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

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.

Economic Policy Voting and Incumbency: Unemployment in Western Europe

“…Given that our interest concerns the causal effect of unemployment on left party voting regardless of contextual differences, we begin with a fixed effects approach. Thus, the variance at the country level is controlled for by means of country dummies, leaving just the within-country effects to be estimated (Allison 2009;Bell and Jones 2012). However, to provide robustness checks, we go on to include other approaches as well.…”

Life-course and cohort trajectories of mental health in the UK, 1991–2008 – A multilevel age–period–cohort analysis

“…Some attempt to control for both periods and cohorts (Blanchflower & Oswald, 2008;Clark & Oswald, 2006), some control only for periods (Blanchflower & Oswald, 2009;Howden-Chapman et al, 2011) whilst others are cross-sectional analyses that cannot control for cohorts due to exact collinearity with age (Blanchflower & Oswald, 2011;Deaton, 2008;Lang et al, 2011). Papers finding no U-shape (Frijters & Beatton, 2012;Kassenboehmer & Haisken-DeNew, 2012) tend to be fixed effects analyses, controlling for all individual level variability using dummies or demeaning (Bell & Jones, 2014d). Because cohort is an unchanging attribute of individuals, this controls for cohort effects (unless periods are additionally controlled).…”

“…This is because covariates can have different effects at different levels of analysis, often termed between-and within-individual effects (Bell & Jones, 2014d). However using a variant of the formulation suggested by Mundlak (1978) mitigates this problem by specifying within and between effects explicitly.…”

Estimation of Vulnerability to Poverty Using a Multilevel Longitudinal Model: Evidence from the Philippines

“…Heterogeneity bias in the RC model is corrected by using Bell and Jones's (2015) 'within-between' formulation to explicitly model both time-series (or 'within') variations in means of household-and province-level variables and crosssectional (or 'between') variations across different households and provinces. While Bell and Jones argue that this method overcomes the limitation of the RC model and is preferable to the fixed-effects (FE) model, both RC and FE models are estimated in this study.…”