ECON 710 Final: ECON 710 UW Madison Final Exam 2013
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Final exam, spring 2013: take the linear instrumental variables equation yi = xi(cid:12) 1 + zi(cid:12) 2 + ei. [hint: write down the implied reduced form equation for xi. ] (e) in a generic application, would you be comfortable with the assumptions in (c) and (d): take the linear homoskedastic cef i(cid:12) + ei i = x0 y(cid:3) E(e2 ijxi) = (cid:27)2 (1) and suppose that y(cid:3) i is measured with error. Instead of y(cid:3) i ; we observe yi which satis(cid:133)es where ui is measurement error. Suppose that ei and ui are independent and yi = y(cid:3) i + ui. E(u2 u(xi) (a) derive an equation for yi as a function of xi. E(ziui) = 0 (a) write down the standard 2sls estimator ^(cid:12) 2sls for (cid:12) using zi as an instrument for xi: (b) find the asymptotic distribution for ^(cid:12) 2sls: Show that (cid:12) = (cid:21)=(cid:13) if (cid:13) 6= 0; and that.
