Panel Data (Fixed & Random Effects)
Following units over time: sweeping out fixed characteristics to get closer to causality.
Definition
Data following units over time. Fixed effects sweep out each unit's time-invariant character; random effects treat it as noise (efficient, but only valid if uncorrelated with regressors).
Key equation
FE (within): y_it − ȳ_i = β(x_it − x̄_i) + …
The intuition
FE answers 'when THIS unit's x changes, what happens to ITS y?', killing every never-changing confounder for free. The price: anything constant (gender, geography) is swept away too, and only within-unit variation identifies β.
Exam tip
FE vs RE is decided by the Hausman test; and remember FE cannot estimate time-invariant regressors, a favorite trick question.
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