Fixed Effects for Panel Data : How to interpret?

[Manon Raynier Dupeyrat]

Hello,

I am writing a thesis on the impact of ESG scores on firms' market capitalisation. My sample is composed of 655 firms studied between 2017 and 2021. Because I use Panel Data, I have decided to use the Fixed Effects model to draw my regression.

However, I'm having a hard time understanding how I should interpret and understand the results.

. xtreg lnMC lnESG lnCash lnDebt, fe vce(cluster compnam)

Fixed-effects (within) regression Number of obs = 3,275
Group variable: compnam Number of groups = 655

R-squared: Obs per group:
Within = 0.1975 min = 5
Between = 0.4292 avg = 5.0
Overall = 0.4078 max = 5

F(3,654) = 58.12
corr(u_i, Xb) = 0.2792 Prob > F = 0.0000

(Std. err. adjusted for 655 clusters in compnam)
------------------------------------------------------------------------------
| Robust
lnMC | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
lnESG | .7377874 .0705044 10.46 0.000 .599345 .8762297
lnCash | .088393 .0177318 4.98 0.000 .0535748 .1232112
lnDebt | .1232436 .0264432 4.66 0.000 .0713198 .1751674
_cons | 16.18162 .6720601 24.08 0.000 14.86197 17.50128
-------------+----------------------------------------------------------------
sigma_u | .9208027
sigma_e | .33265643
rho | .88455303 (fraction of variance due to u_i)
------------------------------------------------------------------------------

Here I know what to say about the coefficients, st errors and significance.

However what does sigma_u, sigma_e and rho mean ?

[Carlo Lazzaro]

Manon:
welcome to this forum.
What you're asking for is covered in any decent textbook on panel data econometrics (as well as in -xtreg- entry, Stata .pdf manual).
Please note that this issue is one of the builiding blocks of this subject.
In brief, your results show that there's evidence of a panel-wise effect in your data.
Yet, you're recommended to check for the correctness of the functional form of the regressand of your model.
Last but not least, as per FAQ please use CODE delimiters (#-shaped toggle available from the advcanced editor A) to share what you typed and what Stata gave you back. Thanks.