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Is it true that under the Gauss Markov assumptions the ordinary least squares method gives efficient and unbiased estimators?

So:

$$E(u_t)=0 $$ for all $t$

$$E(u_tu_s)=\sigma^2 $$ for $t=s$

$$E(u_tu_s)=0 $$ for $t\neq s$

where $u$ are the residuals.

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    $\begingroup$ You might want to see my related question, and clearly the answer seems to be "yes", but only among linear estimators. $\endgroup$
    – Patrick
    Apr 22, 2013 at 7:45

1 Answer 1

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The Gauss-Markov Theorem is telling us that in a regression model, where the expected value of our error terms is zero, $ E(\epsilon_{i}) = 0$ and variance of the error terms is constant and finite $\sigma^{2}(\epsilon_{i}) = \sigma^{2} < \infty$ and $\epsilon_{i}$ and $ \epsilon_{j}$ are uncorrelated for all $ i$ and $ j$ the least squares estimator $ b_{0}$ and $ b_{1}$ are unbiased and have minimum variance among all unbiased linear estimators. Note that there might be biased estimator which have a even lower variance.

A proof that actually shows that under the assuptions of the Gauss-Markov Theorem an linear estimator is BLUE can be found under

http://economictheoryblog.com/2015/02/26/markov_theorem/

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