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


From   Alexandra Guisinger <Guisinger.1@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: "V_b-V_B is not positive definite" / XTOVERID
Date   Tue, 2 Sep 2008 13:20:53 -0400

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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