Why the Two-Way Fixed Effects Model Is Difficult to Interpret, and What to Do About It

27 Pages Posted: 1 Nov 2017 Last revised: 17 May 2018

See all articles by Jonathan Kropko

Jonathan Kropko

University of Virginia

Robert Kubinec

University of Virginia

Date Written: May 14, 2018


The two-way fixed effects (FE) model, an increasingly popular method for modeling time-series cross-section (TSCS) data, is substantively difficult to interpret because the model's estimates are a complex amalgamation of variation in the over-time and cross-sectional effects. We demonstrate this complexity in the two-way FE estimate through mathematical exposition. As an illustration, we develop a novel simulation that enables us to generate TSCS data with varying over-time and cross-sectional effects and examine the behavior of the two-way FE model as these effects change. We demonstrate that the two-way FE model makes specific assumptions about TSCS datasets, and if these assumptions are not met, the model may be unidentified even if substantial variation exists along both dimensions. Because of the difficulty in interpretation, we do not recommend that applied researchers rely on the two-way FE model except for situations in which the assumptions are well-understood, such as the canonical difference-in-difference design.

Keywords: time series cross section, TSCS, political methodology, panel data

JEL Classification: C23

Suggested Citation

Kropko, Jonathan and Kubinec, Robert, Why the Two-Way Fixed Effects Model Is Difficult to Interpret, and What to Do About It (May 14, 2018). Available at SSRN: https://ssrn.com/abstract=3062619 or http://dx.doi.org/10.2139/ssrn.3062619

Jonathan Kropko

University of Virginia ( email )

1400 University Ave
Charlottesville, VA 22903
United States

Robert Kubinec (Contact Author)

University of Virginia

PO Box 400787
Charlottesville, VA 22904
United States

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