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

Jonathan Kropko,Robert Kubinec,Talib Al-Ameri

doi:10.1371/journal.pone.0231349

Jonathan Kropko, Robert Kubinec + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0231349

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Journal: PloS one	Publication Date: Apr 21, 2020
Citations: 100	License type: CC BY 4.0

Affiliation: University of Virginia, New York University Abu Dhabi

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.

Highlights

In designing a statistical model, applied researchers take steps to help the model achieve unbiasedness, consistency, and efficiency
While one-way fixed effects (FE) models can be understood as generalizations of the effects that exist within one case or within one time point, the two-way FE model can only be understood as a generalization of the effect of deviations from the case-means at a particular point in time, or equivalently, as a generalization of the effect of deviations from the time-means for each particular case
Because of the restrictive assumptions and difficulty in substantive 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

Summary

Introduction

In designing a statistical model, applied researchers take steps to help the model achieve unbiasedness, consistency, and efficiency. An even more important goal is for the model to be useful. For a model to be useful it must have an interpretation that provides a clear answer to the research question posed. We show that the commonly applied two-way fixed model (two-way FE) only has such an interpretation in the difference-in-differences (DiD) causal framework. Many if not most empirical applications involve data that has a structure that does not meets the stringent criteria of the DiD framework. What is the appropriate interpretation to assign to the two-way FE model coefficient if it cannot be understood as the DiD treatment effect?

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