Semi-elasticities from margins command after multinomial logit

[Jill Adona]

Dear all,

I'm looking into expressing the estimation results of my mlogit model of school choice in terms of semi-elasticities. I understand that the interpretation for eydx is: "a % change in the probability of choosing y1 given a unit/discrete change in x."

But I know that multinomial logit estimates are always relative to the base outcome, say y0. Marginal effects, however, stay the same when you change bases. I've found studies that report semi-elasticities "relative to alternative y0." So I tried switching the base outcomes in mlogit, then running the margins, eydx command. But I get the same semi-elasticities!

If the margins/semi-elasticities stay the same when changing the reference group, how can we interpret these?

[John Mullahy]

Jill: I think your initial intuition is correct and that papers that "report semi-elasticities 'relative to alternative y0'" might somehow be mis-stating what's being computed. Baseline choice shouldn't matter for partial effects, elasticities, etc., in a MNL model so long as the conditional probabilities are the objects of interest.