This exercise set builds the weighted least squares estimator from first principles: derive the WLS formula by minimising a weighted sum of squared residuals, assess when it is unbiased, and establish when weighting delivers efficiency gains over OLS under heteroskedasticity. The solutions file proves or refutes each claim in full.
What these materials cover
- Deriving the WLS estimator from the weighted SSR minimisation
- Proof-based question: is WLS unbiased, and does that depend on the weights?
- Efficiency comparisons between OLS, WLS and GLS under heteroskedasticity
- Working with conditional variance assumptions E[u²ₜ|X] = σ²ₜ
- Full worked solutions with the algebra shown
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Free to download and use for personal study. Written for my own university teaching; shared here as evidence of teaching style and depth.
Tutorial sheet: WLS & heteroskedasticity exercises (PDF) Tutorial solutions, fully worked (PDF)
Who this is for
MSc and advanced undergraduate students practising estimator derivations and proof-style questions of the kind that appear in econometrics exams.
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