Question

7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or not? (c) In this case, does @1 converge in probability? If yes, calculated the probability limit. If no, show why.

Answer 1

(C) - .. '-) ( -5) -R)- 2 ) (E-7)- , - -R) (A + Aurus) , - -..... 2 -)- , 5 . + 9, 2 -R)< <!-) PRE-) -) ० + 60 + X-R)u/- ) - SECO. 14 - . .) = 2+ a ca-K) 2 -) 29 +Q :: x-K) (E-X)]]

w iki (0) Elå 14.&N) = B. ta&P as ELê) + Bi, ü not uingiased for B.. e, If i converger in probability, it wie converge to pita, not to B.. From 6 å = Bit a unui/seiner. Var [ R 18.xw] = a sci-age or iris] } Iecināja42 - E var Cêje, kto] 26/5628-232 var {ELB, 19, 2N) = var (Bi tagao VarCÅ) = Varece pe la Elvar Cêrel je Ilkină)? MSELÊ, a Val (8) + ECP By I '- ) 1. C o does not Po as N700, converge in probability.
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