Margins Interpretation

[Carl Baier]

Hey guys I have the following question. I am currently trying to interpret the marginal effects for an average individual of my probit estimation. Since I have the dummy variable 'male' in the model, the reference individual is a female.

I used the following code:

quietly probit healthy i.insured i.anylim i.degree i.race i.region i.male i.married c.age_adj, r
margins, dydx(*) atmeans

Now for the interpretation. For example, if I have the following coefficient for the variable 'insured': 0.013
Which of the two interpretations is then correct?
1) For an average individual, the probability of being healthy increases by 1.30\% if she is additionally insured, ceteris paribus.
2) For an average woman, the probability of being healthy increases by 1.30\% if she has additional health insurance, ceteris paribus.

[Clyde Schechter]

I assume that when you say "coefficient" you mean marginal effect in the -margins- output, not the coefficient in the -probit- itself.

I'm not sure what the notation \% means. In any case, the correct unit is percentage point, not percent. Also you should not use the word "increases" because that term implies causality and nothing you have shown suggests you are looking at experimental data. Causality cannot be inferred from observational data without additional stringent (and usually false or unverifiable) assumptions. You should say "ceteris paribus, the probability of an insured woman being healthy is 1.3 percentage points greater than that of an uninsured woman."

As for the two interpretations, 1) incorporates the correct logic. There are no interaction terms in your model, so you have constrained the model to impl that the marginal effect of being insured is the same in both sexes, in all races, in all marital statuses, etc. If you wish to have separate marginal effects in subgroups, the model needs interaction terms.