Marginal effect of interaction variable in probit regression using Stata

Question

I am running a probit regression with an interaction between one continuous and one dummy variable. The coefficient is displayed in the regression output but when I look at the marginal effects the interaction is missing.

How can I get the marginal effect of the interaction variable?

probit move_right c.real_income_change_percent##i.gender

Iteration 0:   log likelihood = -345.57292  
Iteration 1:   log likelihood = -339.10962  
Iteration 2:   log likelihood = -339.10565  
Iteration 3:   log likelihood = -339.10565  

Probit regression                                 Number of obs   =        958
                                                  LR chi2(3)      =      12.93
                                                  Prob > chi2     =     0.0048
Log likelihood = -339.10565                       Pseudo R2       =     0.0187

-----------------------------------------------------------------------------------------------------
                         move_right |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------------+----------------------------------------------------------------
         real_income_change_percent |   .0034604   .0010125     3.42   0.001      .001476    .0054448
                                    |
                             gender |
                            Female  |   .0695646   .1139538     0.61   0.542    -.1537807    .2929099
                                    |
gender#c.real_income_change_percent |
                            Female  |  -.0039908   .0015254    -2.62   0.009    -.0069805   -.0010011
                                    |
                              _cons |  -1.263463   .0798439   -15.82   0.000    -1.419954   -1.106972
-----------------------------------------------------------------------------------------------------


margins, dydx(*) post

Average marginal effects                          Number of obs   =        958
Model VCE    : OIM

Expression   : Pr(move_right), predict()
dy/dx w.r.t. : real_income_change_percent 1.gender

--------------------------------------------------------------------------------------------
                           |            Delta-method
                           |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
real_income_change_percent |   .0002846   .0001454     1.96   0.050    -4.15e-07    .0005697
                           |
                    gender |
                   Female  |  -.0102626   .0207666    -0.49   0.621    -.0509643    .0304392
--------------------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

Answer 1

Your question seems strange to me. You asked about a dummy-dummy interaction, but your example involves continuous-dummy interaction.

Here's how to do either one:

webuse union, clear

/* dummy-dummy iteraction */
probit union i.south##i.black grade, nolog
margins r.south#r.black

/* continuous-dummy iteraction */
probit union i.south##c.grade
margins r.south, dydx(grade)

You should try to reproduce these by "hand" (using differences of predicts) to understand what the margins command is doing behind the scenes.

Answer 2

This sounds like a question specific to a piece of software (Stata), hence the close votes, but there is a statistical question lurking here: What would a marginal effect of an interaction effect look like?

Such marginal effects are not trivial, and tend to depend strongly on the values of the other covariates, see this article. Often this marginal effect is so variable that it makes no sense to try to summarize it with one number. In my opinion, this is a major weakness. To the extend that in general I tend to prefer using logistic regression and interpret the interaction term as a ratio of odds ratios, see this article.