Econometrics

[Xiang]

A researcher runs Yi = β0 + β1X1,i + β2Di+ β3 Di X1,i  +ui       where  is the salary of worker i, X1,i  is the years of experience, and Di is a dummy that takes the value of 1 if the worker is female and 0 otherwise. Which of the following would indicate that female workers’ salary increases at a slower rate with years of experience.
 
a)      β2 < 0    
b)      β2  > 0      
c)      β3 < 0    
d)      β3 > 0

I really don't understand how to solve this. Please help. Steps please :)

thanks

[yushi.]

i think d ans is c. as X increases female will earn less if B3 is negative.. ie. increase in experience will have a negative impact on female salary...  

[Do bats eat cats?]

Is the answer β3 < 0?

Since Di takes the value 1 for females, the effect is to make the equation equivalent to Yi = (β0 + β2) + (β1 + β3)X1i + ui for females.
For males the regression is equivalent to Yi = β0 + β1X1i + ui (because Di takes the value 0).

So, the slope effect for males is β1 and for females it is β1 + β3.

Female workers' salary increases at a slower rate than male workers' salary with years of experience if β1 + β3 < β1, which is the same as β3 < 0.

Please correct me if there is something wrong with my understanding.

[Mauli]

i agree with the above answers.
explanation same as given by do bats eat cats.

[Ayushya Kaul]

I agree with Bats here.