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Re:st:Re-asking Generated regressor problem


From   Woong.Chung@colorado.edu
To   statalist@hsphsun2.harvard.edu
Subject   Re:st:Re-asking Generated regressor problem
Date   Mon, 16 Oct 2006 16:03:05 -0600

Dear statlist:
I should have asked questions more specific as suggested by.

How about this, then?

As a basic example,

Y = β0 + β1X + U (2nd stage)
and

X = α0 + α1Z + Q.(1st stage)

We are interested in the effect of X on Y . If we plug X into the equation for
Y we get

Y = β0 + β1 (α0 + α1Z + Q) + U
= (β0 + β1α0) + β1α1Z + β1Q + U.
= k0 + k1Z + β1Q + U

In the above example the standard errors from the second stage OLS are not
correct! The
reason is that the estimate of σ2 is wrong. Using the usual estimator of
σ2 the
second stage
OLS would give us
ˆσ2 =1/N*sum^2 {Yi − (ˆk0 + ˆk1Zi + ˆβ1ˆQi)}

when in fact it should have to be
ˆσ2 =1/N*sum^2{Yi-(ˆk0 + ˆk1Zi + ˆβ1Qi)}

technically speaking, we need to convert Qihat into Qi

 How to implement this at Stata? Looks like we need to create matrix for this
implementation? I am so pleased if anyone shows me some matrix codes for this
example.
Someone mentioned a Wooldridge's "econometric analysis..." chapter #6 but it
was so hard for identifying m matrix as well as other matrix form.

Any helpful codes or words are glad to solve my long-term concerns.

WT


WT:
Whether inference is valid depends on whether your model is appropriate for
your data and your question. I don't see how we can answer your question,
since you haven't told us anything about these three things.
HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

--- Woong Chung wrote:
> Regarding "generated Regressor problem", there are many same questions-"how to
> deal with varaince-covariance matrix that make the inference valid" in STATA.
> Unfortunately, I have yet found any clear answers about the questions. Is it
> because there are no ways or commands in stata to solve? or hard to explain to
> making a coding to create var-covariance matrix? (or maybe it is too easy to
> answer?)


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