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13 - Chapter 2 Exercise Solutions Principles of...

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Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 13 Exercise 2.8 (continued) (e) To convince E.Z. Stuff that var( b 2 ) < var( b EZ ), we need to show that () 22 21 2 i x xx x σσ > −− or that 2 2 2 i x x −> Consider 2 2 2 1 2 1 2 2 xx xx x x x x x x x x ⎡−−− −+ ⎣⎦ == Thus, we need to show that 222 2 1 1 N i i x x x x x x = −>−+ or that 2 12 2 1 3 0 N i i xxxx = −+−+ + or that 2 2 3 20 . N i i = ⎡−+ −⎤ + − > This last inequality clearly holds.
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