st: Heckman with variables that perfectly predict selection

[Maria Alva <marialiliana.alva@gmail.com>]

Dear Statalist,

I recently came across  the following statement in
http://www.stata.com/support/updates/ado/whatsnew.html

"(STB-43) heckman heckman now has the capability to estimate models
with variables that perfectly predict selection. Previously heckman
would simply drop such variables from the selection equation, which is
inappropriate in most cases."

Puzzled, I tried estimating a heckman selection correction model in a
data set where death is observed, and where deaths perfectly predict
non-responses to questionnaires.

heckman y $x, select(selected= death $x) // selected=1 if a person
completes a questionnaire

this gives me a negative single digit and statistically significant
coefficient. If instead I use

probit selected death $x

as expected, death drops out

My question is twofold: what is the innovation in the Stata command
that causes death not to be dropped out of the selection equation as
it perfectly predicts the selection indicator? and most importantly,
what would be a valid instance for which it would be appropriate to
include a variable in the selection equation when this variable
perfectly predicts selection?

Many thanks for your help.

Maria
-- 
Maria Alva
PhD Candidate in Public Health
Health Economics Research Centre
University of Oxford
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