econ483midterm2010sol

econ483midterm2010sol - Solution: Econ 483 Midterm, Spring...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solution: Econ 483 Midterm, Spring 2010 1. (6) E V ar 1 2 3 R1 + 3 R 2 1 2 3 R1 + 3 R2 2 = 1 E (R1 ) + 2 E (R2 ) = 1 r1 + 3 r2 . 3 3 3 = V ar 1 3 R1 + V ar 2 3 R2 + 2Cov 1 2 3 R1 ; 3 R2 = 12 91 + 42 92 + 4 9 12 . 2. (1) E (X ) = V ar (Y ) = V ar ( (2) b R1 R2 x 0:5 1 (0 x 2) dx = 0 0:5xdx = 1. h1 i V ar (X ) = E (X E (X ))2 = E X 2 2X + 1 = E X 2 0 2E (X )+E (1) = 1 Cov (X; U ) + 1X + U) = 2V 1 ar (X ) + V ar (U ) + 2 = 4:22 V ar (X ) + 36. R2 0 1 0:5x2 dx 2+1 = 3 . 1 = Pn = = Xi X ( 0 + 1 Xi + Ui ) Pn 2 X i=1 Xi Pn Pn Pn 2 X X X Ui 0 1 i=1 Xi i=1 Xi i=1 Xi Pn 2 + Pn 2 + Pn 2 X X X i=1 Xi i=1 Xi i=1 Xi Pn X Ui i=1 Xi 1 + Pn 2: Xi X i=1 i=1 of (3) E b 1 jX = E 1. 1 + (4) b 1 !p (5) Therefore, b 1 is unbiased. 1 Pn i=1 Pn i=1 1 Xi Xi X Ui X 2 jX ! = 1+ Pn i=1 Xi Pn X E (Ui jX ) Xi X 2 = 1 for any value i=1 + Cov (X; U ) = V ar (X ) as n ! 1 because Cov (X; U ) = 0. Therefore, b 1 is consistent. (A): de…nition of variance (B): unbiasedness or from (3) (C): from (2) and conditional on X , any function of X is nonrandom (D): properties of variance and conditional on X , any function of X is nonrandom (E): homoskedasticity and random sampling (6) e 1 = + 2 Pn i=1 Pn i=1 Xi X Ui 2 Xi X V ar (2Ui jX ) V ar e 1 jX = Pn X i=1 Xi fore, se e 1 jX = 2se b 1 jX . 1 6= 1 2 d = 4V ar b 1 jX . Similarly, V ar e 1 jX i + P=1 n Pn Xi Xi X Ui X 2 i=1 = b1 d = 4V ar b 1 jX . There- 1 ...
View Full Document

This note was uploaded on 04/04/2011 for the course ECON 401 taught by Professor Staff during the Spring '08 term at University of Washington.

Ask a homework question - tutors are online