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.
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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