Hi I have a question about the interaction term for two dummies (In fact, my question is little bit more complex that the title I think)

<Notations>
y = (log)wage
x = a continuous regressor
d1 = a dummy variable that equals to one if a person's education level is less than high school
d2 = a dummy variable that equals to one if a person's education level is high school graduate
d3 = a dummy variable that equals to one if a person's education level is college graduate or higher
d' = a dummy variable that equals to one if a person is female

Here, d1 is the reference category for the education level.
So, if we run the regression:
Code:
reg y x d2 d3 d', vce(r)
the estimate for d2 may be the difference in wave between high school graduate and less than high school on average.

<What I want to estimate>
Whether the effects of high school degree and college degree have different effects in male and female.

<What I did>
To test the difference, I run the regression below,
Code:
reg y x d2 d3 d' 1.d2#1.d' 1.d3#1.d', vce(r)
Then, I check the significance of the estimates for the interaction terms above.

Although I think it is not problematic, I need to check this estimation for experts like you guys.

(What I am pretty confusing part is if the "1." command is appropriate in this situation)

Thank you for your time spent to read this question.