slides_Ch2_W[1]

5 var u jx e u 2 jx 0 all x 2 2 e u var u it

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Var [ui jx ] (xi = M elissa Tartari (Yale) x )2 ¯ i =1 SLR .5 = x ) jx ] ¯ 1 2n σ (xi 4 sx i∑ =1 x )2 ¯ 1 22 σ2 σ sx = 2 . 4 sx sx Econometrics 79 / 93 The Variance of the OLS Estimator - Remarks We do not need SLR.5 to prove unbiasedness of OLS estimators. Melissa Tartari (Yale) Econometrics 80 / 93 The Variance of the OLS Estimator - Remarks We do not need SLR.5 to prove unbiasedness of OLS estimators. We add SLR.5 b/c it simpli…es the variance calculations and, importantly, b/c it implies that OLS has certain e¢ ciency properties. Melissa Tartari (Yale) Econometrics 80 / 93 The Variance of the OLS Estimator - Remarks We do not need SLR.5 to prove unbiasedness of OLS estimators. We add SLR.5 b/c it simpli…es the variance calculations and, importantly, b/c it implies that OLS has certain e¢ ciency properties. We see that σ2 is the unconditional variance of u : Var [u jx ] = E u 2 jx (E [u jx ])2 &amp; E [u jx ] = 0 hence σ2 Melissa Tartari (Yale) by SLR.5 = Var [u jx ] = E u 2 jx 0 all x 2 2 ) σ = E u = Var [u ] Econometrics 80 / 93 The Variance of the OLS Estimator - Remarks We do not need SLR.5 to prove unbiasedness of OLS estimators. We add SLR.5 b/c it simpli…es the variance calculations and, importantly, b/c it implies that OLS has certain e¢ ciency properties. We see that σ2 is the unconditional variance of u : Var [u jx ] = E u 2 jx (E [u jx ])2 &amp; E [u jx ] = 0 hence σ2 by SLR.5 = Var [u jx ] = E u 2 jx 0 all x 2 2 ) σ = E u = Var [u ] it is useful to rewrite SLR.3 and SLR.5 as E [y jx ] = βo + β1 x Var [y jx ] = σ Melissa Tartari (Yale) Econometrics 2 (2.55) (2.56) 80 / 93 The Variance of the OLS Estimator - Remarks We do not need SLR.5 to prove unbiasedness of OLS estimators. We add SLR.5 b/c it simpli…es the variance calculations and, importantly, b/c it implies that OLS has certain e¢ ciency properties. We see that σ2 is the unconditional variance of u : Var [u jx ] = E u 2 jx (E [u jx ])2 &amp; E [u jx ] = 0 hence σ2 by SLR.5 = Var [u jx ] = E u 2 jx 0 all x 2 2 ) σ = E u = Var [u ] it is useful to rewrite SLR.3 and SLR.5 as E [y jx ] = βo + β1 x Var [y jx ] = σ 2 (2.55) (2.56) See Figure 2.8 Melissa Tartari (Yale) Econometrics 80 /...
View Full Document

Ask a homework question - tutors are online