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321w6p1

# 321w6p1 - We found that the variance of our ols estimators...

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Unformatted text preview: We found that the variance of our ols estimators is: Var j = 2 [ ∑ i = 1 n X ij − X j 2 1 − R j 2 ] because we do not know the u i , we cannot calculate 2 = n − 1 ∑ i = 1 n u i 2 An unbiased estimator of σ 2 is 2 = n − k − 1 − 1 ∑ i = 1 n u i 2 In the case of k+1 parameters, df=n-k-1 3. If the errors are homoskedastic, then an estimate of the var( β ) using σ 2 is unbiased Var j = 2 [ ∑ i = 1 n X ij − X j 2 1 − R j 2 ] ^ ^ 4. Gauss Markov Theorem – The OLS estimator is the Best Linear Unbiased Estimator (BLUE) Linear – linear in parameters Unbiased – E[ β ]= β Best – smallest variance Under assumptions 1-4 and homoskedasticity, β is the BLUE of β . These are known as the Gauss-Markov Assumptions ^ ~ ^ Interpreting OLS Paramter Estimates Recall, in our regression Y i = β + β 1 X 1i + β 2 X 2i +...+ β k X ki + u i i=1,...,n β 1 is the partial effect of X 1 on Y....
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321w6p1 - We found that the variance of our ols estimators...

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