How to compare differences in coeficients from an interaction of two dummy variables?

[Aneesh Banerjee]

My main hypothesis tests the differences between the coefficients of a regression with interaction between two dummy variables.
Y = i.Dummy1#i.Dummy2
Which gives the following
Variable coefficient
0.Dummy1*0.Dummy2 beta1
1.Dummy1*0.Dummy2 beta2
0.Dummy1*1.Dummy2 beta3
1.Dummy1*1.Dummy2 beta4

I want to show
beta4 – beta 2 > beta3 – beta1
1.Dummy1*1.Dummy2 – 1.Dummy1*0.Dummy2 > 0.Dummy1*1.Dummy2 – 0.Dummy1*0.Dummy2

Can I simply subtract the coefficients (because these are dummy variables) if the coefficients are significant?

[Clyde Schechter]

regress y i.dummy1##i.dummy2
margins dummy1#dummy2, post
lincom 1.dummy1#1.dummy2 - 1.dummy1#0.dummy2 - (0.dummy#1.dummy2 - 0.dummy1#0.dummy2)

The significance of the coefficients is completely irrelevant to what you want to do here.

[Aneesh Banerjee]

Thanks.