Robust SE test in Panel data "Random Effect Model"?

[Abdelmoneam Khaled]

Dears,
Kindly find my output of the random effect model after determining it by Hausman test.

Iam doing the data test needed like (Hetero,Auto etc) and I found that I have Auto-correlation problem, so I checked for the Cluster robust SE test, however I can not interpret the output of this test.

Another point, I want to test for Heteroskedasticity for Random effect.
And finally what are the expected and needed tests for my model.


Tags: None

[Carlo Lazzaro]

Abdelmoneam:
your attachments (by the way: please share what you typed and what Stata gave you back via CODE delimiters and/or data example/excerpt via -dataex-; see the FAQ on these and other posting-related topics. Thanks) are not attached, actually.

[Abdelmoneam Khaled]

Dears,
Kindly find my output of the random effect model after determining it by Hausman test.

Iam doing the data test needed like (Hetero,Auto etc) and I found that I have Auto-correlation problem, so I checked for the Cluster robust SE test, however I can not interpret the output of this test.

Another point, I want to test for Heteroskedasticity for Random effect.
And finally what are the expected and needed tests for my model.



. xtreg logTotal INS INFO Fopen Topen Diff INF GDP CC,re

Random-effects GLS regression Number of obs = 150
Group variable: Country1 Number of groups = 10

R-sq: Obs per group:
within = 0.1557 min = 15
between = 0.4881 avg = 15.0
overall = 0.4633 max = 15

Wald chi2(8) = 73.45
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
logTotal | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
INS | -.6317093 .2410946 -2.62 0.009 -1.104246 -.1591727
INFO | -.0294963 .012743 -2.31 0.021 -.0544721 -.0045205
Fopen | -.2053808 .1235719 -1.66 0.097 -.4475772 .0368156
Topen | -.0080162 .0047028 -1.70 0.088 -.0172335 .0012012
Diff | .0019685 .0079653 0.25 0.805 -.0136433 .0175802
INF | -.0337759 .0224268 -1.51 0.132 -.0777317 .0101798
GDP | -.0013678 .0051221 -0.27 0.789 -.0114069 .0086712
CC | 4.537129 .7135425 6.36 0.000 3.138612 5.935647
_cons | 9.542764 1.962833 4.86 0.000 5.695682 13.38985
-------------+----------------------------------------------------------------
sigma_u | .41088547
sigma_e | .54630694
rho | .36129845 (fraction of variance due to u_i)
------------------------------------------------------------------------------




. xtreg logTotal INS INFO Fopen Topen Diff INF GDP CC,re vce(cluster Country1) theta

Random-effects GLS regression Number of obs = 150
Group variable: Country1 Number of groups = 10

R-sq: Obs per group:
within = 0.1557 min = 15
between = 0.4881 avg = 15.0
overall = 0.4633 max = 15

Wald chi2(8) = 1732.13
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
theta = .67530324

(Std. Err. adjusted for 10 clusters in Country1)
------------------------------------------------------------------------------
| Robust
logTotal | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
INS | -.6317093 .4718317 -1.34 0.181 -1.556482 .2930638
INFO | -.0294963 .0160755 -1.83 0.067 -.0610036 .002011
Fopen | -.2053808 .2510108 -0.82 0.413 -.697353 .2865913
Topen | -.0080162 .0086158 -0.93 0.352 -.0249028 .0088705
Diff | .0019685 .0036999 0.53 0.595 -.0052832 .0092202
INF | -.0337759 .0410913 -0.82 0.411 -.1143134 .0467616
GDP | -.0013678 .0028828 -0.47 0.635 -.0070181 .0042824
CC | 4.537129 1.555989 2.92 0.004 1.487448 7.586811
_cons | 9.542764 3.982039 2.40 0.017 1.738111 17.34742
-------------+----------------------------------------------------------------
sigma_u | .41088547
sigma_e | .54630694
rho | .36129845 (fraction of variance due to u_i)
------------------------------------------------------------------------------

[Abdelmoneam Khaled]

Dears,
Kindly find my output of the random effect model after determining it by Hausman test.

Iam doing the data test needed like (Hetero,Auto etc) and I found that I have Auto-correlation problem, so I checked for the Cluster robust SE test, however I can not interpret the output of this test.

Another point, I want to test for Heteroskedasticity for Random effect.
And finally what are the expected and needed tests for my model.

 xtreg logTotal INS INFO Fopen Topen Diff INF GDP CC,re

Random-effects GLS regression                   Number of obs     =        150
Group variable: Country1                        Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.1557                                         min =         15
     between = 0.4881                                         avg =       15.0
     overall = 0.4633                                         max =         15

                                                Wald chi2(8)      =      73.45
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
    logTotal |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         INS |  -.6317093   .2410946    -2.62   0.009    -1.104246   -.1591727
        INFO |  -.0294963    .012743    -2.31   0.021    -.0544721   -.0045205
       Fopen |  -.2053808   .1235719    -1.66   0.097    -.4475772    .0368156
       Topen |  -.0080162   .0047028    -1.70   0.088    -.0172335    .0012012
        Diff |   .0019685   .0079653     0.25   0.805    -.0136433    .0175802
         INF |  -.0337759   .0224268    -1.51   0.132    -.0777317    .0101798
         GDP |  -.0013678   .0051221    -0.27   0.789    -.0114069    .0086712
          CC |   4.537129   .7135425     6.36   0.000     3.138612    5.935647
       _cons |   9.542764   1.962833     4.86   0.000     5.695682    13.38985
-------------+----------------------------------------------------------------
     sigma_u |  .41088547
     sigma_e |  .54630694
         rho |  .36129845   (fraction of variance due to u_i)
-----------------------------------------------------------------

 xtreg logTotal INS INFO Fopen Topen Diff INF GDP CC,re vce(cluster Country1) theta

Random-effects GLS regression                   Number of obs     =        150
Group variable: Country1                        Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.1557                                         min =         15
     between = 0.4881                                         avg =       15.0
     overall = 0.4633                                         max =         15

                                                Wald chi2(8)      =    1732.13
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000
theta          = .67530324

                              (Std. Err. adjusted for 10 clusters in Country1)
------------------------------------------------------------------------------
             |               Robust
    logTotal |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         INS |  -.6317093   .4718317    -1.34   0.181    -1.556482    .2930638
        INFO |  -.0294963   .0160755    -1.83   0.067    -.0610036     .002011
       Fopen |  -.2053808   .2510108    -0.82   0.413     -.697353    .2865913
       Topen |  -.0080162   .0086158    -0.93   0.352    -.0249028    .0088705
        Diff |   .0019685   .0036999     0.53   0.595    -.0052832    .0092202
         INF |  -.0337759   .0410913    -0.82   0.411    -.1143134    .0467616
         GDP |  -.0013678   .0028828    -0.47   0.635    -.0070181    .0042824
          CC |   4.537129   1.555989     2.92   0.004     1.487448    7.586811
       _cons |   9.542764   3.982039     2.40   0.017     1.738111    17.34742
-------------+----------------------------------------------------------------
     sigma_u |  .41088547
     sigma_e |  .54630694
         rho |  .36129845   (fraction of variance due to u_i)
-------------------------------------------------------------------------

[Carlo Lazzaro]

Abdelmoneam:
as -hausman- does not support non-default standard errors, you have probably tested -fe- and -re- specifications with default standard errors, obtained -hausman- outcome and then added clustered robust standard errors. This approach is not correct.
You should have used the community-contributed command -xtoverid- to check whether the -re- specification was right for your data.

[Abdelmoneam Khaled]

Thank you Carlo,

the output of the command -xtoverid is

 
xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(Country1)
Sargan-Hansen statistic  2.8e+04  Chi-sq(8)   P-value = 0.0000

So, FE is the appropriate model?

[Carlo Lazzaro]

Yes.

[Abdelmoneam Khaled]

thank you, could you tell me what is the next step ?

[Carlo Lazzaro]

Abdelmoneam:
asd per -xtoverid- outcome, go -fe- .
If you have already invoked cluster robust standard errors, they take both heteroskedasticity and/or autocorrelation into account (just a side note: your number of cluster is probably a bit small to make non-default standard errors work efficiently).
More substantively, you should (have) checked whether your model gives a fair and true view of the data generating process.
To investigate this issue, you can consider the following toy-example:

. use "http://www.stata-press.com/data/r15/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age, fe robust

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

R-sq:                                           Obs per group:
     within  = 0.1026                                         min =          1
     between = 0.0877                                         avg =        6.1
     overall = 0.0774                                         max =         15

                                                F(1,4709)         =     884.05
corr(u_i, Xb)  = 0.0314                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0181349   .0006099    29.73   0.000     .0169392    .0193306
       _cons |   1.148214   .0177153    64.81   0.000     1.113483    1.182944
-------------+----------------------------------------------------------------
     sigma_u |  .40635023
     sigma_e |  .30349389
         rho |  .64192015   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fitted, xb
(24 missing values generated)

. g sq_fitted=fitted^2
(24 missing values generated)

. xtreg ln_wage fitted sq_fitted, fe rob

Fixed-effects (within) 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 = 0.1006                                         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 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      fitted |   7.143466    .738485     9.67   0.000      5.69569    8.591242
   sq_fitted |  -1.816243   .2188485    -8.30   0.000    -2.245289   -1.387198
       _cons |  -5.167788   .6209677    -8.32   0.000    -6.385175   -3.950401
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1,  4709) =   68.87
            Prob > F =    0.0000
*As -test- outcome reaches statistical significance, the model is ill-specified*

See also -linktest- entry in Stata .pdf manual.

[Abdelmoneam Khaled]

Thank you for your quick response,

Actually, my supervisor asked me to check for Stationarity " Unite root test" but my problem is that I cant determine the lag length in panel data set.
So, please suggest me a test to determine the number of lags.

thank you again for your help