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


From   Austin Nichols <austinnichols@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 10:57:01 -0500

Nick Kohn <coffeemug.nick@gmail.com>:
Or better, instrument for X1*X2 using Z, Z*X1, and X1.
For maximal efficiency given your assumptions you may prefer
to instrument for X1*X2 using Z*X1, or even
to instrument for X1*X2 using X2hat*X1,
but you should build in an overid test whenever feasible.

Just because a well-cited paper does something wrong does not mean you
have to, though.

Including the main effects of X1 and X2 makes for harder interpretation, but
will make you a lot more confident of your answers once you have worked out the
interpretation.

On Wed, Dec 21, 2011 at 9:20 AM, Tirthankar Chakravarty
<tirthankar.chakravarty@gmail.com> wrote:
> 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 <coffeemug.nick@gmail.com> 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
>> <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:
>>>>>> 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

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