st: propensity score and mills ratio

["francesca.modena" <francesca.modena@email.unitn.it>]

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