T-test for coefficients in one regression

[Biny Hao]

Hello everyone,
I would like to test if two coefficients in the same regression are significantly different from each other. I have seen someone use t-test for this, but don't know how they do it . Could anyone here pls tell me how exactly I could conduct the t-test for this? I know the wald test. I just want to learn different techniques.
Thanks a lot for your help,
Biny

[Carlo Lazzaro]

Biny:
are you looking for something like this?:

use auto.dta, clear
reg price mpg weight
test weight=mpg

[Biny Hao]

Thanks Carlo,
It looks like the Wald test. I have seen someone using it. But some others used the T-test. I guess there should be some differences. I just don't know how the T-test can be used for comparing coefficients in the same regression.
Thanks for your kind help,
Best,
Biny

[Maarten Buis]

For a linear regression the Wald test of one constraint, in your case two coefficients are equal, is a t-test. So in this special case Carlo is right.

The Wald test can also be applied to other situation: If you test multiple constraints (e.g. three coefficients are all equal) it becomes an F-test. A Wald test after a model estimated with maximum likelihood becomes a Chi-square test.

[Biny Hao]

Thanks Maarten, that really helps.