[Kevin Musoni]

Kevin:
not quite.
I referred to the F-test comparing as a footnote of the -xtreg,fe- outcome table (if you stick with default standard errors):

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey. Young Women 14-26 years of age in 1968)

. xtreg ln_wage c.age##c.age, fe

Fixed-effects (within) regression Number of obs = 28,510
Group variable: idcode Number of groups = 4,710

R-sq: Obs per group:
within = 0.1087 min = 1
between = 0.1006 avg = 6.1
overall = 0.0865 max = 15

F(2,23798) = 1451.88
corr(u_i, Xb) = 0.0440 Prob > F = 0.0000

------------------------------------------------------------------------------
ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0539076 .0028078 19.20 0.000 .0484041 .0594112
|
c.age#c.age | -.0005973 .0000465 -12.84 0.000 -.0006885 -.0005061
|
_cons | .639913 .0408906 15.65 0.000 .5597649 .7200611
-------------+----------------------------------------------------------------
sigma_u | .4039153
sigma_e | .30245467
rho | .64073314 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.74 Prob > F = 0.0000

.

Thank you!

I register that -xttest0- refers to -xtreg,re- only. Parallel, I need to check whether the F-Test on -xtreg,fe- is difficult from zero. As compared to your screenshot above (post #5), my results here are are different to zero (F = 0.0176 --> red colour). As far as I understand you correctly, both -re- and -fe- give me now indication that the data doesnt have panel character and I can move on using POLS instead. Am I right?

xtreg ihs_private_invest $xlist, fe
Fixed-effects (within) regression	Number of obs =	102
Group variable: country_ID	Number of groups =	19
R-sq:	Obs per group:
within = 0.3640	min =	1
between = 0.0424	avg =	5.4
overall = 0.0360	max =	11
	F(18,65) =	2.07
corr(u_i, Xb) = -0.9821	Prob > F =	0.0176
ihs_private_invest Coef.	Std. Err. t P>t	[95% Conf.	Interval]
ihs_public_invest .2106019	.0929392 2.27 0.027	.0249895	.3962144
feed_in_tariff .0258679	2.438288 0.01 0.992	-4.843729	4.895464
RE_quota -30.9277	12.6595 -2.44 0.017	-56.21047	-5.64493
lag_1_log_hydro_share -43.2662	32.88646 -1.32 0.193	-108.945	22.41261
lag_1_log_wind_share .4984848	8.59074 0.06 0.954	-16.65841	17.65538
lag_1_log_other_share .5947077	29.00884 0.02 0.984	-57.33995	58.52936
lag_1_ihs_foss_fuel_prod_pc -.5078519	.2987402 -1.70 0.094	-1.104477	.0887734
lag_1_ihs_energy_imported 2.965144	7.132689 0.42 0.679	-11.27982	17.21011
lag_1_ihs_elect_growth -3.448043	10.11406 -0.34 0.734	-23.64722	16.75113
ihs_gdp_per_cap 9.097981	3.325796 2.74 0.008	2.455909	15.74005
lag_1_ihs_public_RDD .3796887	.2031912 1.87 0.066	-.0261123	.7854896
lag_1_ihs_private_RDD -.7833984	.6166896 -1.27 0.208	-2.015013	.4482157
log_oil_price_opec -3.354455	1.735316 -1.93 0.058	-6.82012	.1112103
log_coal_price 5.18414	3.449341 1.50 0.138	-1.704669	12.07295
ihs_carbon_tax -.1764783	.3693016 -0.48 0.634	-.9140246	.561068
ihs_carbon_permit_price -.4737073	.490767 -0.97 0.338	-1.453837	.5064221
gov_effectiveness -1.14208	2.436401 -0.47 0.641	-6.00791	3.723749
regulatory_quality 2.694556	2.466562 1.09 0.279	-2.231508	7.620621
_cons -172.8241	83.92556 -2.06 0.043	-340.435	-5.213189
sigma_u 9.4711611
sigma_e 2.0360552
rho .95582748	(fraction of variance due to	u_i)
F test that all u_i=0: F(18, 65) = 2.18	Prob > F =	0.0117

[Carlo Lazzaro]

Kevin:
the outcome of the F test that all u_i=0 actually rejects the null (p<0.05): hence, it gives you evidence of a panel-wise effect.