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I'm thinking whether there exists cases where OLS estimator is closer to the true coefficient than WLS estimator in probability limit in a misspecified model.

Specifically, I'm working on a case where:

The true model consists of a dummy D, a control X and their interaction DX. But the misspecified model misses the interaction term.

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  • $\begingroup$ What sort of weighting are you doing? WLS and OLS are both unbiased. WLS is just often more efficient, which isn't to do with coefficient accuracy. $\endgroup$
    – ahorn
    Jan 5 at 8:03

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