st: cmp with censored observations set to missing

[Will Cooper <twcmisc@gmail.com>]

Dear Statalist members,

I am trying to understand a regression that used David Roodman's -cmp-
module (http://ideas.repec.org/c/boc/bocode/s456882.html). It looks like an
ivtobit regression except the right-censored observations have 'missing' as
the dependent value. How would the interpretation of the endogenous
regressor's coefficient differ from a regression where the right-censored
are at some non-missing value?

Also, the ivtobit documentation states that it is not appropriate for use
with discrete endogenous regressors, but I am not clear as to why.

Below is a hypothetical example using the laborsup dataset (assuming there
is no issue with left-censoring for income variables). Much thanks in
advance!

cmp setup
webuse laborsup, clear

* simulate right censoring (at a finite value) replace fem_inc = 50 if
fem_inc >= 50

* simulate a discrete regressor
gen have_other_inc = other_inc > 50

* results using ivtobit, coefficient of have_other_inc in 2nd stage is
-16.25926 ivtobit fem_inc kids (have_other_inc = male_educ), ul(50) first

* results using cmp, coefficient is -16.25942 cmp (have_other_inc = kids
male_educ) (fem_inc = have_other_inc kids), ind($cmp_cont "cond(fem_inc >=
50, $cmp_right, $cmp_cont)")

 * set right-censored value to missing, coefficient is -11.11619 replace
fem_inc = . if fem_inc == 50 cmp (have_other_inc = kids male_educ) (fem_inc
= have_other_inc kids), ind($cmp_cont "cond(missing(fem_inc), $cmp_right,
$cmp_cont)")

I noticed while the 1st stage estimates are the same in all 3 regressions,
the "starting point" fit for the 2nd stage differs in the number of
observations used (the 17 censored obs were dropped in the 2nd cmp).
However, the mixed-process regression still states 500 observations.

Regards,
Will
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