ECON 710 Final: ECON 710 UW Madison Final Exam 2013a
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There is only one instrument yet two coe cients. Thus the 2sls estimator is not de(cid:133)ned. (b) yes. With two instruments we can de(cid:133)ne the 2sls estimator. This is generically arbitrary, and i would not be comfortable with these assumptions (especially the second) in a general application. = x0 i(cid:12) + ei + ui i(cid:12) + vi vi = ei + ui: where. E(v2 i jxi) = e(e2 ijxi) + e(u2 ijxi) + 2e(eiuijxi) This means that the estimates are less precise. (c) standard errors should be calculated with the heteroskedasticity-consistent formula: just-identi(cid:133)ed 2sls (a) = 1 n nxi=1 zixi! (cid:0)1 1 n ziyi! nxi=1 (b) note that using xi = (cid:13)zi + ui and e (ziui) = 0. E (zixi) = e (zi ((cid:13)zi + ui)) = (cid:13)q. Hence: indirect least squares (a) by substitution, zixi !p e (zixi) = (cid:13)q. 1 n nxi=1 pn(cid:16)^(cid:12) (cid:0) (cid:12)(cid:17) = 1 n nxi=1 zixi! (cid:0)1 1.
