How to predict for residuals after running a RE Panel regression to check for heteroscedasticity manually.

[Radhika Channanamchery]

Hi,

After running a RE regression model, I could not run a predict residuals command. I did the same for OLS regression, which shows a constant variance. Do the same results apply to RE also? How do we test for heteroskedasticity if my chosen model is RE regression?

Please help with this
Thank you
Radhika C

[Carlo Lazzaro]

Radhicka:
you may want to consider a visual inspection, as there's no test for heteroskedasticity after -xtreg,re-, as far as I know:

use "https://www.stata-press.com/data/r17/nlswork.dta"
. xtreg ln_wage age, re

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1026                                         min =          1
     Between = 0.0877                                         avg =        6.1
     Overall = 0.0774                                         max =         15

                                                Wald chi2(1)      =    3140.35
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0185667   .0003313    56.04   0.000     .0179174    .0192161
       _cons |   1.120439   .0112038   100.01   0.000      1.09848    1.142398
-------------+----------------------------------------------------------------
     sigma_u |  .36972456
     sigma_e |  .30349389
         rho |  .59743613   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict epsilon, e
. predict fitted, xb

. twoway (scatter epsilon fitted)

[Radhika Channanamchery]

Radhicka:
you may want to consider a visual inspection, as there's no test for heteroskedasticity after -xtreg,re-, as far as I know:

use "https://www.stata-press.com/data/r17/nlswork.dta"
. xtreg ln_wage age, re

Random-effects GLS regression Number of obs = 28,510
Group variable: idcode Number of groups = 4,710

R-squared: Obs per group:
Within = 0.1026 min = 1
Between = 0.0877 avg = 6.1
Overall = 0.0774 max = 15

Wald chi2(1) = 3140.35
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ln_wage | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
age | .0185667 .0003313 56.04 0.000 .0179174 .0192161
_cons | 1.120439 .0112038 100.01 0.000 1.09848 1.142398
-------------+----------------------------------------------------------------
sigma_u | .36972456
sigma_e | .30349389
rho | .59743613 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict epsilon, e
. predict fitted, xb

. twoway (scatter epsilon fitted)

Thank you Carlo for your kind reply. I have one more question.

I have run the above commands in my model and the results show that there is no heteroscedasticity in the RE model.

In addition, I run xtserial command which shows significant p value i.e.., there is serial autocorrelation.

My panel is short panel with four years and 27 districts. Should I use robust standard errors using the command re, vce(cluster clusterid) or should I run only re with default standard error?

Please help with this. Thank you a lot for your support.
Best regards

Radhika

[Carlo Lazzaro]

Radhika:
your diagnosis and therapy are both correct.
You have a N>T panel dataset with serial correlation of the epsilon: therefore, you should go -vce(cluster panelid)- or -robust- standard errors (they do the very same job under -xtreg-).
Unfortunately, the devil is in the details: non-default standard errors with less than 30 clusters are at risk of being more misleading that their (theoretically also misleading) default counterparts (see Cameron_Miller_JHR_2015_February.pdf (ucdavis.edu).
It's up to the researcher to decide which way to go.

[Radhika Channanamchery]

Radhika:
your diagnosis and therapy are both correct.
You have a N>T panel dataset with serial correlation of the epsilon: therefore, you should go -vce(cluster panelid)- or -robust- standard errors (they do the very same job under -xtreg-).
Unfortunately, the devil is in the details: non-default standard errors with less than 30 clusters are at risk of being more misleading that their (theoretically also misleading) default counterparts (see Cameron_Miller_JHR_2015_February.pdf (ucdavis.edu).
It's up to the researcher to decide which way to go.

Thank you Carlo, for your kind reply.

It helps a lot.

Thank you for sharing the reference, which discusses the problem of few clusters and correction mechanisms (though I could not understand it completely ).

Best Regards

Radhika C