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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 <[email protected]>
To
[email protected]
Subject
Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression
Date
Wed, 21 Dec 2011 06:20:28 -0800
In that case, none of this is necessary. Just instrument for X1*X2
using Z. All standard results apply.
T
On Wed, Dec 21, 2011 at 6:03 AM, Nick Kohn <[email protected]> wrote:
> 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
> <[email protected]> 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 <[email protected]> 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
>>> <[email protected]> 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 <[email protected]> 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
>>>>> <[email protected]> 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 <[email protected]> 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
>>>>>> [email protected]
>>>>>> [email protected]
>>>>>>
>>>>>> *
>>>>>> * 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
>>>> [email protected]
>>>> [email protected]
>>>>
>>>> *
>>>> * 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
>> [email protected]
>> [email protected]
>>
>> *
>> * 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
[email protected]
[email protected]
*
* 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/