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,

The described IV procedure for interaction terms differs from canned 2SLS in two ways:
1. The first stage of 2SLS where all instruments are regressed on the endogenouss variable preprocessed manually in the first step
2. For each interaction term, an additional instrument is constructed in the second step
3. By construction, the -ivreg2- procedure uses as exactly many instruments in the second step as there are endogenous regressors (including interaction terms) 

Interestingly, the second-stage regression cannot be over-identified when using this specific method. Does this affect the possible inference that can be drawn from the Sargan test statistic in -ivreg2- ?

It's important to gather some ideas because I am dealing with a similar IV setting where there are two endogenous variables, X1 and X2, which interact with each other. If I apply the described IV procedure to my model, would the three steps now be as following:

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

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

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


Thank you for your help.

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:
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>>
>>
>>
>> --
>> 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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