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Re: st: endogenous interaction term


From   Gordon Gordon <gordon.stat@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: endogenous interaction term
Date   Sat, 25 Oct 2008 18:22:53 -0700 (PDT)

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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> > 
> > 
> >      
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> 
> 
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registered under charity number SC000278.


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