多元線性回歸模型估計(jì)(完整版)
【正文】 ?? ?? ?? ?? ???????????????????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 assuming the x’s are uncorrelated, as a useful guide even if this assumption is not strictly true 23 Variance of the OLS Estimators Now we know that the sampling distribution of our estimate is centered around the true parameter Want to think about how spread out this distribution is Much easier to think about this variance under an additional assumption, so Assume Var(u|x1, x2,…, xk) = s2 (Homoskedasticity) 24 Variance of OLS (cont) Let x stand for (x1, x2,…xk) Assuming that Var(u|x) = s2 also implies that Var(y| x) = s2 The 4 assumptions for unbiasedness, plus this homoskedasticity assumption are known as the GaussMarkov assumptions 25 Variance of
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