Lecture+5+Regression+with+dummy+variables

Interactionsamongdummies

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Unformatted text preview: etween hsgrad and the default category (hsdropout); while δ 2 represents the mean wage difference between colgrad and the default category. o Recall that with an intercept, the coefficient of a dummy represents the mean difference in outcome between the dummy represented category and the default category (captured by the intercept). • If there are n categories, can only include n–1 dummy variables in the regression. 3 • • • The intercept is for the base (default) group. The estimated regression can be represented by n parallel lines. Any categorical variable can be converted into a set of dummy variables as above. If there are a lot of categories, it may make sense to combine some categories. Interactions among Dummies • • Interacting dummy variables is like subdividing the group The interaction or product of dummies is still a dummy. Example1:Let female be a dummy indicating female. colgrad is dummy indicating college or above education, so colgrad=1 if one has college or above education, and =0 if one has less than college education. We have the following model wage = α + δ1 female + δ 2colgrad + δ 3 female * colgrad + β X + u, • • Same as before, a dummy for male and a dummy for female provide the same information, so can’t include both. College grads and non­college grads provide the same information for both groups, so can’t include dummies for both. Can only include these two dummies and one possible interaction term female*colgrad For both female and male, we have two education categories, so in total, we have four categories. These two dummies and one possible interaction term give a total of three dummy variables. They give the full set of information about the four categories in the data. How to interpret the model? • • • Base group is male non‐college grads. female is for female non‐college grads, so the coefficient represents the mean wage difference between female non‐college grads and male non‐college grads. colgrad is for male college grads, so the coe...
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This document was uploaded on 03/11/2014.

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