Because the base group is represented by the

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Because the base group is represented by the intercept, if there are n categories there should be n – 1 dummy variables If there are a lot of categories, it may make sense to group some together Example: top 10 ranking, 11 – 25, etc.
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 7 Interactions Among Dummies Interacting dummy variables is like subdividing the group Example: have dummies for male, as well as hsgrad and colgrad Add male*hsgrad and male*colgrad, for a total of 5 dummy variables –> 6 categories Base group is female HS dropouts hsgrad is for female HS grads, colgrad is for female college grads The interactions reflect male HS grads and male college grads
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 8 More on Dummy Interactions Formally, the model is y = β 0 + δ 1 male + δ 2 hsgrad + δ 3 colgrad + δ 4 male*hsgrad + δ 5 male*colgrad + β 1 x + u, then, for example: If male = 0 and hsgrad = 0 and colgrad = 0 y = β 0 + β 1 x + u If male = 0 and hsgrad = 1 and colgrad = 0 y = β 0 + δ 2 hsgrad + β 1 x + u If male = 1 and hsgrad = 0 and colgrad = 1 y = β 0 + δ 1 male + δ 3 colgrad + δ 5 male*colgrad + β 1 x + u
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 9 Other Interactions with Dummies Can also consider interacting a dummy variable, d , with a continuous variable, x y = β 0 + δ 1 d + β 1 x + δ 2 d*x + u If d = 0, then y = β 0 + β 1 x + u If d = 1, then y = ( β 0 + δ 1 ) + ( β 1 + δ 2 ) x + u This is interpreted as a change in the slope
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu 10 y x y = β 0 + β 1 x y = ( β 0 + δ 0 ) + ( β 1 + δ 1 ) x Example of δ 0 > 0 and δ 1 < 0 d = 1 d = 0
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Fall 2008 Under Econometrics Prof. Keunkwan Ryu
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