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When you know the variance, weight instead of just robustifying

Each observation in your regression is an average over a group of firms: row ii summarizes nin_i firms, and group sizes range from a handful to thousands. Averaging over more firms means less noise, so the error variance of row ii is σ2/ni\sigma^2 / n_i, which you can compute because you know each nin_i.

Ordinary least squares with robust standard errors would give valid inference. Explain why weighted least squares is the better choice here, how you would set it up, and what you gain.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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