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

[andreas.zweifel@uzh.ch]

Hi all,

I am dealing with a similar setting where two endogenous variables X1 and X2 interact with each other. Would the correct IV procedure applied to this setting be as following:

1) -regress- X1 and X2 on _all_ instruments (included exogenous controls and
excluded instruments) and get predictions X1hat and X2hat.

2) Form interactions of X1hat and X2hat, that is, X2hat*X1hat.

3) -ivregress- instrumenting for X1, X2 and X2*X1 using X1hat, X2hat and X2hat*X1hat.

What's interesting with this procedure, you are deemed to construct exactly as many instrument as there are endogenous variables in the regression model. Therefore it is practically impossible to get overidentification. How do I have to interpret the Sargan statistic for overidentifying restriction given that the number of instruments is a priori fixed to be equal to the number of endogenous regressors now?

Any help is highly appreciated.

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:
> Thanks for the reply.
>
> 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
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>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>> --
>> Tirthankar Chakravarty
>> tchakravarty@ucsd.edu
>> tirthankar.chakravarty@gmail.com
>>
>> *
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>> *   http://www.ats.ucla.edu/stat/stata/
>
> *
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-- 
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

*
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