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Chapter 7, Dummy Variable
Dummy variable can only take values 1 and 0. It is categorical, that means the numbers 1 and 0 have no numerical
meanings (we cannot say 1 is greater than 0). In this chapter we use dummy as regressor. Chapter 17 (covered in eco411)
shows how to use dummy as the dependent variable. First letโs use wage data and consider a simple regression
๐ค๐๐๐ = ๐ฝ0+ ๐ฝ1๐ท + ๐ข (1)
where ๐ท = 0 for male, and ๐ท = 1 for female. For dummy variable, you have to be clear ๐ท = 0 is for which group (called
base group). Later all comparisons are made relative to the base group. You can report the frequency of ๐ท using tab D.
The key to understand the dummy-variable-model is to discuss:
when = 0, ๐ค๐๐๐ = _____________________. If we take expectation we get ___________________
when = 1, ๐ค๐๐๐ = _____________________. If we take expectation we get ___________________
So ๐ฝ0 can be interpreted as ________________________; and ๐ฝ1 can be interpreted as____________________
This result suggests that we can conduct the two-sample t test (the comparison of means test, stata command:
ttest wage, by(D)) using the simple regression (1) that involves dummy. Now consider a multiple regression
๐ค๐๐๐ = ๐ฝ0+ ๐ฝ1๐ท + ๐ฝ2๐ฅ + ๐ฝ3(๐ท โ ๐ฅ)+ ๐ข (2)
For example x can be exper, and ๐ท โ ๐ฅ is the interaction term (product of) x and dummy. Letโs discuss again:
when ๐ท = 0, _________________________________________________________________________________________
when ๐ท = 1, _________________________________________________________________________________________
๐ฝ0 can be interpreted as _________________________________________________________;
๐ฝ1 can be interpreted as _________________________________________________________;
๐ฝ2 can be interpreted as _________________________________________________________;
๐ฝ3 can be interpreted as _________________________________________________________;
How to show ๐ฝ1 and ๐ฝ3 in graph?
