1

Paper

Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data Bell, Andrew Jones, Kelvyn Uploaded 07-13-2012 Keywords Random Effects models Fixed Effects models Random coefficient models Mundlak formulation Fixed effects vector decomposition Hausman test Endogeneity Panel Data Time-Series Cross-Sectional Data Abstract This article challenges Fixed Effects (FE) modelling’s status as the ‘default option’ when using time-series-cross-sectional and panel data. We argue that understanding the difference between within- and between-effects of predictor variables is important when considering what modelling strategy to use. The downside of Random Effects (RE) compared to FE modelling – correlation between lower-level covariates and higher-level residuals - is a case of omitted variable bias, readily solvable using a variant of Mundlak’s (1978a) formulation. Consequently, RE modelling provides everything that FE modelling promises, and more. It allows time-invariant variables to be modelled, more parsimoniously than Plümper and Troeger’s (2007) suggested method. It is also readily extendable to Random Coefficients Models, allowing reliable, differential effects of variables without heavy parameterisation, the use of cross-level interactions between time-variant and invariant variables, and the modelling of complex variance functions. We are arguing not simply for technical solutions to endogeneity, but for the substantive importance of modelling context, and RE models’ ability to do so. Two empirical examples show that failing to do this can lead to misleading results. This paper is distinctive in stressing the substantive interpretations of within- and between-effects. This has implications beyond political science, to all datasets with multilevel structures.