st: logit average "marginal" effect of dummy variable with predict

[Chris <chris.stata@gmail.com>]

Dear statalist,

I want to compute the average marginal effect of an interaction
effect, so I have to simultaneously "switch on and off" two treatment
dummies (one treatment dummy, and one subgroup dummy interacted with
the treatment dummy). Margins can't do that, as Richard Williams
recently pointed out here on statalist.
(http://www.stata.com/statalist/archive/2013-01/msg00263.html)

So I am trying to compute it manually. However, I don't even manage to
compute the average marginal effect with the predict command; somehow,
there is a discrepancy between margins and predict even for simple
cases. Does anybody know why? Example:

-------------------------------
webuse lowbirth, clear
logit low lwt ptd smoke age
margins, dydx(smoke) //AME of smoke

replace smoke=1 //set entire sample smoke=1
predict withsmoke //predict probability
replace smoke=0 //set entire sample smoke=0
predict withoutsmoke //predict probability
gen me=withsmoke-withoutsmoke //compute discrete "marginal" effect
egen ame=mean(me) //AME of smoke
-------------------------------

The margins command gives an AME of .2198375, while the predict
version gives .2297. Which is right and why do they differ?

Thanks!
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