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.

• 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

Average Effect on Y of a change in X in Nonlinear Models

Example

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?!

http://xkcd.com/985/

Example

Example

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)

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

Linear-Log Functional Form

Log-Linear Functional Form

Log-Linear Functional Form

Log-Log Functional Form

Log-Log Functional Form

Examples

Examples

Examples

Examples

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)

Dummy Variable Example (with 2 categories)

• E[ GPA | EconMajor = 1] = ?• E[ GPA | EconMajor = 0] = ?• Take the difference to interpret EconMajor