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

 From Nick Kohn 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 15:03:13 +0100

```Hmmm I see what you mean, but I'm following the methodology of a well
cited paper that does the same thing.

I'll be sure to discuss this limitation, but in terms of using this
model, would the 3 steps in my last message be correct?

On Wed, Dec 21, 2011 at 2:56 PM, Tirthankar Chakravarty
<tirthankar.chakravarty@gmail.com> wrote:
> I wanted to indirectly confirm that you did have the main effect in
> the regression because even though I don't know the nature of your
> study, a hard-to-defend methodological position arises when you
> include interaction terms without including the main effect. You might
> want to take that on the authority of someone who (literally) wrote
> the book on the subject:
>
> http://www.stata.com/statalist/archive/2011-03/msg00188.html
>
> and reconsider your decision to not include the main effect.
>
> T
>
> On Wed, Dec 21, 2011 at 5:46 AM, Nick Kohn <coffeemug.nick@gmail.com> wrote:
>> My model doesn't have X2 as a separate term, so in terms of the model
>> you had it looks like:
>>  Y = b*X1*X2 + controls
>> So the only place the endogenous variable comes up is the interaction term
>>
>> At the risk of being repetitive, would these be the correct steps (so
>> essentially only step 3 changes from what you said):
>> 1) regress X2 on all instruments, exogenous variables and controls
>> 2) Form interactions of X2hat with the exogenous variable X1, that is, X2hat*X1
>> 3) ivregress instrumenting for X2*X1 using X2hat*X1.
>>
>> On Wed, Dec 21, 2011 at 1:44 PM, Tirthankar Chakravarty
>> <tirthankar.chakravarty@gmail.com> wrote:
>>> 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/
>>
>> *
>> *   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/

*
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```