Ceteris paribus when interpreting marginal effects in probit model?

[Li Zhou]

Hello, I hope you are having a good day

I have some doubts about how to interpret maginal effects in a probit model.

I'm working with these dummy variables (among others):
savings = 1 if the individual has savings (dependent variable)
calculated = 1 if the individual has calculated the amount of money he needs for retirement (explanatory variable)
plan = 1 if the individual has made a savings plan (explanatory variable)

In the survey, when calculated == 0, they don't ask the plan question, so my data is like this:

 developed |   Has calculated or
a plan for |   thought amount of
saving for |     money needed
retirement |         0          1 |     Total
-----------+----------------------+----------
         0 |     7,897        726 |     8,623 
         1 |         0        202 |       202 
-----------+----------------------+----------
     Total |     7,897        928 |     8,825

The marginal effects are:
calculated = 0.032
plan = 0.063

So the probability of having savings is 6.3 percentage points higher if the individual has made a savings plan, ceteris paribus, right?
My doubt is that it can't be ceteris paribus knowing that if plan==1, necessarily calculated==1, so actually having a plan should increase 8.5 percentage points the probability of having savings. Is this correct?

I tried adding interaction between those two variables but Stata says it's not estimable.

Thanks!

Li.

[Clyde Schechter]

My doubt is that it can't be ceteris paribus knowing that if plan==1, necessarily calculated==1

You are right. BUT, by using a non-interaction model, you have stipulated that the marginal effect of plan is the same regardless of the value of calculated, and vice versa. That is the meaning of a non-interaction model.

So your instinct to try estimating an interaction model was correct. BUT, you don't have the right data for that. Precisely because the combination of calculated = 0 and plan = 1 is never observed in your data, the interaction cannot be estimated. There is simply no information in the data about what happens in that situation.

So, either you have to have the courage of your convictions in using a non-interaction model and assert that the marginal effect of plan is the same regardless of the value of calculated and use the result you have gotten, or, you have to acknowledge that the data set you have is inherently incapable of answering the question you are asking it.

[Li Zhou]

Thank you very much, Clyde. Your explanation is very clear.
Probably I'll have the courage of my convictions with a caveat.

Have a good day!

Edited: I changed my mind. I better go for the second option.