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From |
Tirthankar Chakravarty <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression |

Date |
Wed, 21 Dec 2011 08:44:34 -0800 |

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 <[email protected]> wrote: > Nick Kohn <[email protected]>: > 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 > <[email protected]> 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 <[email protected]> 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 >>> <[email protected]> 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 <[email protected]> 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 >>>>> <[email protected]> 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 <[email protected]> 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 >>>>>>> <[email protected]> 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 <[email protected]> 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 [email protected] [email protected] * * 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**:

**References**:**st: Using ivregress when the endogenous variable is used in an interaction term in the main regression***From:*Nick Kohn <[email protected]>

**Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression***From:*Tirthankar Chakravarty <[email protected]>

**Re: st: Using ivregress when the endogenous variable is used in an interaction term in the main regression***From:*Nick Kohn <[email protected]>

*From:*Tirthankar Chakravarty <[email protected]>

*From:*Nick Kohn <[email protected]>

*From:*Tirthankar Chakravarty <[email protected]>

*From:*Nick Kohn <[email protected]>

*From:*Tirthankar Chakravarty <[email protected]>

*From:*Austin Nichols <[email protected]>

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