ECON 710 Final: ECON 710 UW Madison Final Exam 2012a
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One way to see this is to think of the just-identi(cid:133)ed case, and write the moment conditions. Then the moment estimator of the parameters (cid:0)(cid:12); (cid:27)2(cid:1) are the solutions to the two empirical analogs. Another way to see this is write out the estimators. 2. (a) the gmm/iv/2sls estimators for (cid:12) 1 and (cid:12) 2 are with asymptotic distributions. 2x2(cid:1)(cid:0)1(cid:0)z 0 b(cid:12) 1 = (cid:0)z 0 b(cid:12) 2 = (cid:0)z 0 pn(cid:16)b(cid:12) 1 (cid:0) (cid:12) 1(cid:17) d(cid:0)! N (0; v1) pn(cid:16)b(cid:12) 2 (cid:0) (cid:12) 2(cid:17) d(cid:0)! N (0; v2) where the two normal distributions are independent, A wald-type test for h0 : (cid:12) 1 = (cid:12) 2 is pn(cid:16)(cid:16)b(cid:12) 1 (cid:0) (cid:12) 1(cid:17) (cid:0)(cid:16)b(cid:12) 2 (cid:0) (cid:12) 2(cid:17)(cid:17) d(cid:0)! Wn = n(cid:16)b(cid:12) 1 (cid:0) b(cid:12) 2(cid:17)0(cid:16)bv1 + bv2(cid:17)(cid:0)1(cid:16)b(cid:12) 1 (cid:0) b(cid:12) 2(cid:17) where. ^e2i = y2i (cid:0) x0 d(cid:0)! (cid:31)2 z1iz0 z2iz0.
