What's random effects in panel data and when is it appropriate?

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AcadiFi · Accepted Answer

Random effects (RE) treats the entity-specific intercept alpha_i as a random variable drawn from a distribution, rather than a parameter to estimate: y_{i,t} = alpha + u_i + beta*x_{i,t} + e_{i,t}, where u_i ~ N(0, sigma_u^2) and e_{i,t} ~ N(0, sigma_e^2). The model is estimated by GLS, weighting within and between variation optimally.

Key assumption: Cov(u_i, x_{i,t}) = 0—the entity-specific effect must be uncorrelated with regressors. If firms with high u_i (unobserved quality) systematically have higher x (e.g., higher R&D spend), RE is biased.

Advantages over FE when assumption holds: (1) more efficient (uses both within and between variation); (2) can estimate coefficients on time-invariant variables (industry, region); (3) works well for short panels where FE burns degrees of freedom.

Hausman test compares FE and RE coefficients. Under H0 (RE valid), they should be similar; large differences reject RE. For Orchard's rejected Hausman, use FE. RE is appropriate when entities are randomly sampled from a larger population and you believe unobserved heterogeneity is uncorrelated with covariates—common in small-group studies, experimental settings, or when using instrumental variable approaches for alpha_i.

Practical tip: Mundlak (1978) correction nests FE within RE by including entity means of time-varying regressors; if coefficients on means are zero, RE is valid. This is often preferred to the binary FE/RE choice in applied panel econometrics.

What's random effects in panel data and when is it appropriate?

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