[Carlo Lazzaro]

Jana:
no, the opposite holds.
The -xtoverid- null is that -re- is the way to go.
Your S-H test outcome actually rejects the null and, implicitly, points you out to -fe- estimator (with the -vce(cluster clusterid)- standard errors, I would add).
Put differently, -xtoverid- statistic confirms -hausman- test outcome.
Do not be worried about that and keep in mind that, if -fe- is actually the way to go (as in your case), -re- would be inconsistent and, as such, your results will be unreliable, being them statistically signficant or not (that, at the risk of being boring, is not the most relevant issue in inferential statistics).

[Jana Schue]

Hello Carlo,

Could you please help me once more?
I needed to change a bit the control variables of my model.
Now I am a bit confused if fixed effects or random effects are more appropriate.

I run the hausman test and the results are:


. hausman FE_Hausmann_15 RE_Hausmann_15

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| FE_Hausma~15 RE_Hausma~15 Difference Std. err.
-------------+----------------------------------------------------------------
educationa~y | -.2929625 .1761708 -.4691333 .2413822
gender_div~y | 1.995784 1.350281 .6455028 .5457782
background~y | 2.64074 2.128953 .5117864 .3814051
tenure_div~y | .6882448 .811687 -.1234422 .2152849
itraffic | 1.326357 1.258083 .0682744 .023235
ihs_growth | -.2820148 -.2654793 -.0165355 .0072915
TMT_size | .0410745 .1011069 -.0600324 .0326718
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 24.64
Prob > chi2 = 0.0009
(V_b-V_B is not positive definite)


That indicates fixed effects are more appropriate.

But when I do the -xtoverid- test it is still significant and therefore indicate random effects.



Random-effects GLS regression Number of obs = 679
Group variable: group_id Number of groups = 168

Random-effects GLS regression Number of obs = 679
Group variable: group_id Number of groups = 168

R-squared: Obs per group:
Within = 0.6171 min = 1
Between = 0.1335 avg = 4.0
Overall = 0.2330 max = 7

Wald chi2(21) = 1575.99
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. err. adjusted for 168 clusters in group_id)
---------------------------------------------------------------------------------------
| Robust
ln_totalplatact_w | Coefficient std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
educational_diversity | .0663482 .6462079 0.10 0.918 -1.200196 1.332892
gender_diversity | 1.972238 .9075356 2.17 0.030 .1935014 3.750975
background_diversity | 2.653952 1.349596 1.97 0.049 .008793 5.299111
tenure_diversity | .8987573 .4534722 1.98 0.047 .0099682 1.787546
itraffic | .2627056 .1584818 1.66 0.097 -.0479131 .5733243
ihs_growth | .2431311 .1266522 1.92 0.055 -.0051027 .4913649
TMT_size | .0831183 .0917919 0.91 0.365 -.0967906 .2630272
_Iyear_2015 | .7762876 .158279 4.90 0.000 .4660665 1.086509
_Iyear_2016 | 1.343406 .2416147 5.56 0.000 .8698504 1.816963
_Iyear_2017 | 2.146033 .2848947 7.53 0.000 1.587649 2.704416
_Iyear_2018 | 2.866536 .3628715 7.90 0.000 2.155321 3.577751
_Iyear_2019 | 3.373138 .4125678 8.18 0.000 2.56452 4.181756
_Iyear_2020 | 2.707434 .4906644 5.52 0.000 1.745749 3.669118
_Iindustry__2 | -.663232 1.378209 -0.48 0.630 -3.364472 2.038008
_Iindustry__3 | -1.837836 1.167326 -1.57 0.115 -4.125752 .4500796
_Iindustry__4 | -3.165036 1.06093 -2.98 0.003 -5.24442 -1.085651
_Iindustry__5 | -1.924371 .9894228 -1.94 0.052 -3.863604 .014862
_Iindustry__6 | -.762909 .8189995 -0.93 0.352 -2.368119 .8423006
_Iindustry__7 | -4.539799 1.37363 -3.30 0.001 -7.232065 -1.847534
_Iindustry__8 | -1.971971 .9512826 -2.07 0.038 -3.83645 -.1074909
_Iindustry__9 | -1.923242 1.095847 -1.76 0.079 -4.071062 .2245782
_cons | 8.08293 2.598407 3.11 0.002 2.990146 13.17572
----------------------+----------------------------------------------------------------
sigma_u | 2.8039731
sigma_e | .97882364
rho | .89137681 (fraction of variance due to u_i)
---------------------------------------------------------------------------------------

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(group_id)
Sargan-Hansen statistic 76.225 Chi-sq(13) P-value = 0.0000





Which test do I have to follow now?

Best regards
Jana

[Carlo Lazzaro]

Jana:
the -xtoverid- null is that -re- is the way to go.
Your S-H test outcome actually rejects the null and, implicitly, points you out to -fe- estimator (with the -vce(cluster clusterid)- standard errors, I would add).
Put differently, -xtoverid- statistic confirms -hausman- test outcome (despite being a bit limping as - (V_b-V_B is not positive definite)-).

[Jana Schue]

Hi Carlo,

my results changed a bit.
I did the Hausman test and found that fixed effects are more appropriate. At the same time, my other test showed that heteroskedasticity and no autocorrelation occur. So I adjusted my model to include robust standard errors -vce(robust).
Now I am not sure if I still have to go with the Sargan Hansen test and how to interpret the result if P-value=0.000. Do they confirm the use of fixed effects model?

Could you help me once more, please?

Thanks in advance and best regards
Jana