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Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data*

  • Andrew Bell and Kelvyn Jones
Abstract

This article challenges Fixed Effects (FE) modeling as the ‘default’ for time-series-cross-sectional and panel data. Understanding different within and between effects is crucial when choosing modeling strategies. The downside of Random Effects (RE) modeling—correlated lower-level covariates and higher-level residuals—is omitted-variable bias, solvable with Mundlak's (1978a) formulation. Consequently, RE can provide everything that FE promises and more, as confirmed by Monte-Carlo simulations, which additionally show problems with Plümper and Troeger's FE Vector Decomposition method when data are unbalanced. As well as incorporating time-invariant variables, RE models are readily extendable, with random coefficients, cross-level interactions and complex variance functions. We argue not simply for technical solutions to endogeneity, but for the substantive importance of context/heterogeneity, modeled using RE. The implications extend beyond political science to all multilevel datasets. However, omitted variables could still bias estimated higher-level variable effects; as with any model, care is required in interpretation.

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Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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*Andrew Bell is a lecturer and PhD candidate, School of Geographical Sciences, University of Bristol, University Road, Bristol, BS8 1SS (andrew.bell@bristol.ac.uk). Kelvyn Jones is co-director of the Centre for Multilevel Modelling, and Professor of Quantitative Human Geography, School of Geographical Sciences, University of Bristol, University Road, Bristol, BS8 1SS (kelvyn.jones@bristol.ac.uk). Thanks to Fiona Steele, Paul Clarke, Malcolm Fairbrother, Alastair Leyland, Mark Bell, Ron Johnston, George Leckie, Dewi Owen, Nathaniel Beck, Chris Adolph, and Thomas Plümper for their help and advice. Also, thanks to the two anonymous reviewers for their suggestions. All mistakes are our own.
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References
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