The consequences of omitting variable bias(X3) (1 If X, X, are correlated: Oa, and a, are biased ar, a, can have an upward or downward bias E(a1)≠B1E(a1)=B1+B3(X3-b2X2)(13.4) E(a2)+B2 E(a2)=B2+B3 b32 o ar and a, are inconsistent (2)f×2and×3 are not correlated a2 is unbiased, consistent, b32 will be zero a, biased, unless X, is zero in the model(13. 4)（1）If X2 ,X3 are correlated: ◎a1 and a2 are biased, a1 , a2 can have an upward or downward bias E(a1 )≠B1 E(a1 )= B1 +B3（ (13.4) E(a2 ) ≠B2 E(a2 )= B2 +B3b32 ◎ a1 and a2 are inconsistent. （2）If X2 and X3 are not correlated a2 is unbiased, consistent, b32 will be zero a1 biased, unless is zero in the model(13.4) X b X ) 3 − 32 2 The consequences of omitting variable bias (X3 ) X3