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st: RE: propensity score and mills ratio

From   "Martin Weiss" <[email protected]>
To   <[email protected]>
Subject   st: RE: propensity score and mills ratio
Date   Tue, 28 Oct 2008 13:01:03 +0100


-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of francesca.modena
Sent: Tuesday, October 28, 2008 12:40 PM
To: [email protected]
Subject: st: propensity score and mills ratio

Dear all,
This is a classical problem of treatment effect.

I have two outcomes: 
Y1i: the outcome of unit i if i were exposed to the treatment (T=1)
Y0i: the outcome of unit i if i were not exposed to the treatment (T=0)

I want to regress Y1i on a set of characteristics Z. OLS regression of Y1i
on Z can be biased because of sample selection problem. 

Let us assume that the probability of being exposed to the treatment can be
described by a probit equation 

Ti = alpha*X + error

>From the probit equation I can derive the selection terms for the two
T=0 and T=1 (i.e. inverse mills ratio)
Now I can consistently regress Y1i on Z for the sample with T=1, augmenting
the regression with the corresponding selection term (i.e. I include the
mills ratio for those with T=1 in the regression).

Another procedure to deal with selection bias is the propensity score
matching. If I am right the Stata commands are:

pscore treat X, pscore(scorename)

attr Y1i treat, pscore(scorename) (Is this equation estimated on all the
sample or only for those with T=1 or T=0?)

What is the difference between the two procedures? Can I use both mills
ratio and propensity score to deal with selection problems? 


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