RE: st: RE: RE: Using ivhettest to test for heterogeneity

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Andreas, 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> andreas.zweifel@uzh.ch
> Sent: 01 March 2012 09:01
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: RE: Using ivhettest to test for heterogeneity
> 
> Hi
> 
> As far as I have understood, reducing the degrees of freedom 
> may increase the power of the heterogeneity test if the 
> number of observations is small. With my sample, the opposite 
> is apparently the case because the p-value of the test 
> increases with decreasing degrees of freedom:
> 
> 
> . reg COC DRANK D_LBAGE LBAGE  LNMV LNBM LNLEV CapInt ROA 
> AssTr LTG LVOL MAFE

<snip>

> . imtest, white
> 
> White's test for Ho: homoskedasticity
>          against Ha: unrestricted heteroskedasticity
> 
>          chi2(89)     =    120.87
>          Prob > chi2  =    0.0139
> 
> Cameron & Trivedi's decomposition of IM-test
> 
> ---------------------------------------------------
>               Source |       chi2     df      p
> ---------------------+-----------------------------
>   Heteroskedasticity |     120.87     89    0.0139
>             Skewness |      17.08     12    0.1464
>             Kurtosis |       1.14      1    0.2852
> ---------------------+-----------------------------
>                Total |     139.10    102    0.0086
> ---------------------------------------------------
> 
> . ivhettest, ivcp nr2
> OLS heteroskedasticity test(s) using levels and cross 
> products of all IVs
> Ho: Disturbance is homoskedastic
>     White/Koenker nR2 test statistic    : 120.871  Chi-sq(89) 
> P-value = 0.0139
> 
> . ivhettest, ivsq nr2
> OLS heteroskedasticity test(s) using levels and squares of IVs
> Ho: Disturbance is homoskedastic
>     White/Koenker nR2 test statistic    :  39.427  Chi-sq(24) 
> P-value = 0.0246
> 
> . ivhettest, nr2
> OLS heteroskedasticity test(s) using levels of IVs only
> Ho: Disturbance is homoskedastic
>     White/Koenker nR2 test statistic    :  19.416  Chi-sq(12) 
> P-value = 0.0790
> 
> 
> I appreciate your help with interpreting this counterintuitive result.

It's not really all that counterintuitive.  The null hypotheses that are
being rejected are different in the 3 cases.

The White test is based on a vector of contrasts between the elements of
the heteroskedastic-robust VCV and the corresponding elements of the
classical homoskedasticity-assumed VCV.

The different options of -ivhettest- correspond to the different
elements used to construct the contrast.  The squares correspond to the
diagonals of the VCVs, the cross-products correspond to the
off-diagonals, and the levels correspond to the cross-products of the
constant (a column of ones) with the other Xs.

The different contrasts are composed of different elements, and hence
you can get different results.  It's perfectly possible for
heteroskedasticity to mess up some elements of the classical VCV but not
others.

--Mark

> 
> Best,
> Andreas
> 
> 
> -----owner-statalist@hsphsun2.harvard.edu wrote: ----- 
> To: statalist@hsphsun2.harvard.edu
> From: Nick Cox 
> Sent by: owner-statalist@hsphsun2.harvard.edu
> Date: 02/29/2012 11:01AM
> Subject: Re: st: RE: RE: Using ivhettest to test for heterogeneity
> 
> The motivation for power calculations seems to be compromised when the
> hypotheses being tested are determined by looking at results.
> 
> I am a great fan of looking at results to see whether I should revise
> my analysis. But then I don't ever do power calculations and I sit
> loose to most significance tests.
> 
> Nick
> 
> On Wed, Feb 29, 2012 at 9:03 AM,  <andreas.zweifel@uzh.ch> wrote:
> 
> > Yes, I see now that the two commands (-imtest, white- and 
> -ivhettest, ivcp nr2-)
> > produce equivalent results also for my sample. I think it 
> is a good idea to
> > reduce the degrees of freedom because I have only 98 
> observations in my sample.
> > Maybe I could even drop the -ivsq- option (and hence 
> ignoring also the squares
> > of the instruments). By calling just -ivhettest, nr2- I 
> could enhance the
> > power of the test by decreasing the degrees of freedom to 12.
> >
> 
> [very big snip]
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