ECON 710 Final: ECON 710 UW Madison Final Exam 2014
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Final exam, spring 2014: you have n iid observations (yi; x1i; x2i); and consider two alternative regression models yi = x0. 2i(cid:12) 2 + e2i (1) (2) where x1i and x2i have at least some di erent regressors. (for example, (1) is a wage regression on geographic variables and (2) is a wage regression on personal appearance measurements. ) You want to know if model (1) or model (2) (cid:133)ts the data better. H0 : (cid:27)2 e1i and e2i are observed. You decide that the model with the smaller variance (cid:133)t (e. g. , model (1) You decide to test for this by testing the hypothesis of equal (cid:133)t: for simplicity, suppose that. 2 against the alternative of unequal (cid:133)t h1 : (cid:27)2. 2: (a) construct an estimate b(cid:18) of (cid:18) = (cid:27)2 (b) find the asymptotic distribution of pn(cid:16)b(cid:18) (cid:0) (cid:18)(cid:17) as n !
