Economics 105: Statistics
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Transcript of Economics 105: Statistics
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)
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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