Test for heteroskedasticity in model with random effects

[Jana Schue]

Hello everyone,

I am using an unbalanced panel dataset and want to use -xtreg-.
Actually I am a bit confused regarding testing my model.
I started with PB-LM test and F-test to find random and fixed effects and found both.
Afterwards I run a Hausman test which recommanded me to use re model.
Furthermore I ran a test for autocorrlation which was significant and therefore I idenfitied autocorrelation.

Now i want to do a test for heteroskedasticity. I know that for a fixed effects model I can use the -xttest3- command. But since I identified random effects are appropriate I need to run a different test.
In my research I found that I may have to switch to -xtgls- and use the -xttest2- to identify weather there is heteroskedasticity or not, but I get an error:

Code:

local controls "fs lev itq rdi growth cap_exp"
xtgls tq cvc1 `controls'
estimates store RE
xttest2

Error:

.         local controls "fs lev itq rdi growth cap_exp"

.         xtgls tq cvc1 `controls'

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        homoskedastic
Correlation:   no autocorrelation

Estimated covariances      =         1          Number of obs     =        182
Estimated autocorrelations =         0          Number of groups  =         17
Estimated coefficients     =         8          Obs per group:
                                                              min =          8
                                                              avg =   10.70588
                                                              max =         11
                                                Wald chi2(7)      =     934.72
Log likelihood             = -127.4512          Prob > chi2       =     0.0000

------------------------------------------------------------------------------
          tq | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        cvc1 |  -.0019507   .0010543    -1.85   0.064     -.004017    .0001157
          fs |  -.1371241   .0409864    -3.35   0.001    -.2174559   -.0567922
         lev |    .067518   .0457678     1.48   0.140    -.0221852    .1572211
         itq |   1.038877   .0551196    18.85   0.000     .9308442    1.146909
         rdi |   2.562943   .9972166     2.57   0.010     .6084342    4.517451
      growth |   .0984387   .1628702     0.60   0.546     -.220781    .4176585
     cap_exp |   3.262956   1.287108     2.54   0.011     .7402705    5.785642
       _cons |   1.158686   .4346392     2.67   0.008     .3068091    2.010563
------------------------------------------------------------------------------

.         estimates store RE

.         xttest2

Correlation matrix of residuals is singular.
not possible with test

Is there anything wrong in my command or is it still the worng command to use?
Or do I still have to stick to -xtreg- and the fe model, since after running a Sargan Hansen test (-xtoverid-) it recommends me to go with the fe model. So do I have to do the test for heteroskedasticity after my Sargan Hansen test? Actually I think I have to do it before.


Hopefully you can help me I got a bit confused with all these tests.


Best regards

Jana

[Carlo Lazzaro]

Jana:

Furthermore I ran a test for autocorrlation which was significant and therefore I idenfitied autocorrelation.

Your statement is enough to go -xtreg,re robust- or, in the very same fashion, -xtreg,re vce(cluster clusterid)- as both these options take care of heteroskedasticity and/or autocorrelation.

[Jana Schue]

Carlo:
thanks for your fast answer. I am thinking in the same way.

But for my thesis it is needed that I show how I tested for heteroskedasticity.
Do you have an advice for me how to do it?

Best regards

Jana

[Carlo Lazzaro]

Jana:
you can use visual inspection, as in the following toy-example (in which -e- distribution is heteroskedstic):

use "https://www.stata-press.com/data/r16/nlswork.dta"

. xtreg ln_wage c.age##c.age, re

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

R-sq:                                           Obs per group:
     within  = 0.1087                                         min =          1
     between = 0.1015                                         avg =        6.1
     overall = 0.0870                                         max =         15

                                                Wald chi2(2)      =    3388.51
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0590339   .0027172    21.73   0.000     .0537083    .0643596
             |
 c.age#c.age |  -.0006758   .0000451   -15.00   0.000    -.0007641   -.0005876
             |
       _cons |   .5479714   .0397476    13.79   0.000     .4700675    .6258752
-------------+----------------------------------------------------------------
     sigma_u |   .3654049
     sigma_e |  .30245467
         rho |  .59342665   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict res, e

. predict fitted, xb

. twoway (scatter res fitted)

.

[Jana Schue]

Thank you Carlo!

Am I correct to interpret this output as having heteroskedasticity because of the clustering at 0 and the cone shape?

Thank you for all the help!

Kind regards,
Jana

[Carlo Lazzaro]

Jana:
yes, you are.
But are you sure that you've plotted the entire residual distribution vs. fitted values?

[Jana Schue]

Carlo:
thanks for confirmation!

I think so. I followed your instructions.

Code:

local controls "fs lev itq rdi growth cap_exp"
    xtreg tq cvc `controls' i.fyear, re 
    predict res, e
    predict fitted, xb
    twoway (scatter res fitted)

Thanks for all your help.

Best regards
Jana

[Carlo Lazzaro]

Jana:
another more substantive issue rests on the correct specification of your model, as a misspecified model can cause heteroskedastciity among other nuisances.
If you're 100% sure that your model is not misspecified, go -xtreg,re- with non-default standard errors as per #2. This way you will manage both heteroskedasticity and autocorrelation.
Eventually, you can test the joint significance of -i.fyear- via -testparm-.

[Remy Delacourt]

Jana:
another more substantive issue rests on the correct specification of your model, as a misspecified model can cause heteroskedastciity among other nuisances.
If you're 100% sure that your model is not misspecified, go -xtreg,re- with non-default standard errors as per #2. This way you will manage both heteroskedasticity and autocorrelation.
Eventually, you can test the joint significance of -i.fyear- via -testparm-.

Hello Mr. Lazzaro,

I have a solution as I am in the same situation, what if :

As we know that the classic Breusch-Pagan will not be directly applicable to panel data, we could still apply it by extracting the residuals of the random effect model, applying a regression using the residuals as dependant variable and we will be able to detect heteroscedasticity ?

[Carlo Lazzaro]

Remy:
welcome to this forum.
See stata - Testing for heteroskedasticity in panel data vs time series? - Economics Stack Exchange