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st: RE: Different approcah to estimate treatment effect


From   "Shehzad Ali" <sia500@york.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Different approcah to estimate treatment effect
Date   Wed, 28 May 2008 12:07:57 +0100

In the past I have used the first approach, i.e. using both imr as well as
the endogenous variable in the final OLS. IMR corrects for the unobserved
heterogeneity.

HTH,

Shehzad


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Gordon
Sent: 27 May 2008 16:30
To: statalist@hsphsun2.harvard.edu
Subject: st: Different approcah to estimate treatment effect

Greetings!

Suppose I want to estimate a treatment effect model,

Y = b*X+a*D + e

D is the treatment and endogenous, where D = 1 if g*Z>0, and 0 otherwise.

If I understand correctly, treatreg in Stata does the following:

1. in the first stage  using a probit model (regress D on probit(g*Z))
to estimate g.

2. In the second stage, add the inverse mills ratio to the equation Y
= Xb+a*D + e and estimate using OLS.

However, I have seen another approach to estimate the treatment effect:

1.  in the first stage  using a probit model (regress D on
probit(g*Z)) to estimate g.

2. replacing D with the estimated probabilities from the first stage
and then run the OLS.

I am not clear how this second approach is derived. I read through Lee
and Trost (1978 journal of econometrics) but there is not much
details.

Most important, which approach is the preferred one?

Thanks for your attention.

Gordon
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