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Introduction to Econometrics

by: Kaden Orn

Introduction to Econometrics ECO 4305

Marketplace > Texas Tech University > Economcs > ECO 4305 > Introduction to Econometrics
Kaden Orn
GPA 3.96


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This 10 page Class Notes was uploaded by Kaden Orn on Thursday October 22, 2015. The Class Notes belongs to ECO 4305 at Texas Tech University taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/226395/eco-4305-texas-tech-university in Economcs at Texas Tech University.


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Date Created: 10/22/15
Mu mp e regresswon Multiple regression ECO 4305 October 8 2008 Muitipie regression Gender wage gap Is wage gap evidence of gender discrimination Maybe but other factors might be important gt education V experience gt type ofjob gt industrysector Multiple regression Gender wage gap gt Our simple model is eg problem 52 Wage 1252 i 212 x Male L All factors other than gender say education are captured by the error term L gt Suppose that education differs systematically by gender gt whether or not this is likely and what it would mean if true are separate questions gt If so then education is correlated with gender the X variable and gt It39s also correlated with the error term gt This results in bad juju otherwise known as Multiple regression Omitted variable bias gt We have OVB when two things happen gt Omitted variable is correlated with one or more of the included regressors X39s and gt The dependent variable Y depends on the omitted variable gt First OLS assumption EulX 0 Still true gt Some factor in u education differs according to the value of X gender gt So u and X are correlated EulX y O gt OLS estimator 31 is biased bad and inconsistent worse Muitipie regression Inconsistency gt Remember that if the OLS assumptions are satisfied then 39 3151 51 39 51 N NleUfh gt 0231 A O as n A 00 gt the last bit means that 31 L 51 gt But now Ema 7 Bl bias gt and 31 L 31 pXu039u039X inconsistency gt mm is correlation between X 84 u gt Inconsistent means the bias doesn39t go away in large samples Multiple regression Sign of omitted variable bias gt Back to gender gap example Suppose males have more years of education than females gt More education means higher wages gt Error term would tend to be positive for males higher wages than would be predicted by gender alone gt PXu gt 07 and 31 is too high gender gap is over estimated gt Other examples gt Test scores class size and of students learning English p 188 191 gt Crime rate 7 police per capita and problem 66 Multiple regression Multiple regression We want to estimate the effect of gender on wages say taking account of or controlling for other factors like age education etc gt Multiple regression model see p 196 Yi o 1X1i52X2iquot39 kai Hi gt For example Wage 30 l 31 Male l 32 YrsEXp l u gt 31 measures wage differential between males amp females controlling for experience ie comparing male amp female with equal experience gt example problems 61 64 Multiple regression Multiple regression Most of what we learned in the singlevariable case chapters 4 amp 5 carries over to the k variable case A couple exceptions concern model fit gt Standard error of the regression SER 55R 1 SER 77 k7 1 see eqn 613 Multiple regression Multiple regression Most of what we learned in the singlevariable case chapters 4 amp 5 carries over to the k variable case A couple exceptions concern model fit gt We also use the adjusted R R2 rather than R2 55R 2 7 7 7 R 7 1 T55 R2 7 17 n 7 1 5 R Hikil see eqn 615 gt R2 can39t decrease as we add more variables danger of getting a kitchen sink model gt R2 can decrease is the extra variable worth it gt Kitchen sink still a danger though Mu mp e regresswon OLS Assumptions in the k variable case gt Eui X1i7X2i7 7in 0 gt finite fourth moments gt X39s and Y39s are iid gt no perfect multicollinearity


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