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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 12:44:48 -0500 |
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/