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I have a model: $$ \ln({\rm earnings}) = 2.618656-0.0899657{\rm female}+0.382019{\rm white}-0.2754126{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables.

t= female=-1.65 white=8.86 female*white=-4.61 cons=66.07

p>|t|= female=(0.100) white=0.000 female*white=0.000 cons=0.000

std error= female=0.0546456 white=0.043098 female*white=0.059699 cons=0.0396351

95% confidence interval.

                   male          female        Gender Effect
white            a (2.62)      a+b1 (2.53)       b1 (-0.09)       
non-white        a+b2 (3)   a+b1+b2+b3 (2.63)    b1+b3 (-0.37)   b3=-0.28
Ethnic Effect    b2 (0.38)     b2+b3 (0.1)       
                          b3=-0.28

Now i know there is gender pay difference with b1 (9%), I also know there is race pay difference with b2(38%). Now i need to know is their a gender pay gap for whites only. How can I figure that out regression above.

Note:( my last question had two parts, part 1 interpreting b3 which was answered, it is part 2 which has not been asnwered yet I have edited my question with more detail so now it can be looked at more appropriately Thanks)

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Since all the coefficients are significant, you can tell if there is gender-gap for non-whites just by looking at the coefficients. For Non-white male, the expected log(income) is 2.618656, for Non-white female it is 2.618656 - 0.0899657 = 2.52869. So there is a gap.

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  • $\begingroup$ thanks that was helpful. last question we multiple every coefficient with 100 for % change because of lnearnings, does that we multiple alpha (2.62) also by 100 for % change effect but that will be like 262% which doesn't sound right. please do comment on this how to treat alpha in this case? $\endgroup$
    – user59740
    Nov 2, 2014 at 20:18
  • $\begingroup$ The %change interpretation makes sense only when you think about a change of the X variables, not the intercept. The interpretation os intercept is the one of an log-income of an infividual with 0 for all the dummies - i.e. a non-white male. $\endgroup$
    – DatamineR
    Nov 3, 2014 at 4:12

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