handout9_1

handout9_1 - Econ 139: Introduction to Econometrics Andrew...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 139: Introduction to Econometrics Andrew Sweeting 1 Department of Economics Duke University Spring 2011 Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 1 / 57
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Nonlinear Regression Functions Up until now, we have assumed that the population regression function was linear. Since the slope of the population regression function was a constant, the e/ect on Y of a unit change in X did not depend on the value of X . But what if the e/ect on Y of a unit change in X does depend on the value of one (or perhaps several) of the independent variables? If so, the population regression function is nonlinear. Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 2 ± 57
Background image of page 2
Nonlinear Regression Functions We will look at two methods for modeling nonlinearities: Allowing the average e/ect on Y of a unit change in X 1 to depend on the value of X 1 . This method uses nonlinear functions of the X and logarithms. Allowing the average e/ect on Y of a unit change in X 1 to depend on the value of another (or perhaps many) independent variable X 2 . This method uses dummy variables and interaction terms. Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 3 ± 57
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
variables (also called binary variables) and interaction terms. Dummies and interactions are a useful way to expand the ²exibility of OLS. Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 4 / 57
Background image of page 4
Dummies and Interactions We have already seen examples where a single regressor is a dummy variable. 1 on earnings, gender and years of education: Gender (female) is a dummy variable that takes on the value 1 for females and 0 for males Wage is average hourly wage in 1998 (in $) Yrseduc is years of education (between 6 and 20 years) We know that we can test the null hypothesis that average earnings are equal for males and females by running the regression Wage = β 0 + β 1 Gender + u 1 This data is drawn from the 1998 Current Population Survey (CPS) and includes full-time workers, age 25 to 64. Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 5 / 57
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Dummies and Interactions Recall that β 0 is the population mean value of male earnings, β 0 + β 1 is the mean value of female earnings, and β 1 the di/erence in means across genders. per hour than men. If we test the null hypothesis H 0 : β 1 = 0 , we see that it is rejected α . Econ 139 Handout 9 (Duke) Nonlinear Regression Functions Spring 2011 6 ± 57
Background image of page 6
Dummies and Interactions We can also assess the impact of education on earnings (we will ignore the omitted variable bias associated with not including ability) by running the regression Wage = β 0 + β 1 Yrseduc + u Each additional year of school is expected to increase hourly wages by $1.33. But what if we want to analyze both e/ects at the same time?
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 57

handout9_1 - Econ 139: Introduction to Econometrics Andrew...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online