Preference to FE or RE model with Driscoll-Kraay SE

[Connor Hart]

Hello,

Is there a similar test that I can run to the Hausman test, with FE/RE models with Driscoll-Kraay standard errors. I am using Driscoll-Kraay standard errors to control for autocorrelation and heteroskedasticity, but the Hausman test won't run returning "sigma option not allowed." Does anyone know a way around this or a similar test that can be run to determine which model is preferred? Thank you for your time.

[Andrew Musau]

You can run a test of overidentifying restrictions by means of an artificial regression. The following replicates the results produced by Schaffer and Stillman's xtoverid command from SSC.

webuse grunfeld, clear
xtreg invest mvalue kstock, re cluster(company)
*RUN XTOVERID COMMAND
xtoverid
*GENERATE MEAN DEVIATED REGRESSORS
foreach var in mvalue kstock{
bys company: egen m`var'=mean(`var')
gen md`var'=`var' -m`var'
}
*ARTIFICIAL REGRESSION
xtreg invest mvalue kstock mdmvalue mdkstock, re cluster(company)
*TEST OF OVERIDENTIFYING RESTRICTIONS
test mdmvalue mdkstock

Res.:

. *RUN XTOVERID COMMAND

. 
. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(company)
Sargan-Hansen statistic   7.320  Chi-sq(2)    P-value = 0.0257

. 
. *ARTIFICIAL REGRESSION

. 
. xtreg invest mvalue kstock mdmvalue mdkstock, re cluster(company)

Random-effects GLS regression                   Number of obs     =        200
Group variable: company                         Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.7668                                         min =         20
     between = 0.8578                                         avg =       20.0
     overall = 0.8359                                         max =         20

                                                Wald chi2(4)      =     125.84
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

                               (Std. Err. adjusted for 10 clusters in company)
------------------------------------------------------------------------------
             |               Robust
      invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1346461    .016897     7.97   0.000     .1015286    .1677635
      kstock |   .0320318   .0836383     0.38   0.702    -.1318962    .1959598
    mdmvalue |  -.0245223   .0149885    -1.64   0.102    -.0538991    .0048546
    mdkstock |   .2780335   .1030273     2.70   0.007     .0761037    .4799633
       _cons |  -8.527168   19.42001    -0.44   0.661    -46.58968    29.53534
-------------+----------------------------------------------------------------
     sigma_u |  90.234986
     sigma_e |  52.767964
         rho |  .74517193   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. *TEST OF OVERIDENTIFYING RESTRICTIONS

. test mdmvalue mdkstock

 ( 1)  mdmvalue = 0
 ( 2)  mdkstock = 0

           chi2(  2) =    7.32
         Prob > chi2 =    0.0257

[Connor Hart]

Thanks for the help -

While the second part of your solution works great, I am having trouble with the 'xtoverid' command returning the following error:

Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS

[Andrew Musau]

Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS

Don't run -xtoverid- after the artificial regression. Run it after the original random effects regression. I think that -xtoverid- is not compatible with -xtscc- (Stata Journal), which gives you DK standard errors. Therefore, my suggestion was to use the artificial regression instead.