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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 18:58:44 +0100 |

Sorry for the confusion - X1 is included as a stand alone term. To be more detailed, my model looks like this (X is exogenous, E is endogenous): dY = X1 + X2 + X1*X3 + X1*X3*E1 + X1*X3*E2 + X1*X3*E3 + controls X3 is an indicator variable that is equal to 1 when X1 <= 0 On Wed, Dec 21, 2011 at 6:44 PM, Austin Nichols <austinnichols@gmail.com> wrote: > Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>: > I don't see anywhere that the X1 is included as a main effect as > opposed to just being included in the product X1*X2. (Though it is > not clear what is included in "+controls" in the post.) It seems that > X1 is exogenous by assumption, i.e. X1 is uncorrelated with e while X2 > is correlated with e. There are no quadratic terms in Z in my > suggestion. Note that you suggested instrumenting with X2hat*X1 and > X2hat is linear in Z. > > On Wed, Dec 21, 2011 at 12:15 PM, Tirthankar Chakravarty > <tirthankar.chakravarty@gmail.com> wrote: >> " It does not seem too much of a stretch to assume Z*X1 >> uncorrelated with e as well (which implies X2hat*X1 uncorrelated with >> e)" >> >> This part is the problem. When you form cross-products of the >> instrument matrix, you will end up with quadratic terms in Z, coming >> from terms like the one you mention, which will need to be >> uncorrelated with the structural errors, hence the independence >> requirement. >> >> Again, note that X1 is included so there is no overidentification (or, >> at best, the same degree of overidentification as without the >> interaction term). >> >> T >> >> On Wed, Dec 21, 2011 at 8:57 AM, Austin Nichols <austinnichols@gmail.com> wrote: >>> Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>: >>> No conditional independence assumed, though of course an independence >>> assumption lets you form all kinds of transformations of Z to use as >>> excluded instruments. >>> >>> We need Z, Z*X1, and X1 uncorrelated with e, but Z and e were already >>> assumed uncorrelated and X1 is exogenous by assumption as well, in the >>> original post. It does not seem too much of a stretch to assume Z*X1 >>> uncorrelated with e as well (which implies X2hat*X1 uncorrelated with >>> e), but if we use all 3 as instruments we will see evidence of any >>> violations of assumptions in the overid test (assuming no weak >>> instruments problem). >>> >>> On Wed, Dec 21, 2011 at 11:44 AM, Tirthankar Chakravarty >>> <tirthankar.chakravarty@gmail.com> wrote: >>>> 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 > > * > * 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/

**Follow-Ups**:**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>

**References**:**st: Using ivregress when the endogenous variable is used in an interaction term in the main regression***From:*Nick Kohn <coffeemug.nick@gmail.com>

**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>

*From:*Nick Kohn <coffeemug.nick@gmail.com>

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*Nick Kohn <coffeemug.nick@gmail.com>

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*Nick Kohn <coffeemug.nick@gmail.com>

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*Austin Nichols <austinnichols@gmail.com>

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*Austin Nichols <austinnichols@gmail.com>

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*Austin Nichols <austinnichols@gmail.com>

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