Interaction dummy-continuous variable: Preventing the automatic inclusion of the continuous variable

[Simon Loewe]

The specification I would like is the following:

y = a + b x + c d*z

where x and z are continuous variable and d a dummy. Now I know that there are arguments against having the interaction without the interacted terms on their own (i.e. not including z as such in this case) but I believe that in my case this is appropriate.
The problem is that the command

reg y x i.d#c.z

automatically includes z as a variable, meaning it is equivalent to the command

reg y x z i.d#c.z

I have not been able to find any way around this. I should also mention that the "naive" way of solving this by creating the interaction by hand is very problematic in my case because I very much need to use margins after the estimation, which is made impossible by that solution.

Thank you for your help!

[William Lisowski]

The example below attempts to reproduce the problem, but regress dose not include the continuous variable separately, so I'm not sure I understand the statement of your problem.

. sysuse auto, clear
(1978 Automobile Data)

. regress price weight i.foreign#c.mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     18.57
       Model |   281459158         3  93819719.5   Prob > F        =    0.0000
    Residual |   353606238        70  5051517.68   R-squared       =    0.4432
-------------+----------------------------------   Adj R-squared   =    0.4193
       Total |   635065396        73  8699525.97   Root MSE        =    2247.6

-------------------------------------------------------------------------------
        price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
       weight |    2.70761    .614654     4.41   0.000     1.481721    3.933499
              |
foreign#c.mpg |
    Domestic  |  -87.42007   77.51779    -1.13   0.263    -242.0244    67.18428
     Foreign  |   36.07147    79.5086     0.45   0.651    -122.5034    194.6464
              |
        _cons |  -1057.949   3289.443    -0.32   0.749    -7618.535    5502.637
-------------------------------------------------------------------------------

[Richard Williams]

Does this do what you want?

webuse nhanes2f, clear
constraint 1 tibc = 0
cnsreg weight height tibc i.female#c.tibc, constraint(1)

[Richard Williams]

Or else maybe

webuse nhanes2f, clear
reg weight height 1.female#c.tibc

[Richard Williams]

Note that both of the above produce the same results as

webuse nhanes2f, clear
gen femtibc = fem *tibc
reg weight height femtibc

Factor variable notation can be tricky and confusing, especially if you are trying to do something a little unconventional. Constraints are one way of forcing unwanted coefficients to be 0, but I suspect there are usually other ways using only factor variable notation.

[Simon Loewe]

The example below attempts to reproduce the problem, but regress dose not include the continuous variable separately, so I'm not sure I understand the statement of your problem.

So it actually doesn't, and I think that Statas somewhat confusing notation can be blamed here. Indeed if you run

regress price weight mpg i.foreign#c.mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     18.57
       Model |   281459158         3  93819719.5   Prob > F        =    0.0000
    Residual |   353606238        70  5051517.68   R-squared       =    0.4432
-------------+----------------------------------   Adj R-squared   =    0.4193
       Total |   635065396        73  8699525.97   Root MSE        =    2247.6

-------------------------------------------------------------------------------
        price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
       weight |    2.70761    .614654     4.41   0.000     1.481721    3.933499
          mpg |  -87.42007   77.51779    -1.13   0.263    -242.0244    67.18428
              |
foreign#c.mpg |
     Foreign  |   123.4915   28.45584     4.34   0.000     66.73816    180.2449
              |
        _cons |  -1057.949   3289.443    -0.32   0.749    -7618.535    5502.637
-------------------------------------------------------------------------------

you see that the "Domestic" coefficient on your specification is the one of the continuous variable.

[Simon Loewe]

Or else maybe

webuse nhanes2f, clear
reg weight height 1.female#c.tibc

Thank you for your quick answer. This option does seem to work. I didn't think of doing it in that way at all, but I tried using the omitted notation of factor variables, which didn't work.

Anyway thank you very much for your help.