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

This article challenges Fixed Effects (FE) modelling as the ‘default’ for time-series-cross-sectional and panel data. Understanding different within- and between-effects is crucial when choosing modelling strategies. The downside of Random Effects (RE) modelling – correlated lower-level covariates and higher-level residuals – is omitted-variable bias, solvable with Mundlak’s (1978a) formulation. Consequently, RE can provide everything 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 the substantive importance of context/heterogeneity, modelled 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.