Economics 105: Statistics

1. Economics 105: Statistics Go over GH 22 GH 23 due Monday Individual Oral Presentations … see RAP handout. Dates are Tue April 24th and Thur April 26th in lab. But we can’t fit them all into 75 minutes … so extra sessions to be announced.

2. Average Effect on Y of a change in X in Nonlinear Models • Consider a change in X1 of ΔX1 • X2 is held constant! • Average effect on Y is difference in pop reg models • Estimate of this pop difference is

3. Example

4. Example • What is the average effect of an increase in Age from 30 to 40 years? 40 to 50 years? • 2.03*(40-30) - .02*(1600 – 900) = 20.3 – 14 = 6.3 • 2.03*(50-40) - .02*(2500 – 1600) = 20.3 – 18 = 2.3 • Units?!

5. http://xkcd.com/985/

6. Example

7. Example

8. Log Functional Forms • Linear-Log • Log-linear • Log-log • Log of a variable means interpretation is a percentage change in the variable • (don’t forget Mark’s pet peeve)

9. Log Functional Forms • Here’s why: ln(x+x) – ln(x) = • calculus: • Numerically: ln(1.01) = .00995 = .01 • ln(1.10) = .0953 = .10 (sort of)

10. Linear-Log Functional Form

11. Linear-Log Functional Form

12. Log-Linear Functional Form

13. Log-Linear Functional Form

14. Log-Log Functional Form

15. Log-Log Functional Form

16. Examples

17. Examples

18. Examples

19. Examples

20. Dummy Variables • A dummy variable is a categorical explanatory variable with two levels: • yes or no, on or off, male or female • coded as 0’s and 1’s • Regression intercepts are different if the variable is significant • Assumes equal slopes for other explanatory variables • If more than two categories, the number of dummy variables included is (number of categories - 1)

21. Dummy Variable Example (with 2 categories) • E[ GPA | EconMajor = 1] = ? • E[ GPA | EconMajor = 0] = ? • Take the difference to interpret EconMajor