1 · Panel data & unobserved heterogeneity
What panel data is, why repeated observations on the same entities help, and how an unobserved entity effect αᵢ creates correlation that biases naive regression.
Panel Data: Fixed & Random Effects
Unobserved heterogeneity, pooled-OLS bias, the within estimator, FE vs RE.
Course overview
Learn Panel Data: Fixed & Random Effects interactively
This free course uses real Python and statsmodels in your browser. Work through the modules below with explanations, executable examples, interactive controls, and questions.
2 · Pooled OLS and its bias
Pooled OLS ignores the panel structure and treats αᵢ as part of the error. We show, in code and with a slider, that this biases β₁ whenever αᵢ correlates with x.
3 · Fixed effects: within transformation & entity dummies
Fixed effects estimate β₁ from within-entity variation only, sweeping out αᵢ. We do it two equivalent ways — entity dummies and hand-coded demeaning — and confirm both kill the bias.
4 · Random effects & choosing FE vs RE
Random effects treats αᵢ as random noise uncorrelated with x, gaining efficiency and time-invariant coefficients — but only if that assumption holds. The Hausman idea tells you which to trust.