How to interpret sigma_u (between subject) and sigma_e (within subject) in Fixed-effects model

[Luana Goveia]

Dear all,

I'm running a fixed-effects model and need help interpreting sigma_u (between subject) and sigma_e (within subject) because an assessor requested me to fully explain their meaning. I have uploaded the output of model below. My dependent variable is school-mean test scores in maths. The independent variables include the years of the tests were performed: pb2009, pb2011, pb2013 and pb2015 compared to the base category pb2007.

Any help will be highly appreciated.

Thank you.

Luana.

[Carlo Lazzaro]

Luana:
please do not post screenshots but share what you typed and what Stata gave you back via CODE delimiters (as recommended by FAQ). Thanks.
See Example #2 under -xtreg- entry, Stata .pdf manual for a comprehensive explanation of what you're interested in.
Obviously, reading a handbook on panel data econometrics can do no harm. Statalisters used to panel data econometrics have on their shelf https://www.stata.com/bookstore/micr...metrics-stata/

[Luana Goveia]

Question not answered....

[Marcos Almeida]

From the example 2 of fixed-effects model , as shared by Carlo, we clearly read that

If the unobserved time-invariant component nu is not correlated with the regressors, estimates from
the fixed-effects model are consistent but inefficient relative to estimates from the random-effects
model. In this case, the interpretation of sigma_u in the coefficient table is the same for the fixed-effects
and random-effects models. However, sigma_u is a nuisance parameter when nu is correlated with the
covariates.

Also, an overarching definition of both is found by reading the Stata Manual reference on the stored results: the first is the "panel-level standard deviation" and the second is standard deviation of E<sub>it

P.S.: Sorry but I couldn't find the correct font for the epsilon.</sub>

[Carlo Lazzaro]

Luana:
your question was (seemingly) left unanswered because it was too broad to be replied in few lines, given that you do not seem to be aware of the building blocks of panel data econometrics.
That said, please note that this forum is based on good willingness of those interested to reply.
Obviously, if the replies are read as unsatisfactory (being that true or false), the original poster is free to address her/his query to other forums/experts.