cmp marginal effects of censored multinomial probit model

[Naveen Abedin VT]

Dear All,

I am currently working on a paper examining online grocery shopping behavior and am using cmp to estimate a two-stage model.

In the first stage, I estimate a probit model for whether an individual shops for groceries online (onlshop=1). In the second stage, I estimate a multinomial probit model (with three levels) representing the main reason for shopping online. The second-stage outcome is only observed for those who shop online (i.e., the data are censored in the second equation).

The model runs successfully and converges. My question pertains to marginal effects: In a standard multinomial probit model, the marginal effects across categories typically sum to zero. However, in my censored multinomial probit model, this does not seem to be the case. Even when I condition the margins command on onlshop = 1, the average marginal effects still do not sum to zero. I understand from Greene (1996, 1998) that sample selection and correlated errors between the first and second stages can affect marginal effects, but I have struggled to find resources that specifically address why the sum-to-zero property fails in my case, even after conditioning on selection.

Any guidance or references would be greatly appreciated.

[George Ford]

what margins command are you running? If atmeans, for instance, then you won't get a sum to 1.

Or, that's true for ologit.

[Naveen Abedin VT]

Thanks for your response George Ford. This is a shortened version of my cmp command:

cmp (onlshop = i.sex i.age i.educ i.race i.marital i.employed childnum hhsize i.faminc access i.month i.year i.region) ///
(onatt = i.sex i.age i.educ i.race i.marital i.employed childnum hhsize i.faminc i.month i.year i.region) [pweight=wgt], ///
indicators($cmp_probit "cond(onlshop==1, $cmp_mprobit, $cmp_out)") nolrtest nonrtol difficult tech(nr 3 bhhh 20) vce(robust)

My second stage multinomial probit model has 3 categories. To obtain the Average Marginal Effects for each category, I am running:

margins, dydx(sex) predict(pr eq(#2)) //AME of first category of multinomial probit dependent variable
margins, dydx(sex) predict(pr eq(#3)) //AME of second category of multinomial probit dependent variable
margins, dydx(sex) predict(pr eq(#4)) //AME of third category of multinomial probit dependent variable