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Re: st: endogenous interaction term


From   "Kyle K. Hood" <kyle.hood@yale.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: endogenous interaction term
Date   Sat, 25 Oct 2008 21:45:30 -0400

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" <M.E.Schaffer@hw.ac.uk>
To: statalist@hsphsun2.harvard.edu
Sent: Wednesday, October 22, 2008 3:28:55 PM
Subject: RE: st: endogenous interaction term

Gordon,

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Gordon Gordon
Sent: 22 October 2008 17:46
To: statalist@hsphsun2.harvard.edu
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" <M.E.Schaffer@hw.ac.uk>
To: statalist@hsphsun2.harvard.edu
Sent: Wednesday, October 22, 2008 7:43:30 AM
Subject: RE: st: endogenous interaction term

Gordon,

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Gordon Gordon
Sent: Tuesday, October 21, 2008 7:27 PM
To: statalist@hsphsun2.harvard.edu
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 <austinnichols@gmail.com>
To: statalist@hsphsun2.harvard.edu
Sent: Monday, October 20, 2008 3:59:08 PM
Subject: Re: st: endogenous interaction term

Gordon <gordon.stat@yahoo.com>:
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 <gordon.stat@yahoo.com> 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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