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Interpretation and identification of within-unit and cross-sectional variation in panel data models

Jonathan Kropko and Robert Kubinec

PLOS ONE, 2020, vol. 15, issue 4, 1-22

Abstract: 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.

Date: 2020
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DOI: 10.1371/journal.pone.0231349

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