ECON 710 Final: ECON 710 UW Madison Final Exam 2008a
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Sample answers: the question was not speci(cid:12)c regarding the dimensions of zi and xi. Therefore you should presume that the model could be overidenti(cid:12)ed, which includes just-identi(cid:12)ed as a special case, so it is su(cid:14)cient to focus on the overidenti(cid:12)ed case. The assumptions are minimal, with the only restriction e(xiei) = 0: In particular, homoskedasticity is not assumed. (the equation ee2 i = (cid:27)2 is not a restriction and does not imply homoskedasticity as it is an unconditional moment. ) The e(cid:14)cient gmm estimator for (cid:12) is where. ^(cid:12) =(cid:16)z 0x ^(cid:10)(cid:0)1x 0z(cid:17)(cid:0)1 nxi=1 nxi=1 i (cid:0) 1 xix0 i~e2. ~(cid:12) and ~(cid:12) is a preliminary consistent estimator for (cid:12): ols is inconsistent under the assumptions, but 2sls is feasible and consistent: Given ^(cid:12) a moment estimator for (cid:27)2 is. ^(cid:12) where are residuals from the gmm estimation. As an alternative, ((cid:12); (cid:27)2) could be jointly estimated.
