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st: RE: "V_b-V_B is not positive definite" / XTOVERID


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: "V_b-V_B is not positive definite" / XTOVERID
Date   Tue, 2 Sep 2008 21:35:58 +0100

Alexandra,

The problem is that you are combining -hausman- with -robust-.  This
isn't quite kosher.

First, the -sigmamore- and -sigmaless- options are designed for the
classical VCV where homoskedasticity is assumed (i.e., that there is
actually a sigma!).

Second, the Hausman test is based on the comparison of an efficient with
a consistent estimator.  Since the random effects estimator is the
efficient estimator by assumption, you should be using the classical VCV
anyway.  If it isn't efficient (which you are implying by the use of
-robust-) then the standard Hausman test doesn't apply, and you need to
use other methods (such as those provided by -xtoverid- or -suest-).

My guess is that the "not positive definite" error message arises
because you have dummy variables, and not because using -hausman- and
-robust- isn't kosher.

BTW, you should probably not use -robust- with -xtreg,fe-, because the
VCE isn't consistent; cluster-robust is OK, though.  Kit Baum posted on
this earlier today - as he noted, in Stata 10.1, -xtreg,fe- with
-robust- automatically does this:

from help whatsnew:

     20.  xtreg, fe now uses vce(cluster id) when vce(robust) is
specified, in light of the new results in Stock and Watson,
          "Heteroskedasticity-robust standard errors for fixed-effects
panel-data regression," Econometrica 76 (2008): 155-174.

Cheers,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Alexandra Guisinger
> Sent: 02 September 2008 18:21
> To: statalist@hsphsun2.harvard.edu
> Subject: st: "V_b-V_B is not positive definite" / XTOVERID
> 
> My replies don't seem to be linking to the thread ("V_b-V_B 
> is not positive definite" / XTOVERID) so just a quick 
> summary. Even using the sigmamore or sigmaless option for 
> hausman, I keep getting a "not positive definite message". As 
> requested, I have posted the results from 1) using xtoverid 
> 2) hausman "plain" 3) hausman, sigmamore 4) hausman, sigmaless
> 
> The open question is why I should be getting this message on 
> the last two. I posted the xtoverid and the hausman "plain" 
> results just to provide a baseline.
> 
> Best,
> 
> Alexandra
> 
> . quietly xtreg inf_ln dejure_fix_lag defacto_fix_lag  both_fix_lag
> > cbi_dum demo cbid_demo
> > any_crisis_lag5
> > gdpgr gdppc_ln
> > kaopen trade_gdpln
> > d80 d90 d00, fe robust;
> 
> . estimates store FE_all;
> 
> . quietly xtreg inf_ln dejure_fix_lag defacto_fix_lag both_fix_lag
> > cbi_dum demo cbid_demo
> > any_crisis_lag5
> > gdpgr gdppc_ln
> > kaopen trade_gdpln
> > d80 d90 d00, robust;
> 
> . estimates store RE_all;
> 
> . xtoverid;
> 
> Test of overidentifying restrictions: fixed vs random effects 
> Cross-section time-series model: xtreg re robust
> Sargan-Hansen statistic  47.466  Chi-sq(14)   P-value = 0.0000
> 
> . di r(j);
> 47.466264
> 
> . hausman FE_all RE_all;
> 
>                  ---- Coefficients ----
>              |      (b)          (B)            (b-B)     
> sqrt(diag(V_b-V_B))
>              |     FE_all       RE_all       Difference          S.E.
> -------------+------------------------------------------------
> ----------
> -------------+------
> dejure_fix~g |    -.106678    -.1485591        .0418811       
>  .0214834
> defacto_fi~g |    .1230668     .0495145        .0735523       
>  .0210956
> both_fix_lag |    -.182023    -.1595988       -.0224242       
>  .0237164
>      cbi_dum |    .2066256     .2841449       -.0775193       
>  .0273531
>         demo |    .0979394     .1619413       -.0640018       
>  .0317311
>    cbid_demo |   -.2235295    -.2928343        .0693048       
>  .0332288
> any_crisis~5 |    .0833966     .0925835       -.0091869       
>  .0105338
>        gdpgr |   -.0120385    -.0138431        .0018045       
>  .0013408
>     gdppc_ln |   -.4195892     -.217086       -.2025032       
>  .0542878
>       kaopen |   -.1710387      -.18982        .0187813       
>  .0075126
>  trade_gdpln |    .3195032      .116403        .2031002       
>  .0704085
>          d80 |   -.1043844    -.2006809        .0962965       
>   .028491
>          d90 |   -.3351049    -.5048707        .1697659       
>  .0615218
>          d00 |    -.745062    -.9100827        .1650207       
>   .067007
> --------------------------------------------------------------
> ----------------
>                            b = consistent under Ho and Ha; 
> obtained from xtreg
>             B = inconsistent under Ha, efficient under Ho; 
> obtained from xtreg
> 
>     Test:  Ho:  difference in coefficients not systematic
> 
>                  chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
>                           =       42.13
>                 Prob>chi2 =      0.0001
>                 (V_b-V_B is not positive definite)
> 
> . di r(chi2);
> 42.127934
> 
> . hausman FE_all RE_all, sigmamore;
> 
>                  ---- Coefficients ----
>              |      (b)          (B)            (b-B)     
> sqrt(diag(V_b-V_B))
>              |     FE_all       RE_all       Difference          S.E.
> -------------+------------------------------------------------
> ----------
> -------------+------
> dejure_fix~g |    -.106678    -.1485591        .0418811       
>  .0230684
> defacto_fi~g |    .1230668     .0495145        .0735523       
>   .022366
> both_fix_lag |    -.182023    -.1595988       -.0224242       
>  .0260087
>      cbi_dum |    .2066256     .2841449       -.0775193       
>  .0298705
>         demo |    .0979394     .1619413       -.0640018       
>  .0328377
>    cbid_demo |   -.2235295    -.2928343        .0693048       
>  .0356113
> any_crisis~5 |    .0833966     .0925835       -.0091869       
>  .0149747
>        gdpgr |   -.0120385    -.0138431        .0018045       
>  .0014489
>     gdppc_ln |   -.4195892     -.217086       -.2025032       
>  .0547583
>       kaopen |   -.1710387      -.18982        .0187813       
>   .007898
>  trade_gdpln |    .3195032      .116403        .2031002       
>  .0714139
>          d80 |   -.1043844    -.2006809        .0962965       
>  .0291838
>          d90 |   -.3351049    -.5048707        .1697659       
>  .0622949
>          d00 |    -.745062    -.9100827        .1650207       
>  .0681762
> --------------------------------------------------------------
> ----------------
>                            b = consistent under Ho and Ha; 
> obtained from xtreg
>             B = inconsistent under Ha, efficient under Ho; 
> obtained from xtreg
> 
>     Test:  Ho:  difference in coefficients not systematic
> 
>                  chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
>                           =       32.34
>                 Prob>chi2 =      0.0036
>                 (V_b-V_B is not positive definite)
> 
> . di r(chi2);
> 32.344072
> 
> . hausman FE_all RE_all, sigmaless;
> 
>                  ---- Coefficients ----
>              |      (b)          (B)            (b-B)     
> sqrt(diag(V_b-V_B))
>              |     FE_all       RE_all       Difference          S.E.
> -------------+------------------------------------------------
> ----------
> -------------+------
> dejure_fix~g |    -.106678    -.1485591        .0418811       
>  .0229261
> defacto_fi~g |    .1230668     .0495145        .0735523       
>   .022228
> both_fix_lag |    -.182023    -.1595988       -.0224242       
>  .0258483
>      cbi_dum |    .2066256     .2841449       -.0775193       
>  .0296863
>         demo |    .0979394     .1619413       -.0640018       
>  .0326352
>    cbid_demo |   -.2235295    -.2928343        .0693048       
>  .0353917
> any_crisis~5 |    .0833966     .0925835       -.0091869       
>  .0148824
>        gdpgr |   -.0120385    -.0138431        .0018045       
>    .00144
>     gdppc_ln |   -.4195892     -.217086       -.2025032       
>  .0544206
>       kaopen |   -.1710387      -.18982        .0187813       
>  .0078493
>  trade_gdpln |    .3195032      .116403        .2031002       
>  .0709734
>          d80 |   -.1043844    -.2006809        .0962965       
>  .0290039
>          d90 |   -.3351049    -.5048707        .1697659       
>  .0619107
>          d00 |    -.745062    -.9100827        .1650207       
>  .0677557
> --------------------------------------------------------------
> ----------------
>                            b = consistent under Ho and Ha; 
> obtained from xtreg
>             B = inconsistent under Ha, efficient under Ho; 
> obtained from xtreg
> 
>     Test:  Ho:  difference in coefficients not systematic
> 
>                  chi2(14) = (b-B)'[(V_b-V_B)^(-1)](b-B)
>                           =       32.75
>                 Prob>chi2 =      0.0031
>                 (V_b-V_B is not positive definite)
> 
> . di r(chi2);
> 32.746749
> 
> .
> end of do-file
> 
> . which hausman
> C:\Program Files\oit_licensed\Stata9\ado\updates\h\hausman.ado
> *! version 3.0.14  18jan2007
> 
> . which xtreg
> C:\Program Files\oit_licensed\Stata9\ado\updates\x\xtreg.ado
> *! version 1.5.2  19mar2007
> 
> 
> --
> Alexandra Guisinger
> Assistant Professor
> Political Science
> University of Notre Dame
> 217 O'Shaughnessy Hall
> Notre Dame, IN 46556
> (574) 631-3846
> Guisinger.1@nd.edu
> 
> *
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> 


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