hausman (not positive definite)

[nassim ouali]

Dear Statalist-users,

I need your help. here is the model I use on stata to measure the effect of ESG (Environnmental, Social, Governance) performance on qtobin (performance):
I have an unbalanced panel with large N, small T.

I am trying to choose between RE and FE model however when I conduct an hausman test, the following appear : (V_b-V_B is not positive definite)
Also i downloaded the module xtoverid to account for heteroskedasticty and autocoreelation (source : Mark Schaffer) however it does not work after : "xtreg, re vce(cluster panel id)"
I read some of the post that advised to use hausman with sigmamore and sigmaless however the result are different from the original hausman test, which one should I use please ?


1 attempt with hausman test :
xtreg qtobin esg levier tventes logassets i.year, fe
estimates store fixed
xtreg qtobin esg levier tventes logassets i.year, re
estimates store random
hausman fixed random
chi2(17) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 8.81
Prob>chi2 = 0.9461
(V_b-V_B is not positive definite)


2 attempt with hausman test and sigmamore:
xtreg qtobin esg levier tventes logassets i.year, fe
estimates store fixed
xtreg qtobin esg levier tventes logassets i.year, re
estimates store random
hausman fixed random, sigmamore
Test: Ho: difference in coefficients not systematic
chi2(17) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 94.27
Prob>chi2 = 0.0000

3 attempt with hausman test and sigmaless:
xtreg qtobin esg levier tventes logassets i.year, fe
estimates store fixed
xtreg qtobin esg levier tventes logassets i.year, re
estimates store random
hausman fixed random, sigmaless
Test: Ho: difference in coefficients not systematic
chi2(17) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 94.99
Prob>chi2 = 0.0000


4 attempt with xtoverid:
. xtreg qtobin esg levier tventes logassets i.year, re vce(cluster companynum)

Random-effects GLS regression Number of obs = 8,729
Group variable: companynum Number of groups = 871

R-sq: Obs per group:
within = 0.1687 min = 2
between = 0.2265 avg = 10.0
overall = 0.2046 max = 14

Wald chi2(17) = 778.44
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. Err. adjusted for 871 clusters in companynum)
------------------------------------------------------------------------------
| Robust
qtobin | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
esg | .0040501 .0008212 4.93 0.000 .0024407 .0056596
levier | -.0001237 .0025782 -0.05 0.962 -.0051768 .0049295
tventes | -.0002569 .0000141 -18.16 0.000 -.0002846 -.0002291
logassets | -.5623834 .0389293 -14.45 0.000 -.6386835 -.4860833
|
year |
2003 | .2826151 .0543909 5.20 0.000 .1760109 .3892194
2004 | .1633955 .0536977 3.04 0.002 .0581498 .2686411
2005 | .2557374 .0535302 4.78 0.000 .1508202 .3606546
2006 | .3497602 .0573786 6.10 0.000 .2373002 .4622202
2007 | .455518 .0602367 7.56 0.000 .3374563 .5735796
2008 | -.1981683 .0537734 -3.69 0.000 -.3035623 -.0927743
2009 | -.0686121 .0555378 -1.24 0.217 -.1774641 .0402399
2010 | -.0442643 .0587347 -0.75 0.451 -.1593821 .0708535
2011 | -.0372261 .0591157 -0.63 0.529 -.1530907 .0786386
2012 | .0322761 .058474 0.55 0.581 -.0823308 .1468831
2013 | .2631256 .0613331 4.29 0.000 .1429149 .3833363
2014 | .2181927 .0608679 3.58 0.000 .0988937 .3374917
2015 | .2377145 .0656265 3.62 0.000 .1090889 .3663401
|
_cons | 10.23278 .6051246 16.91 0.000 9.046753 11.4188
-------------+----------------------------------------------------------------
sigma_u | 1.048925
sigma_e | .61969319
rho | .74127255 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtoverid
2002b: operator invalid
r(198);


Thanks again for your time

[Sebastian Kripfganz]

Please see my comment in another Statalist topic about the hausman test after fixed-/random-effects models with time dummies:
Hausman Procedure with Year Dummies

[nassim ouali]

Dear Sebastian,

Thanks for your reply. I tried to follow your advice and The Mundlak approach from http://blog.stata.com/2015/10/29/fix...dlak-approach/

egen esgbar = mean(esg), by(companynum)
egen levierbar = mean(levier), by(companynum)
egen tventesbar = mean(tventes), by(companynum)
egen logassetsbar = mean(logassets), by(companynum)
xtreg qtobin esg levier tventes logassets esgbar levierbar tventesbar logassetsbar i.year, re vce(cluster companynum)
estimates store mundlak
testparm esgbar levierbar tventesbar logassetsbar
chi2( 4) = 17.92
Prob > chi2 = 0.0013

I follow the conclusion from http://blog.stata.com/2015/10/29/fix...dlak-approach/
I reject the null hypothesis. This suggests that time-invariant unobservables are related to the regressors and that the fixed-effects model is appropriate. With robust estimator of the variance-covariance matrix than controls for heteroskedasticity and autocorrelation

Does it mean Fe is the best choice over RE ?
Thanks again for your time and patience

best regards,
nassim ouali

[nassim ouali]

I also just managed to perform the "xtoverid" module (from Mark Schaffer) I get the following :

. xtreg qtobin esg levier tventes logassets, re vce(cluster companynum)
. xtoverid
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(companynum)
Sargan-Hansen statistic 34.279 Chi-sq(4) P-value = 0.0000

This also means that RE is inconsistent and it also controls for HAC. However it does not account for time dummy variables. Does it mean the Mundlak approach is the best method to use in my case ? Thanks again for your time and patience.
best regards,
nassim ouali

[Carlo Lazzaro]

Nassim:
-hausman, sigmamore- and -xtoverid- outcomes point you to -fe- specification.
See also: http://www.stata.com/statalist/archi.../msg01069.html

[nassim ouali]

Thanks a lot Sebastian and Carlo for your help and reply. This really helped me.

Best regards,

nassim