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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 <coffeemug.nick@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 14:46:16 +0100

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.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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