sigma u, sigma e, and rho in panel model

[Mahmoud Gaddallah]

I want to know
1- how sigma u, sigma e, and rho can be calculated by hand or what is the rule of calculation?
2- what is the meaning of each of them, how I can interpret them? and is their meaning differ between fixed effect or random effect?
3- are there any conditions of them to be considered when running regression?

[Carlo Lazzaro]

Mahmoud:
please see -xtreg- entry in Stata .pdf manual.
I' m not clear with question #3.

[Mahmoud Gaddallah]

thank you Mr. Carlo for your fast reply. I already read xtreg manual but I didn't get the point, so I asked if any one can help by answering in a simple manner. the Q#3 is about if (i.e rho = 0.76, or rho= 0.15) are these value effect regression analysis; is there if further investigation should be done on the model based on the rho, in other words is there borderline for rho to trust in the regression results. thank you

[Carlo Lazzaro]

Mahmoud:
1) sigma_u=standard deviation (SD) of the panel-wise effect (ie, u);
2) sigma_e=SD of the idiosyncratic error (ie, epsilon);
3) rho=intraclass correlation of u.

As far as your last question is concerned, the substantive result to look at is the F-test appearing as a footnote of the -xtreg- outcome table whe you use default standard errors: if it reaches statistical significance, there's evidence of a panel effect.

[Rich Goldstein]

a little more to Carlo's excellent answer; rho is in variance terms and this is equal to (sigma_u^2)/(sigma_u^2 + sigma_e^2); also you can think of sigma_e in the same way you think of RMSE from the -regress- command;