I think you have forgotten to account for the correlation of
the two independent variables. There are many algebraically
equivalent formulae for the SE of a given coefficient. but
all of them account for, in one way or another, the correlation
structure of the X's. In the two independent variable case,
this amounts to including the term 1-R-square for the regression
of X1 on X2 in the denominator. The formula you show below does not do this.
When I apply the correct formula I get the same result
as Stata.
I agree with Dick. I think the formula Maarten gave is the formula
for the standard error in a bivariate regression, which is why he may
have seen it in various texts (except I think it should be N-1, not
N). I give a couple of different formulas on p. 1 of the following: