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From |
Tirthankar Chakravarty <tirthankar.chakravarty@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 |
Thu, 22 Dec 2011 11:30:13 -0800 |

Christine, 1) For the two-way interaction with binary endogenous regressor, your question is fully answered in the Prof. Wooldridge's reply here: http://www.stata.com/statalist/archive/2011-03/msg00188.html This is analogous to the procedure suggested earlier in the thread for the continuous interaction in the previous discussions. In fact, that reply also discusses a three-way interaction. 2) The three-way interaction poses no new challenges if the other two terms are both exogenous. 3) If Z, X1 and X3 are exogenous, the interaction X2hat*X1*X3 is necessarily exogenous. T On Thu, Dec 22, 2011 at 11:19 AM, Christine Scheef <christine.scheef@unisg.ch> wrote: > Hey, > > I am following your discussion since I am working on a similar problem at > the moment. However, my endogenous variable in the interaction is binary. > I have 3 questions: > - Since the endogenous variable is binary, is it right to use logit > instead of regress in the first stage? > - I also want to calculate a 3-way interaction with 2 continuous exogenous > variables and the endogenous binary variable. Can I form the interactions > of X2hat with X1 and X3, that is X2hat* X1* X2? > - When calculating the thrid step with ivregress - Do I still need to > check for the exogeneity of the instrument variables X2hat and X2hat*X1? > > I very much appreciate your help. > > Best, > Christine > > > Nick, > > I don't have a specific reference in mind, but I suppose you should be > able to construct a workable explanation from Prof. Wooldridge's reply > (indeed, you can probably directly cite it) and some directed > googling. > > T > > On Wed, Dec 21, 2011 at 10:01 AM, Nick Kohn <coffeemug.nick@gmail.com> > wrote: >> My apologies for spamming but I also wanted to mention that I'm trying >> out the specification that includes the endogenous variables as stand >> alone terms. >> >> I'm not sure whether I'll use it in my paper though because I'll need >> to provide a justification of why I deviate from the paper I cite, and >> going into long winded econometric arguments is beyond the scope of >> what I'm doing. >> >> Is there a paper or book I can cite that explains why adding the >> levels is appropriate? >> >> On Wed, Dec 21, 2011 at 6:58 PM, Nick Kohn <coffeemug.nick@gmail.com> > wrote: >>> 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/ -- Tirthankar Chakravarty tchakravarty@ucsd.edu tirthankar.chakravarty@gmail.com * * 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/

**References**:**Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression***From:*Christine Scheef <christine.scheef@unisg.ch>

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