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# Re: st: pweights, propensity scores

 From Paul To statalist@hsphsun2.harvard.edu Subject Re: st: pweights, propensity scores Date Fri, 18 Jan 2013 09:17:47 -0500

```Thank you very much for your reply.

There seem to be a few problems with that solution though: I don't wan
aweights, which stata is assuming with the [w=w].  This shouldn't
matter for the point estimates though, so it's still a useful
exercise.  Also, using sum over treated and untreated seperately can't
give me the formula I want, since I need N^-1 in front of the summand.
Your solution does at least give me insight into what pweight is
doing in the reg command, which, contrary to the stata journal article
I cite below, seems incorrect.

Thanks.

On Fri, Jan 18, 2013 at 3:59 AM, Christophe Kolodziejczyk
<ck.statalist@gmail.com> wrote:
> Hi Paul
> I think you have to compute the weighted mean separately for the
> different samples, i.e the first weighted sum should be divided by the
> number of treated and the second sum should be divided by the number
> of controls.
>
>
> logit treatment X
> predict p
>
> gen w = cond(treatment,1/p,1/(1-p))
>
> reg y treatment [w=w]
>
> sum y if treatment [w=w]
> local m1 = `r(mean)'
> sum y if !treatment [w=w]
> local m0 = `r(mean)'
>
> di "ATE = " `=`m1'-`m0''
>
>
>
> Best
> Christophe
>
>
> 2013/1/17 Paul <paulburk314@gmail.com>:
>> Hi all,
>>
>> I'm using propensity scores to estimate treatment effects, where
>> treatment is exogenous conditional on the propensity score. I'm using
>> an estimator from Wooldridge's 2010 text book, which is also discussed
>> in The Stata Journal (2008) 8, Number 3, pp. 334–353.
>>
>> Specifically, the treatment effect is estimated using (1/N) sum
>> (T*Y/p) - (1/N) sum ((1-T)*Y/(1-p).
>>
>> According to the Stata Journal article, this can be estimated using a
>> regression with pweights equal to the "inverse of the treatment
>> probability deﬁned using the
>> propensity score." However, when I use just the sum of the weighted
>> variables, I get a different answer from the regression result.  I'm
>> not terribly familiar with pweights, so I could be making some dumb
>> mistake.
>>
>> Below is my code.  Does anyone know what I'm doing wrong, or what the
>> correct way to implement this method is?
>>
>> Thanks,
>> Paul
>>
>> /* Regression using pweights */
>> gen ipw=1/p_x if treated==1
>> replace ipw=1/(1-p_x) if treated==0
>>
>> reg y treated [pweight=ipw]
>>
>> /* IPTW one variable */
>> gen w1=((treated-p_x)/(p_x*(1-p_x)))
>> gen w1_y=w1 *y
>>
>> sum w1_y
>>
>> /* IPTW two variables */
>> gen w2a_y=y*treated/p_x
>> gen w2b_y=y*(1-treated)/(1-p_x)
>>
>> foreach type in a b{
>>   sum w2`type'_y
>>   local mean_w2`type' =r(mean)
>> }
>>
>> di `mean_w2a'-`mean_w2b'
>>
>> /* IPTW two variables weights sum to one */
>> bysort treated: egen w_ipw=total(ipw)
>> gen w3a_y=(1/w_ipw)*y*treated/p_x
>> gen w3b_y=(1/w_ipw)*y*(1-treated)/(1-p_x)
>>
>> foreach type in a b{
>>   sum w3`type'_y
>>   local mean_w3`type' =r(mean)
>> }
>>
>> di `mean_w3a'-`mean_w3b'
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
>
> --
> Christophe Kolodziejczyk
> Research Fellow
>
> AKF, Anvendt KommunalForskning
> Danish Institute of Governmental Research
> DK-1150 København K
>
> *
> *   For searches and help try:
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> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/

*
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```