Omitted Variables

1. Omitted Variables True Model: (1) • is the student’s cumulative college gpa (1-4) • is the student’s high school gpa (1-4) • is the student’s academic ability • is a stochastic error term with where Empirical Specification: where (2)

2. Empirical Specification: where (2) Hence, we can re-write (2) as (3) where

3. Regressing on produces where Students with greater ability are expected to have high school gpa’s. What we hoped to estimate (+) (+) (+) Students with greater ability are expected to have higher college gpa’s. Variances: always positive is upward biased

4. omitted Students who work harder in high school and, as a result, earn higher grades, are likely to earn higher college grades, i.e., But if we don’t control for students’ academic abilities, high school grades will appear more important than they really are, because higher ability students are likely to earn both higher high school grades (and higher college grades (. Hence, higher high school grades explain higher college grades both directly and because it is a proxy for the omitted variable, ability.

5. True Model: Suppose the SAT is a proxy variable for ability. In particular, suppose where In this case, we are assuming that students’ high school grades don’t help explain their academic abilities. Substituting this equation into (1), we have Rewriting, (3) • where where

6. Two Empirical Specifications where (2) (3) As expected, People often tell high school students that they need to study hard to eventually do well in college. The corresponding estimate is . What is the interpretation of ?

7. Sitting outside of High School

8. Regressions run on subsamples of whites and non-whites Fully Interacted Model Non-Hispanic-white students appear to get a bigger boost from studying hard in high school than non-white students. But is the difference statistically significant? But the difference is not statistically significant!

9. Omitted Variables: Youth Smoking and Anti-Smoking Sentiment True Model: • = cigarettes smoked per day • =price per pack • = anti-smoking sentiment in state s. • = stochastic error term with where Empirical Specification: where

10. Stronger anti-smoking sentiment leads to higher cigarette taxes. What we hoped to estimate Stronger anti-smoking sentiment leads to less smoking, e.g., less smoking in public places Variances: always positive is downward biased

11. I chose to present standard errors because it is most natural to test whether our estimate implies that young smokers’ demand for cigarettes is inelastic, which requires we calculate a different t-stat than the one produced by standard software programs.

12. It appears that the young women’s demand for cigarettes is more inelastic than that of young men But the difference is not statistically significant!