EconometricsadvancedConcept explainer
Hausman Test
Testing for endogeneity and choosing between estimators. FE vs. RE, OLS vs. IV.
Definition
A specification test comparing two estimators: one efficient-if-null-true, one consistent-either-way, a large gap rejects the null (e.g., exogeneity, or RE vs FE).
Key equation
H = (β̂₁−β̂₀)′[V₀−V₁]⁻¹(β̂₁−β̂₀) ~ χ²
The intuition
If OLS and IV agree, endogeneity probably wasn't there and OLS's precision is safe to keep; if they diverge, trust the consistent one. Same logic picks fixed over random effects when unit effects correlate with regressors.
Exam tip
State both hypotheses concretely: rejecting in FE-vs-RE means 'use fixed effects', not just 'significant'.
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