st: Testing the difference between coefficients with interaction variables

[Michael Crain <michaelcrain@ymail.com>]

I know testing the difference between coefficients of variables is
straightforward:

reg y x1 x2 x3
test x1 = x2 = x3

Is the test as straightforward for examining coefficients in models
with interactions variables?

reg y x1 x2 x3 x1*x2 x1*x3

   where: 

     x2 and x3 are dummy variables that identify groups

     the base group is when x2=0 and x3=0, group 2
     is when x2=1 and x3=0, group 3 is when x2=0 and x3=1

I am interpreting the effect of the base group as x1's coefficient. The
effect of group 2 is the sum of coefficients of the x1 and x1*x2
variables. Lastly, the effect of group 3 is the sum of coefficients of
the x1 and x1*x3 variables.

Now, I want to examine whether the effects of the three groups are
different.

Is the test:

test x1 = x1*x2 = x1*x3

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