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

 From Tirthankar Chakravarty To statalist@hsphsun2.harvard.edu Subject Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression Date Wed, 21 Dec 2011 04:44:14 -0800

```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

*
*   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/
```