st: More on margins after multinomial probit using cmp

[Alfonso Sánchez-Peñalver <alfonso.statalist@gmail.com>]

Hi everyone,

yesterday I posted an inquiry about how to be able to get the marginal effects on the probability of the base outcome after a multinomial probit estimation using -cmp- (SJ, SSC). No-one has thrown some light yet (though I’m still hopeful someone might) so I played a little bit with it to see if I could figure it out. I am a bit more concerned now that I was yesterday. I’m now comparing the marginal effects obtained after the estimation using both -mprobit- and -cmp-. To illustrate, consider the following code to compare the two estimations posed in the example in -help cmp-:

set more off
webuse sysdsn3, clear
mprobit insure age male nonwhite site2 site3
est store mp
cmp (insure = age male nonwhite site2 site3, iia), nolr ind($cmp_mprobit) qui
est store cm

foreach v in mp cm {
	est restore `v'
	forvalues i = 1(1)3 {
		margins, dydx(*) predict(pr eq(#`i'))
	}
}

* Alternative way of imputing margina effects for the first outcome
est restore cm
margins, dydx(*) expression(1 - predict(pr eq(#2)) - predict(pr eq(#3)))

If you run that code you will see that there is virtually no difference in the estimates produced by -mprobit- and by -cmp-.

However, when you compare the marginal effects, the story is very different! First, as I noted in my previous post, margins is unable to calculate the marginal effects for equation 1 from -cmp- estimates, which is the base case assumed by -cmp-. This I was able to work around it using the -expression- option of margins, and remembering that the probability of the base outcome must be equal to 1 minus the sum of the other probabilities, which is the “alternative” call at the end of the code. Second, for the other two “equations” (outcomes) the marginal effects differ substantially, which is surprising since the estimates do not!

My question then is, am I calling the margins command wrong after -cmp-, and if so why should I be calling it in any different way than after -mprobit-? If this is not the case, why do we get such different marginal effects with such identical estimates?

Thanks for any thoughts,

Alfonso Sánchez-Peñalver, PhD

Visiting Assistant Professor
Suffolk University
Senior Instructor
UMass Boston




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