ECON 710 Midterm: ECON 710 UW Madison Midterm 2008

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31 Jan 2019
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E (cid:0)e2 i j xi(cid:1) = (cid:27)2 where xi = (x1i; x2i); with x1i k1 (cid:2) 1 and x2i k2 (cid:2) 1. Consider the short regression and de(cid:12)ne the error variance estimator yi = x0. ^e2 i : (a) find e (cid:0)s2 j x(cid:1) (b) find the probability limit of s2 as n ! 1: take the model yi = xi(cid:12) + ei. E (xiei) = 0 with xi scalar and ex2 of (cid:12); and let v 0 be the \homoskedastic" form of the asymptotic variance. i = 1. E (cid:0)e2 i j xi(cid:1) = (cid:27)2 i(cid:12) + ei i = z 0 i(cid:13) where zi is a (vector) function of xi: the sample is i = 1; :::; n with iid observations. For simplicity, assume that z 0 i(cid:13) > 0 for all zi. E (ei j xi) = 0 i(cid:12) + ei zi = (cid:0)x0 i(cid:12)(cid:1) (cid:13) + ui.

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