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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 11:57:19 -0500 |

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/

**Follow-Ups**:**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>

**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>

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