st: Calculating marginal effects of interactions in nonlinear models

[Boon Han Koh <bhkoh@unimelb.edu.au>]

Hi Stata users,

I have a question regarding marginal effects of interactions in nonlinear models.

I am running a probit model with y on x1, x2, x3, x1*x3 and x2*x3, where x1, x2 and x3 are binary variables.

The code I am using is:
. probit y i.x1 i.x2 i.x3 x1#x3 x2#x3
. margins, dydx(*)

The -margins- command return the marginal effects of x1, x2 and x3, while acknowledging that there are interaction terms in the model.

I also understand the use of -inteff- to correctly evaluate the marginal effects of the interaction terms (Ai and Norton 2003; Norton et al. 2004).

However the issue here is that I have two interaction terms in the model. So my questions are:

1) Should I use the command -inteff- twice to evaluate the interaction terms?
i.e.
. probit y i.x1 i.x3 i.x1x3 i.x2 i.x2x3
. inteff y i.x1 i.x3 i.x1x3 i.x2 i.x2x3 (which gives marginal effect of x1x3)
and
. probit y i.x2 i.x3 i.x2x3 i.x1 i.x1x3
. inteff y i.x2 i.x3 i.x2x3 i.x1 i.x1x3 (which gives marginal effect of x2x3)

Does this method give the correct marginal effect of interaction terms, or should I use another method altogether?

2) How do I go about testing the null hypothesis that the marginal effect of x1 + x3 + x1*x3 = 0?

Thank you all for your help in this!




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