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Unformatted text preview: ative variables) E (wage jeduc , male ) = δ0 EMET2007/6007 8 st May 2013 8 / 53 The coe¢ cient δ0 captures the di¤erence in the expected y from the base
category: in this case the base category is ‘
If δ0 < 0 then by virtue of being a male, a man with the same level of
education as a woman can expect a higher wage than the woman.
An interesting and important hypothesis, then, is
H 0 : δ 0 = 0 H1 : δ 0 6 = 0
OR H0 : δ 0 Lecture 9 (qualitative variables) 0 H1 : δ 0 < 0 EMET2007/6007 8 st May 2013 9 / 53 Dummy variable trap
Putting too many dummies in and so inducing perfect multicollinearity
wage = β0 + δ0 female + δ1 male + β1 educ + ε This model cannot be estimated (perfect collinearity)
female + male = 1 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 10 / 53 When using dummy variables, one category always has to be omitted:
wage = β0 + δ0 female + β1 educ + ε
The base category are men
wage = β0 + δ1 male + β1 educ + ε
The base category are women Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 11 / 53 Alternatively, one could omit the intercept:
wage = δ0 female + δ1 male + β1 educ + ε Disadvantages:
1) More di¢ cult to test for di¤erences between the parameters
2) R 2 formula only valid if regression contains intercept Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 12 / 53 Estimated wage equation with intercept shift
[ 1.57 (0.72 ) 1.81 female (0.26 ) + 0.572 educ + 0.025 exper + 0.141 tenure
(0.049 ) n = 526 (0.012 ) (0.021 ) 2 R = 0.364 Holding education, experience, and tenure …xed, women are expected
to earn $1.81 less per hour than men Does that mean that women are discriminated against?
Not necessarily. Being female may be correlated with other productivity
characteristics that have not been controlled for. Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 13 / 53 Comparing means of subpopulations described by dummies
[ 7.10 2.51 female (0.21 ) (0.26 )
2 n = 526 R = 0.116 Not h...
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This note was uploaded on 06/15/2013 for the course EMET 2007 taught by Professor Strachan during the Two '13 term at Australian National University.
- Two '13