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Unformatted text preview: 4/21/2010 1 OVB More Formally  I Now lets consider OVB more formally. Specifically, lets consider the effects of OVB on our estimator 1 . Recall our equation for 1 : ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 2 2 1 1 1 1 , n n i i i i i i n n i i i i i i i X X Y Y X X Y Y n X X X X n Cov X Y Var X = = = = = = OVB More Formally  II ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 1 1 , , , , , = , , = , = , = , i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Cov X Y Cov X X u Var X Var X Cov X Cov X X Cov X u Var X Cov X X Cov X u Var X Var X Cov X u Var X Cov X u SD u Corr X u Var X SD X + + = + + + + + + + = + 4/21/2010 2 OVB More Formally  III So we have: What does this equation imply? 1) If Cov ( X i , u i ) = 0, 1 u2248 1 , i.e. 1 is an unbiased and consistent estimator of 1 . (i.e. no OVB) 2) If Cov ( X i , u i ) > 0, 1 will generally be greater than 1 , i.e. 1 is biased upwards (positive bias). 3) If Cov ( X i , u i ) < 0, 1 will generally be less than 1 , i.e. 1 is biased downwards (negative bias). ( 29 ( 29 1 1 , i i i Cov X u Var X + OVB More Formally  IV So the direction of OVB bias depends directly on the sign of Cov ( X i , u i ). Often we can come up with a good guess of whether Cov ( X i , u i ) is positive or negative. This can be helpful, as then we know whether our estimate 1 is biased positively or negatively. So lets think about this more. What determines the sign of Cov ( X i , u i )? 4/21/2010 3 OVB More Formally  V To fix ideas, consider a specific omitted variable V i . Since it is an omitted variable, V i is part of u i . Suppose this relationship is: Note that in this equation , i represents the omitted variables other than V i . Lets assume that Cov ( X i , i ) = 0, i.e. the other omitted variables are not correlated with...
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This note was uploaded on 06/17/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.
 Spring '07
 SandraBlack
 Econometrics

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