marginal effects after three way interaction term

[Nikos Korompos]

Hi,

I am trying to estimate some income elasticities, before and after a time event, and for different population groups (again, before and after a time period) (i.e. low- and high-educated). I suspect I should use a three way interaction, Could you please tell me your opinion about the stata code? Is this okay, or should I use separate regression models for each population group?

glm exp time_dummy#education#c.income gender c.age##c.age i.region c.hhsize##c.hhsize i.marital [pweight = weight], family(gamma) link(log) vce(robust)
margins time_dummy##education, eyex(income) atmeans

Many thanks in advace.

Best regards,

Nikos

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using user-written dataex.

While three way interactions are often hard to interpret, they're easier if two of the interactions are dummies - you're essentially estimating the influence of income for the different subpopulations defined by the interaction of time and education.

Without more on what you're trying to learn, it is hard to think about your margins statement. It looks OK, but that is based on my guess about what you're trying to do.

You certainly can run the model on each of the subpopulations separately. However, you're giving up some efficiency and running a different model (since you're then allowing all the parameters to vary by subpopulation and not just those on income). This is something of a substantive question - do you want to let those parameters vary by sub-population or not?

[Nikos Korompos]

Thank you Phil for your thorough answer. The other two terms are indeed dummies.

In fact, I want to examine whether the elasticity changes between the two periods, but I want to check it for both high- and low-educated. So, that's the reason I thought that three-way interaction could be useful.

Regarding the parameters, I don't really expect the other parameters to vary by subpopulations.