ECON 710 Final: ECON 710 UW Madison Final Exam 2008
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Final exam, spring 2008 yi = z 0. E(cid:0)e2 i(cid:1) = (cid:27)2: take the model. Describe an estimator for (cid:27)2: you are reading a paper, and it reports the results from two nested ols regressions: yi = x0. You are curious if the estimate ^(cid:12) 2 is statistically di(cid:11)erent from the zero vector. Do you have to make any assumptions (beyond the standard regularity conditions) to justify your answer: your model is i = x0 y(cid:3) E (ei j xi) = 0 i(cid:12) + ei is not observed. Suppose you regress yi on xi using ols. Describe the nature of the e(cid:11)ect of the mis-measured observation on the ols estimate. S((cid:12)) = nx i=1 wi(cid:0)yi (cid:0) x0 i(cid:12)(cid:1)2. That is ^(cid:12) = argmin(cid:12) s((cid:12)) (a) find an explicit expression for ^(cid:12) (b) what population parameter is ^(cid:12) estimating? (be explicit about any assumptions you need to impose.
