Multiple Regression: Analyzing the Gender Wage Gap with Controlled Variables, Study notes of Introduction to Econometrics

Download Multiple Regression: Analyzing the Gender Wage Gap with Controlled Variables and more Study notes Introduction to Econometrics in PDF only on Docsity! Multiple regression Multiple regression ECO 4305 October 8, 2008 Multiple regression Gender wage gap Is wage gap evidence of gender discrimination? Maybe, but other factors might be important: I education I experience I type of job I industry/sector Multiple regression Inconsistency I Remember that if the OLS assumptions are satisfied, then I E (β̂1) = β1 I β̂1 ∼ N(β1, σ2β1) I σ2β1 → 0 as n→∞ I the last bit means that β̂1 p−−→ β1 I But now E (β̂1) 6= β1 (bias) I and β̂1 p−−→ β1 + ρXu(σu/σX ) (inconsistency) I ρXu is correlation between X & u I “Inconsistent” means the bias doesn’t go away in large samples Multiple regression Sign of omitted variable bias I Back to gender gap example. Suppose males have more years of education than females. I More education means higher wages I Error term would tend to be positive for males (higher wages than would be predicted by gender alone) I ⇒ ρXu > 0, and β̂1 is too high (gender gap is over-estimated) I Other examples: I Test scores, class size and % of students learning English (p. 188, 191) I Crime rate, # police per capita, and... (problem 6.6) 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. I Multiple regression model (see p. 196): Yi = β0 + β1X1i + β2X2i + · · ·+ βkXki + ui I For example, Wage = β0 + β1Male + β2YrsExp + ui I β1 measures wage differential between males & females, controlling for experience (i.e., comparing male & female with equal experience). I example: problems 6.1-6.4