st: Marginal effects in probit regressions with inteff, testing significance using lincom

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

Good day,

I am currently running a probit model with categorical variables representing treatments in an experiment. For simplicity, the variables x1, x2 and x3 represent treatments 1, 2 and 3 respectively. In our experiment, we made use of 6 treatment combinations:

(a) None of x1, x2 and x3
(b) x1 only
(c) x1 and x2
(d) x1, x2 and x3
(e) x1 and x3
(f) x3 only

The dependent variable y is the probability an individual participates in the project.

(A side note: Because there are no combinations where treatment 2 only is employed, x2 is the variable which takes the value of 1 if treatment 2 is used in addition to treatment 1.)

We ran the probit regression of y on x1, x2, x3, and x1*x3 and x2*x3, and calculated marginal effects using -margins- and -inteff- (Ai and Norton, 2003; Norton et al, 2004) separately. The nature of -inteff- implies that we have to run the code twice to separately work out the marginal effects of x1*x3 and x2*x3.

Here's my question: If we want to test the effectiveness of a particular combination of treatment (say treatments 1 & 3 together), technically it means that we want to compare combination (e) against combination (a). This means that we need to test the null hypothesis that x1 + x3 + x1*x3 = 0.

Given, however, that the marginal effects of the interaction effects (x1*x2 and x2*x3) are calculated using -inteff- separately, how can we use Stata to test the null hypothesis that a linear combination of coefficients (plus interaction terms) = 0? Is it appropriate to save the output of inteff and then use -lincom- on the saved output? However, the marginal effects of the individual explanatory variables under -inteff- are different from that calculated using -margins-

Thanks and appreciate anyone's help on this. If you require me to explain further I will be happy to do so.

Regards,
Boon Han

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