Introduction omitting relevant variable including

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Unformatted text preview: ng Misspecifications OVB vs. IIV Analysis suggests general-to-specific estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. But testing downwards can be problematic: Multicollinearity? Loss of degrees of freedom? What if different ways of dropping variables lead to different specifications? Unintentional proxies? Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Comparing Misspecifications OVB vs. IIV Analysis suggests general-to-specific estimation strategy to avoid OVB: 1 Start with most general model, i.e. including all possible explanatory variables. 2 Test downwards whether to omit certain variables or not. But testing downwards can be problematic: Multicollinearity? Loss of degrees of freedom? What if different ways of dropping variables lead to different specifications? Unintentional proxies? Parsimony? Introduction Omitting Relevant Variable Including Irrelevant Variables 2005 Question 2 Setup of the Question Correct specification: LGEARN = β1 + β2 S + β3 AWE + u Proxy for AWE: PWE=AGE-S-6 Correlation S and PWE: -0.74 Correlation S and AWE: -0.28 Correlation PWE and AWE: 0.47 Note that sample comprises n = 2185 respondents. Past Exam Practice Question Introduction Omitting Relevant Variable 2005 Question 2 Regression Output Including Irrelevant Variables Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)a) Why coefficient of S smaller in (1) than (3) Mathematically: b2 = n i =1 (Si = β2 + β3 ¯ ¯ − S )(LGEARNi − LGEARN ) n ¯2 i =1 (Si − S ) n ¯ ¯ i =1 (Si − S )(AWEi − AWE ) + n ¯ )2 (Si − S i =1 (11) n ¯ i =1 (Si − S )(ui − n ¯2 i =1 (Si − S ) ¯ u) (12) Taking expectations: E(b2 ) = β2 + β3 n i =1 (Si ¯ ¯ − S )(AWEi − AWE ) + n ¯ )2 i =1 (Si − S n i =1 (Si ¯ ¯ − S )(E(ui ) − E(u )) n ¯ )2 i =1 (Si − S (13) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)a) Why coefficient of S smaller in (1) than (3) Continued: E(b2 ) = β2 + β3 n i =1 (Si ¯ ¯ − S )(AWEi − AWE ) n ¯ (Si − S )2 i =1 Bias Term E(b2 ) < β2 since: Corr. S, AWE negative: n i =1 (Si ¯ ¯ − S )(AWEi − AWE ) < 0 Positive effect AWE on earnings: β3 > 0 n ¯ Sum of squares positive: (Si − S )2 > 0 i =1 (14) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question 2005 Question 2 2)a) Why coefficient of S smaller in (1) than (3) Intuition along these lines: Positive effect of schooling on earnings underestimated on expectation in (1). Fail to control for fact that for high S observations, AWE tends to be low. Higher S effect on earnings offset to some extent by less work experience - net effect smaller. (3) coefficient larger as unbiased. Maybe use triangle diagram to illustrate this. Introduction Omitting Relevant Variable Including Irrelevant Variables 2005 Question 2 2)b...
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