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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 <tirthankar.chakravarty@gmail.com>
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 05:56:55 -0800

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:
>>> 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
>>>>> *   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:
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>>> *   http://www.ats.ucla.edu/stat/stata/
>>
>>
>>
>> --
>> Tirthankar Chakravarty
>> tchakravarty@ucsd.edu
>> tirthankar.chakravarty@gmail.com
>>
>> *
>> *   For searches and help try:
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>> *   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:
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