Hello,

I am currently working on my undergrad thesis with the topic factor determinants for imports with panel data of 7 countries and 16 periods (2003-2018), and I am a beginner in econometrics as well as using STATA. There are six variables I used in the model, and I tried to run PLS, Fixed, and Random. The Hausman test suggested using random effects. Here below is the output for Random effects

. xtreg imp gdp pro p ex cons gdpj, robust

Random-effects GLS regression Number of obs = 112
Group variable: neg Number of groups = 7

xtreg imp gdp pro p ex cons gdpj, robust

Random-effects GLS regression Number of obs = 112
Group variable: neg Number of groups = 7

R-sq: Obs per group:
within = 0.0434 min = 16
between = 0.9911 avg = 16.0
overall = 0.7899 max = 16

Wald chi2(6) = 1161.56
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

(Std. Err. adjusted for 7 clusters in neg)
------------------------------------------------------------------------------
| Robust
imp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gdp | .3827558 .0384292 9.96 0.000 .307436 .4580757
pro | .351964 .0729127 4.83 0.000 .2090577 .4948703
p | -.304284 .4000822 -0.76 0.447 -1.088431 .4798627
ex | -.0060916 .0239385 -0.25 0.799 -.0530103 .040827
cons | -1.558034 3.330587 -0.47 0.640 -8.085865 4.969797
gdpj | 2.20647 5.615751 0.39 0.694 -8.800199 13.21314
_cons | 1.985671 22.32831 0.09 0.929 -41.777 45.74835
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .41758527
rho | 0 (fraction of variance due to u_i)
----------------------------------------------------------------------------

which gdp stands for exporter's GDP, pro as exporter's production, p as export's price, ex as exchange rates, cons as importer's consumption, gdpj as importer's GDP. I also run the Breusch-Pagan LM test for the same model (neg as cross-section countries)

. quietly xtreg imp gdp pro p ex cons gdpj, re i(neg)

. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

imp[neg,t] = Xb + u[neg] + e[neg,t]

Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
imp | .7844583 .8856965
e | .1743775 .4175853
u | 0 0

Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000


My questions are:

1. what's sigma_u and rho actually indicates? is it evidence that there were no individual effects?
2. I have limited proficiency in English, and I couldn't grasp the main idea of why chibar2(01) value is 0. Is that mean the model actually not quite right?
3. If turns out the LM test is valid, is that mean PLS is preferred? but I read somewhere on the internet that PLS actually not suitable for panel data (as if means nothing).