Standard Error of Estimation in Panel Data Regression

[Ruowen Shen]

Hello,
I am working on a panel data, N=600, T=10. After running the regression analysis, -xtreg, fe-, I predicted individual unit effect, -predict, u-. Im addition, I want to know the standard error of estimate. I have a a couple of questions regarding the standard error of estimation in panel data analysis.
1. To get the standard error of estimation, should I run the command -predict, e- , which gave me the difference between predicted value and observed value at each time point for each unit?
2. If the answer to the first question is YES, then, how can I get the unit-specific standard error of estimation? Can I simply calculate the standard deviation of the "e" for each unit? In that way, the N in calculating the standard deviation will be 10, because of 10 time points. Is it correct?

Many thanks,

[Carlo Lazzaro]

Ruowen:
my guess is that you're looking for the square root of -sigma_u-, that appears in the -xtreg.fe- output table.

[Joro Kolev]

Generally you are using terminology which is uncommon both in econometrics and in the Stata community. Stata calls your "standard error of estimation" by the name Root Mean Square Error.

The concept of Root Mean Square Error becomes ambiguous, because it might mean at least three different things. As Carlo says, some of these quantities are reported in the output post -xtreg-.

The model is Yit = b*Xit + Ui + Vit.

So there are at least three things that can take the place of Root Mean Square Error of standard linear regression: std(Ui), std(Vit), std(Ui + Vit). It depends what you want.

[Ruowen Shen]

Thank you very much, Carlo and Joro. May I first clarify these concepts with you?

1. After I run the fixed effect regression model, I had -predict, u-, which is the individual unit effect (Ui) in panel data fixed effect model, correct? And the value of "u" is constant for each unit over time.
2. However, I also want to know the the amount of error in predicted values, which I assume should be Vit. So, I had -predict, e-. The value of Vit is different overtime and across units. Is it correct?
3. If yes, should I focus on -sigma_e- instead?
4. Lastly, -sigma- indicators in the output are for the whole model. However, I need to know the unit-specific error in predicted values. That's why I asked at the beginning whether I can simply calculate the standard deviation of the "e" for each unit? In that way, the N in calculating the standard deviation will be 10, because of having 10 time points for each unit. Is it correct?

Thank you very much for any further clarification and suggestions.

[Carlo Lazzaro]

Ruowen:
1. Correct.
2. Correct.
3. -sigma_e- is the standard deviation of the systematic error epsilon. It considers the whole model..
4. Admittedly, I've never come across this issue.
That said, you may want to consider:

use "https://www.stata-press.com/data/r16/nlswork.dta"
xtreg ln_wage c.age##c.age,fe
predict epsilon, e
bysort idcode: sum epsilon

[Ruowen Shen]

Thank you very much, Carlo! Have a good weekend!