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

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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

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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
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

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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
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

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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
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?

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## This note was uploaded on 08/02/2011 for the course ECON 139 taught by Professor Alessandrotarozzi during the Spring '08 term at Duke.

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handout9_1 - Econ 139 Introduction to Econometrics Andrew...

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