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st: Why estimation in first step of two-step Heckman model is different from Probit model for selection


From   ZYD <yiduozh@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Why estimation in first step of two-step Heckman model is different from Probit model for selection
Date   Sat, 12 Mar 2005 23:51:15 -0500

I estimated two-step Heckman model using 
heckman y x1 x2, select(z1 z2) two
predict mill1, mill
I also estimated Probit model using
probit y z1 z2
predict phat, xb
gen mill2=exp(-.5*phat^2)/(sqrt(2*_pi)*normprob(phat))

why the coefficients for z1 z2 in two estimation are different in the
estimating procedure? I also calculate the inverse mill's ratio (IMR)
for the probit model, and not surpriingly, the two IMRs are different?
Which one is more reliable when y is a binary variable? Thanks!

sincerely
yiduo
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