多元線性回歸模型估計-在線瀏覽
2025-07-18 01:36本頁面
【正文】 estimate, and OLS remains unbiased What if we exclude a variable from our specification that does belong? OLS will usually be biased 16 Omitted Variable Bias ? ?? ?????????????21111111022110~ t h e n,~~~ e s t i m a t eb u t w e ,asg i v e n is m o d e l t r u e t h eS u p p o s exxyxxuxyuxxyiiibbbbbb17 Omitted Variable Bias (cont) ? ?? ?? ? ? ? ? ?iiiiiiiiiiiiiuxxxxxxxuxxxxuxxy??????????????????1121122111221101122110b e c o m e sn u m e r a t o r t h eso , t h a tso m o d e l , t r u e t h eR e c a l lbbbbbbbb18 Omitted Variable Bias (cont) ? ?? ?? ?? ?? ?? ?? ?? ?? ?? ???????????????????2112112112111121121121~h a v e wense x p e c t a t i o t a k i n g0,)E( s i n c e~xxxxxEuxxuxxxxxxxiiiiiiiiiibbbbbb19 Omitted Variable Bias (cont) ? ?? ?? ?? ?12112112111110212~~ so~ t h e n ~~~on of r e g r e s s i o n heC o n s i d e r t?bbb????????????Exxxxxxxxxiii20 Summary of Direction of Bias Corr(x1, x2) 0 Corr(x1, x2) 0 b2 0 Positive bias Negative bias b2 0 Negative bias Positive bias 21 Omitted Variable Bias Summary Two cases where bias is equal to zero ? b2 = 0, that is x2 doesn’t really belong in model ? x1 and x2 are uncorrelated in the sample If correlation between x2 , x1 and x2 , y is the same direction, bias will be positive If correlation between x2 , x1 and x2 , y is the opposite direction, bias will be negative 22 The More General Case Technically, can only sign the bias for the more general case if all of the included x’s are uncorrelated Typically, then, we work through the bias assumi
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