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

[Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>]

Austin,

I agree re: well-cited papers.

Note that the efficiency you mention comes at a cost. As I pointed out
in my previous Statalist reply:
http://www.stata.com/statalist/archive/2011-08/msg01496.html
the instrumenting strategy you suggest requires the instruments to be
conditionally independent rather than just uncorrelated with the
structural errors.

T

On Wed, Dec 21, 2011 at 7:57 AM, Austin Nichols <austinnichols@gmail.com> wrote:
> 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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-- 
Tirthankar Chakravarty
tchakravarty@ucsd.edu
tirthankar.chakravarty@gmail.com

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