# Re: st: RE: propensity score and mills ratio

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: propensity score and mills ratio Date Tue, 28 Oct 2008 11:47:20 -0400

```francesca.modena--

Note it is not really a "sample selection problem" so much as a
treatment (T=1) selection problem. Matching or an IV approach (like
the -treatreg- model proposed in the original post) each requires
different assumptions. Propensity score matching requires that T is
essentially random conditional on X or the propensity score, and that
0<p(T|X)<1 where we need to emphasize (very) strict inequality; of
course estimated p is never 0 or 1 but if the density is positive or
even if the slope of the density is positive at 0 or 1 you may have
problems.  IV (or treatreg) requires that components of X not also in
Z (Z is what you called your included instruments, usually called X)
do not have a direct impact on outcomes (your X can affect outcomes in
a matching model), but strongly predict T (note that if your X too
strongly predicts T you will fail the 0<p<1 test in propensity score
http://pped.org/stata/erratum.pdf and references therein.

ps. Thanks for the plug, Martin.

pps. to see what I mean about the density of estimated p being
positive at the boundaries try

use http://pped.org/stata/card
g c=educ>=16
probit c fath moth nearc2 nearc4 south66 smsa66 black
kdens p if c==1, ll(0) ul(1) bw(.1)
kdens p if c==0, ll(0) ul(1) bw(.1)
psmatch2 c fath moth nearc2 nearc4 south66 smsa66 black, out(lwage)
psgraph, bin(50)
treatreg lwage south66 smsa66 black, treat(c=fath moth nearc2 nearc4
south66 smsa66 black)

(note kdens and psmatch2 are on SSC).

On Tue, Oct 28, 2008 at 8:23 AM, Martin Weiss <martin.weiss1@gmx.de> wrote:
> http://www.stata-journal.com/article.html?article=st0136

> -----Original Message-----
> From: francesca.modena
> 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
Pr(T)=f(X)

--> help treatreg

> Another procedure to deal with selection bias is the propensity score
> matching.

--> findit nnmatch and findit psmatch2

> 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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