12 - Chapter 2, Exercise Solutions, Principles of...

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Chapter 2, Exercise Solutions, Principles of Econometrics, 3e 12 EXERCISE 2.8 (a) The EZ estimator can be written as 21 11 E Zi i yy by y k y xx xx xx ⎛⎞ == = ⎜⎟ −− ⎝⎠ where 1 1 k x x = , 2 1 k x x = , and k 3 = k 4 = . .. = k N = 0 Thus, EZ b is a linear estimator. (b) Taking expectations yields () 12 2 1 22 2 1 EZ Eb E Ey xxxx ⎡⎤ ⎢⎥ ⎣⎦ = β +β ββ =−= β = β Thus, b EZ is an unbiased estimator. (c) The variance is given by ( ) 2 var var( ) var E i i i i bk y k e k = σ ∑∑ 2 2 2 112 x x x x σ
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This note was uploaded on 11/23/2011 for the course ECON MPBE taught by Professor Jansveceny during the Spring '11 term at Metropolitní Univerzita Praha.

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