ECON 710 Final: ECON 710 UW Madison Final Exam 2017
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Be speci(cid:133)c about estimators and covariance matrix estimators: consider the model yi = x0. E (eijzi) = 0 i(cid:12) + ei with yi scalar and xi and zi each a k vector. You have a random sample (yi; xi; zi : i = 1; :::; n): (a) write the iv estimator b(cid:12) for (cid:12) (b) suppose that xi is exogeneous in the sense that e (eijzi; xi) = 0. Is b(cid:12) unbiased for (cid:12)? (c) continuing to assume that xi is exogeneous, (cid:133)nd the variance matrix for b(cid:12), var(cid:16)b(cid:12)jx; z(cid:17): consider the model yi = x0 i(cid:12) + ei xi = (cid:0)0zi + ui. E(cid:0)ziu0 i(cid:1) = 0 with yi scalar and xi and zi each a k vector. You have a random sample (yi; xi; zi : i = 1; :::; n): Take the control function equation ei = u0. E (ui"i) = 0 i(cid:13) + "i and assume for simplicity that ui is observed.
