Open AccessInterpretation and identification of within-unit and cross-sectional variation in panel data models
Author(s) -
Jonathan Kropko,
Robert Kubinec
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0231349
Subject(s) - dimension (graph theory) , variance (accounting) , panel data , econometrics , interpretation (philosophy) , identification (biology) , unit (ring theory) , computer science , variation (astronomy) , statistics , decomposition , mathematics , economics , accounting , physics , chemistry , botany , mathematics education , astrophysics , pure mathematics , biology , programming language , organic chemistry
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.