Thanks Shehzad.
I am confident that the first one is the right approach. I am just
curious what the second approach buy us.
Gordon
On Wed, May 28, 2008 at 7:07 AM, Shehzad Ali <[email protected]> wrote:
> 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: [email protected]
> [mailto:[email protected]] On Behalf Of Gordon
> Sent: 27 May 2008 16:30
> To: [email protected]
> 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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