ECON 710 Midterm: ECON 710 UW Madison Midterm 2012
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March 22, 2012 i(cid:12) + ei yi = x0. Consider three estimators for (cid:12) (cid:15) b(cid:12), the unconstrained least squares estimator (cid:15) e(cid:12), the constrained least squares estimator (cid:15) (cid:12), the constrained e cient minimum distance estimator. 2 = ie(cid:12); ei = yi (cid:0) x0 i(cid:12); and variance. = 2 (1) (a) find an explicit expression for the constrained least-squares (cls) estimator e(cid:12) = (e(cid:12) 1;e(cid:12) 2) of (cid:12) = ((cid:12) 1; (cid:12) 2) under (1). E (yi j xi) = ((cid:13) + (cid:18)xi)1=2 (2) De(cid:133)ne ui = yi (cid:0) ((cid:13) + (cid:18)xi)1=2 (b) use yi = ((cid:13) + (cid:18)xi)1=2 + ui to calculate e(cid:0)y2. : show that e (ui j xi) = 0 is i j xi(cid:1).
