ECON 710 Final: ECON 710 UW Madison Final Exam 2016
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Be speci(cid:133)c about estimators and covariance matrix esti- mators: consider the model yi = x0. E (eijxi) = 0 i(cid:12) + ei with yi scalar and xi a k vector. E (ziteit) = 0 it(cid:12) + ui + eit for i = 1; :::; n and t = 1; :::; t . The individual e ect ui is treated as (cid:133)xed. Assume xit and zit are k (cid:2) 1 vectors. You do not need to examine its distributional (e. g. asymptotic) properties: take the model yi = (cid:25)i(cid:12) + ei (cid:25)i = e (xijzi) = (cid:13) 0zi. 1 assuming that (cid:12) = 0: (c) why is the assumption (cid:12) = 0 an important simplifying condition in part (b)? (d) using the result in (c), construct an appropriate asymptotic test for the hypothesis. H0 : (cid:12) = 0: you are at a seminar where a colleague presents a simulation study of a test of a hypothesis.
