Lecture_12_Slides_933909009.pdf

# Lecture_12_Slides_933909009.pdf - I NTRODUCTORY E...

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I NTRODUCTORY E CONOMETRICS Lecture 12 Spring 2017, Tsinghua University Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 1 / 45

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Dummy Variables Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 2 / 45
O UTLINE 1 Binary Categorical Variables 2 Categorical Variables with More than Two Categories 3 Multiple Categorical Variables Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 3 / 45

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C ATEGORICAL V ARIABLES Think about the difference in average wages between men and women. Suppose you want to test whether men make more money than women That is you have the following null hypothesis H 0 : E ( W | Male ) = E ( W | Female ) where W is hourly earnings. How do you do this? Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 5 / 45
You could take means for each group and calculate ¯ W m - ¯ W f se ( ¯ W m - ¯ W f ) 2 It turns out that there is an easier way. Suppose we have data on men’s and women’s wages. We want to run a regression, but how do we do that? 1 “Man” and “Woman” are categories, not numbers 2 To run a regression we can only take numerical variables. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 6 / 45

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Solution: Turn it into a dummy variable . Define m i = ( 1 Person is male ; 0 Person is female. Now let’s see if regression analysis can be useful. We will think of this in a “ descriptive ” way. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 7 / 45
Let E ( W i | m i ) = β 0 + β 1 m i . Now notice that E ( W i | Male ) = E ( W i | m i = 1 ) = β 0 + β 1 E ( W i | Female ) = E ( W i | m i = 0 ) = β 0 Solving out this means that β 0 = E ( W i | Female ) β 1 = E ( W i | Male ) - E ( W i | Female ) Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 8 / 45

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Consequently, testing H 0 : E ( W | Male ) = E ( W | female ) is equivalent to testing H 0 : β 1 = 0 We already know how to do this. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 9 / 45
A DDING C ONDITIONING V ARIABLES But that isn’t all. We might be worried that women have less labor market experience than men. Therefore, we suspect that the potential difference in average wages between men and women may be due to the difference in experience . An interesting null hypothesis might be H 0 : E ( W | Male, Experience ) = E ( W | Female, Experience ) That is, comparing men and women with the same level of experience, do they earn the same amount of money? Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 12 10 / 45

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This is easy to do, we just write the model as E ( W i | m i , Exp i ) = β 0 + β 1 m i + β 2 Exp i . Now notice that E ( W i | Male, Experience ) = E ( W i | m i = 1 , Experience ) = β 0 + β 1 + β 2 Exp i E ( W i | Female, Experience ) = E ( W i | m i = 0 , Experience ) = β 0 + β 2 Exp i Solving out this means that β 1 = E ( W i | Male, Experience ) - E ( W i | Female, Experience ) Again, testing whether H 0 : β 1 = 0 tests exactly what we want.
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• Spring '16
• Hong Shengjie

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