answers2007final

answers2007final - –1– Econ 220B Answers to 220B Winter...

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Unformatted text preview: –1– Econ 220B Answers to 220B Winter 2007 Final Exam 1a.) or · α ˆ γ ˆ ¸ = · 0 T Σzt 0 Σzt Σzt zt ¸−1 · Σyt Σ zt y t ¸ h i 0 −1 [Σ(zt − z)(yt − y )] γ = Σ(zt − z)(zt − z) ˆ 1b.) m = q k =q+1 SSRR from regression of yt on 1 SSRU from regression described in 1a 1c.) no further assumptions needed n1 = q n2 = T − q − 1 1d.) R2 = 1 − SSRU /SSRR m(T − k )−1 F = −1 + SSRR /SSRU 1 SSRU = −1 F 1 + m(T − k ) SSRR R2 = 1 − 1e.) 1 m(T − k )−1 F = 1 + m(T − k )−1 F 1 + m(T − k )−1 F R2 = (T − k )R 2 = mF p →0 (T − k ) + mF (T − k )mF mF p L = → mF → χ2 (m) (T − k ) + mF 1 + mF/(T − k ) –2– Econ 220B 2a.) Yes if we regressed yt on x∗ , no if we regressed yt on xt t y = xβ +u u = ε − vβ E (u|x) 6= 0 −1 2b.) [T −1 Σ(x∗ + vt )2 ] [T −1 Σ(x∗ + vt )(βx∗ + εt )] t t t p 2 2 2 → βq /(q + τ ) 3a.) CLT b.) endogenous regressors c.) valid instrument d.) relevant instrument e.) serial correlation 0 f.) Σxt (yt − zt β ) = 0 0 ˆ β = (Σxt zt )−1 (Σxt yt ) 0 g.) h = xt (yt − zt β ) 0 ˆ D0 = −T −1 Σxt zt h.) · · ¸ ¸ 1 1+ρ ρ S= + Γ0 = Γ0 1−ρ 1−ρ 1−ρ ·³ ´ µ1 + ρ¶ ³ ´¸ 0 −1 −1 ˆ = T −1 Σzt x0t V Γ0 T Σxt zt 1−ρ ˆ (β − 3) q1 ≈ N (0, 1) 0 ˆ e1 (V/T )e1 ...
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answers2007final - –1– Econ 220B Answers to 220B Winter...

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