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

TLDR

Choosing between fixed and random effects requires understanding within‑ and between‑group dynamics, as random‑effects models can suffer omitted‑variable bias from correlated covariates, though this can be mitigated with Mundlak’s formulation. The article argues against treating FE as the default for panel data and instead promotes random‑effects modeling to capture substantive context and heterogeneity. Random‑effects models extend FE by allowing time‑invariant variables, random coefficients, cross‑level interactions, and complex variance structures. Monte‑Carlo simulations show that random‑effects models deliver all the benefits of FE and more, while revealing issues with Plümper and Troeger’s FE vector decomposition in unbalanced data, and these advantages apply to any multilevel dataset.

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.