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EMET2007 Lecture 9 for Wattle

# 0 emet20076007 8 st may 2013 8 53 the coe cient 0

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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 ‘ men’ 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 For example, 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 wage = [ 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 wage = [ 7.10 2.51 female (0.21 ) (0.26 ) 2 n = 526 R = 0.116 Not h...
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