Re: st: RE: Multicollinearity in fixed effects regressions

[Bin Dong <dongbin66@gmail.com>]

Hi Mark,

I see, Thank you very much.

Bin

2010/7/15 Schaffer, Mark E <M.E.Schaffer@hw.ac.uk>:
> Bin,
>
>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Bin Dong
>> Sent: 14 July 2010 11:54
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: RE: Multicollinearity in fixed effects regressions
>>
>> Hi Mark,
>>
>> I, according to your suggestion, tried  Stata's official
>> -areg- ( I add year dummies in the regression). Here are the results:
>>
>> Does Stata drop the time-invariant variables now?  Yes Are
>> the coefficients on the time-varying variables the same as in
>> your original specification, when you included the FEs by
>> hand?  Yes
>
> Then the explanation is the one in my previous posting to Statalist:
>
>> The most likely explanation is that your variables are
>> time-invariant and collinear with the FE dummies, but Stata
>> is dropping some of the FE dummies rather than the
>> time-invariant variables.
>
> This is easy enough to verify - just count the FE dummies.
>
> I'll spell out what is going on in a little more detail, with a hypothetical example.
>
> Say you have 1000 observations, with 100 groups and 10 obs per group.
>
> If you run your regression with 100 dummies for the fixed effects, Stata will drop one, because of the classic "dummy variable trap".  Your 100 dummies and constant term are collinear, and one has to be dropped.  As for the estimated coefficients on the other (non-dummy) variables, it doesn't matter which dummy gets dropped - you will get the same results.  The estimated coefficients on the dummies WILL depend on which one gets dropped, but the others won't.
>
> So you drop one dummy, and now there's no collinearity.  Problem solved.
>
> Now say you include a time-invariant variable as a regressor.  This variable is collinear with your 99 dummies and the constant, so the problem has returned.  Stata will again drop one.  Which one again doesn't matter for the estimated coeffs on the non-dummy variables.  And again, the estimated coeffs on the collinear set - the retained dummies, the constant and the time-invariant variable - WILL depend on which one gets dropped.
>
> What is probably happening in your case is that Stata is dropping one of the dummies, not the time-invariant variable.  But you can NOT interpret the coefficient on the time-invariant variable in the way you seem to want to.  It is simply playing the same role as one of the other fixed effect dummies, and if you are ignoring the coeffs on your fixed effect dummies, you should ignore this coeff as well.
>
> --Mark
>
>> In both my original pooled OLS with dummies and
>> -arge- here, Stata seems not to drop any dummies.
>>
>> So could you please tell me what is happening? Thank you very much.
>>
>> Cheers,
>> Bin
>>
>> 2010/7/14 Schaffer, Mark E <M.E.Schaffer@hw.ac.uk>:
>> > Bin,
>> >
>> >> -----Original Message-----
>> >> From: owner-statalist@hsphsun2.harvard.edu
>> >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Bin Dong
>> >> Sent: 14 July 2010 08:41
>> >> To: statalist@hsphsun2.harvard.edu
>> >> Subject: st: Multicollinearity in fixed effects regressions
>> >>
>> >> Dear all,
>> >>
>> >> I have a maybe stupid question when I estiamte the FE model by
>> >> including individual dummies. Some of independent variables in my
>> >> fixed effects regressions are time-invariant and therefore
>> >> theoretically have perfect multicollinearity with
>> individual dummies.
>> >> However, I always get significant coefficients of these
>> variables in
>> >> my fixed effects regressions with different controls.
>> >
>> > The most likely explanation is that your variables are
>> time-invariant and collinear with the FE dummies, but Stata
>> is dropping some of the FE dummies rather than the
>> time-invariant variables.
>> >
>> > The easiest way to check if this is happening is to
>> estimate the same equation using Stata's official -xtreg,fe-
>> or -areg-.  Does Stata drop the time-invariant variables now?
>>  Are the coefficients on the time-varying variables the same
>> as in your original specification, when you included the FEs
>> by hand?  If the answer to both questions is "yes", then this
>> is what is happening.  And the coefficients on the
>> time-invariants variables mean very little.
>> >
>> > --Mark
>> >
>> >> Are the results reliable because my sample size is large
>> (1600 obs)
>> >> enough to provide adequate information?  If anyone has an
>> idea about
>> >> my results, I would greatly appreciate any assistance you could
>> >> provide.Thanks in advance
>> >>
>> >> Cheers,
>> >> Bin
>> >>
>> >> *
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>> >
>> >
>> > --
>> > Heriot-Watt University is a Scottish charity registered
>> under charity
>> > number SC000278.
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>>
>>
>>
>> --
>> Bin Dong | Doctoral Student
>> School of Economics and Finance | Queensland University of Technology
>> Phone: +61 7 3138 6659 | Email: b.dong@student.qut.edu.au | Location:
>> Z857-06(Gardens Point)
>>
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>
>
> --
> Heriot-Watt University is a Scottish charity
> registered under charity number SC000278.
>
>
> *
> *   For searches and help try:
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>



-- 
Bin Dong | Doctoral Student
School of Economics and Finance | Queensland University of Technology
Phone: +61 7 3138 6659 | Email: b.dong@student.qut.edu.au | Location:
Z857-06(Gardens Point)

*
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