st: two-stage model (probit --> mlogit)

[Ho Youn Koh <hykoh@umd.edu>]

Dear experts and statalists,
I am trying to use a two-stage model to estimate the direct/indirect effect=
 of new voting technology on turnout.
I think there are some selection process in this new technology because vot=
ers have to apply for it before the election day and they actually vote wit=
h that new method (like an absentee ballot). So, in the first stage I want =
to run a probit model to estimate whether or not the voter apply for the ne=
w voting method. For the second stage I have a categorical dependent variab=
le (actual voting method: new method, all other old methods, and didn't vot=
e). So, I want to run a multinomial logit to see the independent effects of=
 my independent vars on each outcome. Not knowing how to run two-stage mult=
inomial logit (TMLM), I ran the first model (probit), then plugged the esti=
mator into the second model(mlogit).

// stage 1
probit z x1 x2 x3 x4 x5
predict double zhat  if e(sample), xb
// stage 2
mlogit y x4 x5 x6 x7 x8 zhat

Note that x1 - x3 are only predicting z; but x4 - x5 are predicting both z =
and y. Also x6 - x8 are predicting y only. Although the result looks making=
 sense to me, I am left with following questions:

1) Is that statistically okay? How can I test iid of errors from stage 1 an=
d 2?
2) What would be the acceptable test for the model?
3) Is there an alternative way to run TMLM in stata?
4) If the above way is acceptable, is it also okay to calculate predicted p=
robabilities from the mlogit model? Or any other issues I should deal with =
before getting predicted probabilities?

Thank you.

Hoyoun Koh
phD Candidate
Government & Politics
University of Maryland, College Park
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