ECON 710 Midterm: ECON 710 UW Madison Midterm 2014a
Document Summary
To evaluate the latter you can use the fact that the regression model implies: the answer could be expressed either with the conditional variance var(b(cid:12) j x) or unconditional var(b(cid:12)): E(b(cid:12) j x) = (cid:12) and thus var(b(cid:12)) = e var(b(cid:12) j x): 1; :::; (cid:27)2 i = e(e2 (a) we know that if we set d = diagf(cid:27)2. Since n(cid:0)1x 0x = ik it follows that ng where (cid:27)2 ijxi); then var(b(cid:12) j x) = (x 0x)(cid:0)1 (x 0dx) (x 0x)(cid:0)1 : It follows that (b) the (conditional) covariances take the form var(b(cid:12) j x) = (nik)(cid:0)1 (x 0dx) (nik)(cid:0)1. = n(cid:0)2 xix0 i(cid:27)2 i nxi=1 nxi=1 xix0 i(cid:27)2 var(b(cid:12)) = e n(cid:0)2 i(cid:27)2 i(cid:1) : i! = n(cid:0)1e(cid:0)xix0 nxi=1 xjix i(cid:27)2 i cov(cid:16)b(cid:12)j;b(cid:12) j x(cid:17) = n(cid:0)2 which can be anything. For example, if (cid:27)2 (c) under conditional homoskedasticity, e(e2 i = xjix i then cov(cid:16)b(cid:12)j;b(cid:12) j x(cid:17) = n(cid:0)2pn ijxi) = 0, then i=1 x2 jix2.
