TY - JOUR
T1 - Interpretation and identification of within-unit and cross-sectional variation in panel data models
AU - Kropko, Jonathan
AU - Kubinec, Robert
N1 - Funding Information:
The authors received no specific funding for this work. A previous version of this manuscript was presented at the annual meeting of the American Political Science Association, Philadelphia, PA, September 2, 2016. We thank Tom Carsey, Marius Radean, Daniel Gingerich, Jeffery J. Harden, Justin Esarey, and Justin Kirkland for their comments and advice.
Publisher Copyright:
© 2020 Kropko, Kubinec. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2020/4
Y1 - 2020/4
N2 - While fixed effects (FE) models are often employed to address potential omitted variables, we argue that these models’ real utility is in isolating a particular dimension of variance from panel data for analysis. In addition, we show through novel mathematical decomposition and simulation that only one-way FE models cleanly capture either the over-time or cross-sectional dimensions in panel data, while the two-way FE model unhelpfully combines within-unit and cross-sectional variation in a way that produces un-interpretable answers. In fact, as we show in this paper, if we begin with the interpretation that many researchers wrongly assign to the two-way FE model—that it represents a single estimate of X on Y while accounting for unit-level heterogeneity and time shocks—the two-way FE specification is statistically unidentified, a fact that statistical software packages like R and Stata obscure through internal matrix processing.
AB - While fixed effects (FE) models are often employed to address potential omitted variables, we argue that these models’ real utility is in isolating a particular dimension of variance from panel data for analysis. In addition, we show through novel mathematical decomposition and simulation that only one-way FE models cleanly capture either the over-time or cross-sectional dimensions in panel data, while the two-way FE model unhelpfully combines within-unit and cross-sectional variation in a way that produces un-interpretable answers. In fact, as we show in this paper, if we begin with the interpretation that many researchers wrongly assign to the two-way FE model—that it represents a single estimate of X on Y while accounting for unit-level heterogeneity and time shocks—the two-way FE specification is statistically unidentified, a fact that statistical software packages like R and Stata obscure through internal matrix processing.
UR - http://www.scopus.com/inward/record.url?scp=85083565641&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85083565641&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0231349
DO - 10.1371/journal.pone.0231349
M3 - Article
C2 - 32315338
AN - SCOPUS:85083565641
SN - 1932-6203
VL - 15
JO - PloS one
JF - PloS one
IS - 4
M1 - e0231349
ER -