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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 10:57:01 -0500 |

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>

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