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st: Different approcah to estimate treatment effect


From   Gordon <[email protected]>
To   [email protected]
Subject   st: Different approcah to estimate treatment effect
Date   Tue, 27 May 2008 11:29:37 -0400

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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