Chapter 9 Dummy Variables 9 1 A Dummy

Chapter 9: Dummy Variables 9. 1 A Dummy Variable: is a variable that can take on only 2 possible values: yes, no up, down male, female union member, non-union member They provide a method for “quantifying” a “qualitative” variable The variable D = 1 if yes, D = 0 if no It doesn’t matter which category gets the 0 or 1.

Estimation with Dummy Variables 9. 2 If the dummy variable is the only independent variable: Yt = 1 + 2 Dt + et If D = 0 Yt = 1 + et If D = 1 Yt = ( 1 + 2) + et Example: Wage data (See class handout) FE = 0 if the person is male FE = 1 if the person is female Waget = 1 + 2 FEt + et Least squares regression will produce a b 1 and b 2 value such that b 1 = the mean of the Wage values for the FE=0 values b 1 + b 2 = the mean of the Wage values for the FE=1 values

Estimation with Dummy Variables 9. 3 If there is one continuous explanatory variable and one dummy variable: Yt = 1 + 2 Xt + Dt + et If D = 0 Yt = 1 + 2 Xt + et Suppose that If D = 1 Yt = ( 1 + ) + 2 Xt + et 1 >0, 2 >0, > 0 It is as though we Y have two regression lines that have the same slope 2 coefficient but have 1 + 2 difference intercepts. 1 X

Estimation with Dummy Variables 9. 4 Example: Wage data (See class handout) FE = 0 if the person is male FE = 1 if the person is female Waget = 1 + 2 EDt + 3 FEt + et We estimate this model as an ordinary multiple regression model. Our estimate b 3 will measure the difference in wages for males vs. females, after controlling for differences in education. See class handout.

Interaction Terms 9. 5 An interaction term is an independent variable that is the product of two other independent variables. These independent variables can be continuous or dummy variables Yt = 1 + 2 Xt + 3 Zt + 4 Xt. Zt + et In this model, the effect of X on Y will depend on the level of Z. In this model, the effect of Z on Y will depend on the level of X.

Interaction Terms Involving Dummy Variables 9. 6 Yt = 1 + 2 Xt + 3 Dt + 4 Dt. Xt + et If D = 0 Yt = 1 + 2 Xt + et If D = 1 Yt = ( 1 + 3 ) + ( 2+ 4 )Xt + et Y 2+ 4 1 + 3 1 2 X Suppose that 1 >0, 2 >0, 3 >0, 4 >0 It is as though we have two regression lines that have different slope coefficients and different intercepts.

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