Yes, with an infinite number of draws, the point estimates would be the same
and the variances would be different. But why is it necessary to go with the
one with more variance? It isn't based on the PATE / SATE distinction
because that just has to do with whether the dependent variable is
conditioned on.
Ben
Ben Goodrich
Graduate Student at Harvard University
Ph.D. Program in Government and Social Policy
-----Original Message-----
From: gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:gov2001-l-
bounces(a)lists.fas.harvard.edu] On Behalf Of Olivia Lau
Sent: Thursday, December 09, 2004 12:37 PM
To: gov2001-l(a)lists.fas.harvard.edu
Subject: RE: [gov2001-l] setx question
The point of the E(Y(1) - Y(0)) is that the variance of this term differs
from E(Y(1)) - E(Y(0)). The point estimate should be the same.
Olivia.
On Thu, 9 Dec 2004, Ben Goodrich wrote:
But E "distributes" over addition and
subtraction. I remember this being
in
Rice, although I do not have my copy with me.
Irwin has a proof here on
the
It
is only multiplication where things are weird
(E[ab] != E[a]E[b]).
Either way, how do Gary's notes imply that we are supposed to take a
draw
from a distribution?
Ben
Ben Goodrich
Graduate Student at Harvard University
Ph.D. Program in Government and Social Policy
www.people.fas.harvard.edu/~goodrich/
goodrich(a)fas.harvard.edu
> -----Original Message-----
> From: gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:gov2001-l-
> bounces(a)lists.fas.harvard.edu] On Behalf Of Olivia Lau
> Sent: Thursday, December 09, 2004 11:51 AM
> To: gov2001-l(a)lists.fas.harvard.edu
> Subject: Re: [gov2001-l] setx question
>
> The expectation is outside Y(1) - Y(0). So you want the expected
value of
> the difference, not the difference of the
expectations.
>
> ----- Original Message -----
> From: "Ben Goodrich" <goodrich(a)fas.harvard.edu>
> To: <gov2001-l(a)lists.fas.harvard.edu>
> Sent: Thursday, December 09, 2004 11:48 AM
> Subject: RE: [gov2001-l] setx question
>
>
> >> And for either model, you should be using the predicted values to
> >> calculate the ATE's.
> >
> > How does this square with the formula for ATE in Gary's notes where
> >
> > ATE = (1/n)\Sigma E(Y(1) - Y(0))
> >
> > To me, that implies that we should be looking at the mean over the
> > difference in expected values rather than the mean over the
predicted
> > values?
> >
> > Ben
> >
> > Ben Goodrich
> > Graduate Student at Harvard University
> > Ph.D. Program in Government and Social Policy
> >
www.people.fas.harvard.edu/~goodrich/
> > goodrich(a)fas.harvard.edu
> >
> >
> >> -----Original Message-----
> >> From: gov2001-l-bounces(a)lists.fas.harvard.edu [mailto:gov2001-l-
> >> bounces(a)lists.fas.harvard.edu] On Behalf Of Olivia Lau
> >> Sent: Thursday, December 09, 2004 11:29 AM
> >> To: gov2001-l(a)lists.fas.harvard.edu
> >> Subject: Re: [gov2001-l] setx question
> >>
> >> And for either model, you should be using the predicted values to
> >> calculate
> >> the ATE's.
> >>
> >> ----- Original Message -----
> >> From: "Olivia Lau" <olau(a)fas.harvard.edu>
> >> To: <gov2001-l(a)lists.fas.harvard.edu>
> >> Sent: Thursday, December 09, 2004 11:17 AM
> >> Subject: Re: [gov2001-l] setx question
> >>
> >>
> >> > that's a great question, Mike.
> >> >
> >> > So here's the deal: Usually, the expected values will differ
across
> >> > columns only because the X
observations are different. In this
case,
> >> the
> >> > X observations are all the same (intercept = 1 and treat = 1, for
> >> > example), so each column looks the same. The ev differ across
rows
> >> > because of the differences in
the simulated betas.
> >> >
> >> > The predicted values are draws from the distribution defined by
the
> >> > corresponding value in the
expected value matrix (and so should
be
> >> > different across rows and
columns).
> >> >
> >> > ----- Original Message -----
> >> > From: "Michael Richard Kellermann"
<kellerm(a)fas.harvard.edu>
> >> > To: <gov2001-l(a)lists.fas.harvard.edu>
> >> > Sent: Thursday, December 09, 2004 11:05 AM
> >> > Subject: Re: [gov2001-l] setx question
> >> >
> >> >
> >> >>
> >> >> Here is the reason for my question: when I look at the expected
> >> >> values
> >> >> generated by the sim command, using a normal model, they are the
> same
> >> in
> >> >> the univariate case:
> >> >>
> >> >> s.out.0$qi$ev[1:8, 1:8]
> >> >>
> >> >> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
> >> >> [1,] 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486 0.4486
> >> >> [2,] 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424 0.4424
> >> >> [3,] 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392 0.4392
> >> >> [4,] 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425 0.4425
> >> >> [5,] 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411 0.4411
> >> >> [6,] 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485
> >> >> [7,] 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477 0.4477
> >> >> [8,] 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485 0.4485
> >> >>
> >> >> and then they are different for the predicted values:
> >> >>
> >> >> s.out.0$qi$pr[1:8, 1:8]
> >> >> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
> >> [,8]
> >> >> [1,] 0.26540 0.69574 -0.30079 0.7086 0.095671 0.56353
0.5045
> >> 0.7559
> >> >> [2,] -0.29949 0.79896 1.81914 -0.2224 0.149480 0.07857
0.9538 -
> >> 0.7112
> >> >> [3,] -0.24355 0.54188 0.47502 1.1169 0.675997 0.88817
0.1099 -
> >> 0.1553
> >> >> [4,] -0.02701 -0.28023 0.75768 -0.2701 0.296251 0.86762
0.3645
> >> 0.5838
> >> >> [5,] 0.27580 0.46741 0.36535 0.4150 1.234477 0.40665
0.5650
> >> 0.9518
> >> >> [6,] 0.33215 0.81140 0.39242 0.7009 0.282338 0.97523
0.7354
> >> 0.1146
> >> >> [7,] -0.29423 0.09349 0.01257 1.0007 0.721501 0.12567
0.3155
> >> 0.0861
> >> >> [8,] 0.24989 0.28098 1.38814 0.6617 -0.007151 -0.19204
0.6433
> >> 0.5431
> >> >>
> >> >> So I guess my question more precisely is, does sim take one set
of
> >> draws
> >> >> from the sampling distribution of the betas and reuse it for all
of
> >> >> the
> >> >> sets of starting values?
> >> >>
> >> >> Also, for the normal model, should we be using the predicted
values
> or
> >> >> the
> >> >> expected values to calculate the ATE and ATT?
> >> >>
> >> >> Cheers,
> >> >> Mike
> >> >>
> >> >> On Thu, 9 Dec 2004, Olivia Lau wrote:
> >> >>
> >> >>> There's nothing random about setx(). The randomness
comes in
> sim().
> >> >>> And my
> >> >>> understanding of how R handles seeds is that it picks up where
it
> >> >>> left
> >> >>> off.
> >> >>> Hence,
> >> >>>
> >> >>> a <- rnorm(10)
> >> >>> b <- rnorm(10)
> >> >>> identical(a, b)
> >> >>>
> >> >>> should be false...
> >> >>>
> >> >>> ----- Original Message -----
> >> >>> From: "Michael Richard Kellermann"
<kellerm(a)fas.harvard.edu>
> >> >>> To: <gov2001-l(a)lists.fas.harvard.edu>
> >> >>> Sent: Thursday, December 09, 2004 10:39 AM
> >> >>> Subject: Re: [gov2001-l] setx question
> >> >>>
> >> >>>
> >> >>> >
> >> >>> > Does Zelig start with the same random number seed for
each
vector
> >> >>> > of
> >> x
> >> >>> > values created by the setx command?
> >> >>> >
> >> >>> > Cheers,
> >> >>> > Mike
> >> >>> >
> >> >>> > On Thu, 9 Dec 2004, Olivia Lau wrote:
> >> >>> >
> >> >>> >> If you can't get Zelig to do what you want
(right now,
before
> >> section
> >> >>> >> this
> >> >>> >> evening), I suggest that you manhandle the output to
get it
to
> >> >>> >> produce
> >> >>> >> what
> >> >>> >> you want...just a thought.
> >> >>> >>
> >> >>> >> ----- Original Message -----
> >> >>> >> From: "Andrew Eggers"
<aeggers(a)gmail.com>
> >> >>> >> To: <gov2001-l(a)lists.fas.harvard.edu>
> >> >>> >> Sent: Thursday, December 09, 2004 10:23 AM
> >> >>> >> Subject: [gov2001-l] setx question
> >> >>> >>
> >> >>> >>
> >> >>> >> > Can anyone help me understand why my setx
function isn't
doing
> >> what
> >> >>> >> > I
> >> >>> >> > thought it would?
> >> >>> >> >
> >> >>> >> > I'm doing part 2a.
> >> >>> >> >
> >> >>> >> >> x.out0<- setx(z.out, fn= NULL, phone =0)
> >> >>> >> >
> >> >>> >> >> x.out0[1:10,]
> >> >>> >> > (Intercept) phone
> >> >>> >> > 1 1 1
> >> >>> >> > 2 1 0
> >> >>> >> > 3 1 1
> >> >>> >> > 4 1 0
> >> >>> >> > 5 1 1
> >> >>> >> > 6 1 1
> >> >>> >> > 7 1 1
> >> >>> >> > 8 1 1
> >> >>> >> > 9 1 1
> >> >>> >> > 10 1 1
> >> >>> >> >
> >> >>> >> > I thought this would produce all 0's in the
phone column
of
> x.out0,
> >>> >> > but clearly it didn't.
> >>> >> >
> >>> >> > Thank you!
> >>> >> >
> >>> >> > Andy
> >>> >> > _______________________________________________
> >>> >> > gov2001-l mailing list
> >>> >> > gov2001-l(a)lists.fas.harvard.edu
> >>> >> >
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
> >>> >> >
> >>> >>
> >>> >> _______________________________________________
> >>> >> gov2001-l mailing list
> >>> >> gov2001-l(a)lists.fas.harvard.edu
> >>> >>
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
> >>> >>
> >>> > _______________________________________________
> >>> > gov2001-l mailing list
> >>> > gov2001-l(a)lists.fas.harvard.edu
> >>> >
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
> >>> >
> >>>
> >>> _______________________________________________
> >>> gov2001-l mailing list
> >>> gov2001-l(a)lists.fas.harvard.edu
> >>>
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> >>>
> >> _______________________________________________
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> >> gov2001-l(a)lists.fas.harvard.edu
> >>
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> >>
> >
> > _______________________________________________
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> >
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> >
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