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Re: st: endogenous interaction term
If you have X1 endogenous and an exogenous instrument Z which is
correlated with X1, and your model includes two terms involving X1, X1
and X1*X2, then you should use two instruments: Z, and Z*X2. This may
be what Mark or you were suggesting, and I believe this is a standard
approach. Here, Z and Z*X2 are different (not perfectly collinear), are
correlated with X1 and X1*X2, and are exogenous.
Kyle
Gordon Gordon wrote:
Thanks again Mark! I think that is the way to go. In theory it is correct, although I have not found much literature on it.
Gordon
----- Original Message ----
From: "Schaffer, Mark E" <[email protected]>
To: [email protected]
Sent: Wednesday, October 22, 2008 3:28:55 PM
Subject: RE: st: endogenous interaction term
Gordon,
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of
Gordon Gordon
Sent: 22 October 2008 17:46
To: [email protected]
Subject: Re: st: endogenous interaction term
Thanks Mark for the reference links! They are very helpful.
My problem is that in the equation I am interested in, the
endogenous binary variable X1 also interacts with another
variable X2, and I am trying to correct the endogeneity of
the interaction term.
One solution is to have the instrument of X1 interacting with
X2 as additional instruments, and then apply a standard
ivreg2 approach. However I haven't been able to find much
literature on this issue.
I don't think that will work. If X1 is endogenous, then an interaction
with X1 will probably be endogenous too - you'd need to work hard to
convince a skeptic otherwise.
You should probably be thinking instead about instruments for X1 and
(X1*X2), i.e., you need at least two instruments. Interactions of
instruments might be appropriate, but it depends completely on your
particular application.
Hope this helps.
Cheers,
Mark
Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html
Could you shed light?
Thanks,
Gordon
----- Original Message ----
From: "Schaffer, Mark E" <[email protected]>
To: [email protected]
Sent: Wednesday, October 22, 2008 7:43:30 AM
Subject: RE: st: endogenous interaction term
Gordon,
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of
Gordon Gordon
Sent: Tuesday, October 21, 2008 7:27 PM
To: [email protected]
Subject: Re: st: endogenous interaction term
Thanks a lot Austin!
However in my case, the endogenous variable X1 is a dummy
variable, and my first stage regression is a probit model,
then I plug the Inverse Mills Ratio to the second stage
regression. It is not clear to me how to use the typical IV
approach in this setting. Could you advice?
I think you're on the wrong track here. You should probably
be thinking along the lines of Stata's built-in -treatreg-,
the add-ins -cdsimeq- or -cmp-, or alternative procedures
such as the one that Jeff Wooldridge describes in his 2002 book.
Have a look at some past discussions on the list and the
threads and references therein:
http://www.stata.com/statalist/archive/2004-09/msg00352.html
http://www.stata.com/statalist/archive/2007-04/msg00945.html
HTH.
Cheers,
Mark
Gordon
----- Original Message ----
From: Austin Nichols <[email protected]>
To: [email protected]
Sent: Monday, October 20, 2008 3:59:08 PM
Subject: Re: st: endogenous interaction term
Gordon <[email protected]>:
See e.g.
http://www.stata.com/statalist/archive/2004-08/msg00780.html
With multiple instruments and multiple endog vars, you may
want to use
LIML so -ivreg2- will give you a little more room to pass
the weak ID
tests of Stock and Yogo (see the help file for -ivreg2-, on
SSC) since
LIML is slightly more robust to multiple weak instruments.
On Mon, Oct 20, 2008 at 1:06 PM, Gordon Gordon
<[email protected]> wrote:
Hi there,
I would like to estimate the following equation:
Y = b0+ b1*X1 +b2* X2 + b3*X1*X2
X1 is a dummy variable and endogenous, X2 is exogenous and
normalized.
If there are no interaction term, I can apply either IV or
Heckman two stage to correct the endogeneity of X1.
However with the interaction term of X1*X2, I do not know
how to deal with it.
Any advice is much appreciated!
Gordon
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