198720000339_r16 doi: 10.1080/07350015.2018.1546591 – ident: S1047198720000339_r13 – ident: S1047198720000339_r12
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Snippet	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... 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...
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SubjectTerms	Applied research Causal models Causality Inference Justification Letter Letters Longitudinal studies Panel data Time periods
Title	On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data
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