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# Antwort: Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression

 From andreas.zweifel@uzh.ch To statalist@hsphsun2.harvard.edu Subject Antwort: Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression Date Fri, 20 Jan 2012 21:05:34 +0100

```Hi,

This all sounds very interesting but leaves an open question for me. I think your approach is based on the assumption
that there is only one conceivable instrument for X1, that is Z. Theory always claims how hard it is to find the right
instruments. In case the choice of the instruments is not very well founded on economic thought, there may be more than
one potential candidate, say Z1 and Z2. Normally, using both instruments would call for an overidentification problem
which might be detected by an overid test given that instruments are not weakly correlated with the endogenous regressor.
Leaving this possibility at first aside, one could just do -ivregress- using Z1 and Z2 as instruments for X1 and X1*X2.
This would intuitively be the most natural way to overcome the problem with the interaction term. Could you please tell
me what the rationale is for using your more complicated procedure (given that there is no strong theoretical argument
for Z1 being the only instrument candidate for X1)?

Andreas Zweifel

-----owner-statalist@hsphsun2.harvard.edu schrieb: -----
An: statalist@hsphsun2.harvard.edu
Von: Tirthankar Chakravarty
Gesendet von: owner-statalist@hsphsun2.harvard.edu
Datum: 21.12.2011 13:44
Betreff: Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression

Not quite; here is the recommended procedure (I am assuming that you
have the main effect of the endogenous variable in there as in Y =
a*X2 + b*X1*X2 + controls):

1) -regress- X2 on _all_ instruments (included exogenous controls and
excluded instruments) and get predictions X2hat.

2) Form interactions of X2hat with the exogenous variable X1, that is, X2hat*X1.

3) -ivregress- instrumenting for X2 and X2*X1 using X2hat and X2hat*X1.

Note that there is distinction between two calls to -regress- and
using -ivregress- for 3).

T

On Wed, Dec 21, 2011 at 3:43 AM, Nick Kohn <coffeemug.nick@gmail.com> wrote:
>
> My simplified model is (X2 is endogenous):
> Y = b*X1*X2 + controls
>
> In regards to the third option you suggest, would I do the following?
>
>  1) First stage regression to get X2hat using the instrument Z
>  2) Run the first stage again but use X1*X2hat as the instrument for
> X1*X2 (so Z is no longer used)
>  3) Run the second stage using (X1*X2)hat (so the whole product is
> fitted from step 2))
>
> On Wed, Dec 21, 2011 at 12:24 PM, Tirthankar Chakravarty
> <tirthankar.chakravarty@gmail.com> wrote:
>> You can see my previous reply to a similar question here:
>> http://www.stata.com/statalist/archive/2011-08/msg01496.html
>>
>> T
>>
>> On Wed, Dec 21, 2011 at 2:24 AM, Nick Kohn <coffeemug.nick@gmail.com> wrote:
>>> Hi,
>>>
>>> I have a specification in which the endogenous variable is interacted
>>> with an exogenous variable. Since I cannot multiply the variables
>>> directly in the regression, I create a new variable. In ivregress it
>>> makes no sense to use the entire interaction term as the endogenous
>>> variable.
>>>
>>> I can do the first stage manually (and then use the fitted value in
>>> the main regression), however, from what I remember the standard
>>> errors will be wrong when doing it manually.
>>>
>>> Is there a way to overcome this?
>>>
>>> Thanks
>>> *
>>> *   For searches and help try:
>>> *   http://www.stata.com/help.cgi?search
>>> *   http://www.stata.com/support/statalist/faq
>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>> --
>> Tirthankar Chakravarty
>> tchakravarty@ucsd.edu
>> tirthankar.chakravarty@gmail.com
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

--
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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```