Test for Heterogeneity in Fixed Effects

[Ravi Patel]

Hi,

I am trying to run a fixed effects model on my panel dataset, I have completed a Hausman test which points me towards a fixed effects model, however I am unsure how to run a test for heterogeneity.

Any suggestions would be greatly appreciated!

[Carlo Lazzaro]

Ravi:
welcome to this forum.
If you mean heteroskedasticity, you may want to type -search xttest3-.

[Ravi Patel]

Thank you, great to be here.
Sorry yes I do mean heteroskedasticity, this redirects me to a help page.

Is there a test for heteroskedasticity that I can apply to the panel data for a fixed effects model?

[Carlo Lazzaro]

Ravi:
the following toy-example can be helpful:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1087                                         min =          1
     Between = 0.1006                                         avg =        6.1
     Overall = 0.0865                                         max =         15

                                                F(2, 4709)        =     507.42
corr(u_i, Xb) = 0.0440                          Prob > F          =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0539076    .004307    12.52   0.000     .0454638    .0623515
             |
 c.age#c.age |  -.0005973    .000072    -8.30   0.000    -.0007384   -.0004562
             |
       _cons |    .639913   .0624195    10.25   0.000     .5175415    .7622845
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (4710)  =  4.4e+35
Prob>chi2 =      0.0000


.

The outcome of the community-contributed module -xttest3- shows evidence of heteroskedasticity.
Next step: do nothing, as the cluster robust standard error was already added (and repeating the test is unhelpful, as it assesses the residual distribution - that remains the same- and not the correction due to heteroskedasticity that the cluster-robust standard error applies to take heteroskedasticity into account).
Eventually, please note that, unlike -regress-, the options -robust- and -vce(cluster clusterid)- do the very same job under -xtreg- (that is, they take heteroskedasticity and/or autocorrelation into account).

[Ravi Patel]

Hi Carlo, thank you for the guidance that does make a lot more sense to me. However, unfortunately STATA is not recognising the -xttest3- command once I regress my model.

[Carlo Lazzaro]

Ravi:
being a community-contributed module, follow the instructions to install it typing -search xttest3- from within Stata.

[Ravi Patel]

Thank you Carlo, I have been able to now observe the results for xttest3

Kind Regards,
Ravi