Different outcome rhausman vs xtoverid

[Indy Reynders]

Hi everyone.

I'm doing research on the effects of CEO personality on the debt ratio of Belgian listed companies. I'm using panel data for 54 firms, observed over 5 years, with a total number of observations of 270 for each variable (strongly balanced panel).

I tested for heteroscedasticity using both Breusch-Pagan test and White test, but they produced different results. Breusch-Pagan fails to reject homoscedasticity with a p-value = 0,1206, but White does reject it (p-value = 0,0000).

As White-test is a more general form of Breusch-Pagan, and it also tests of non-linear forms of heteroscedasticity, I decided to go with results of White-test and use robust standard errors.

For choosing between FEM or REM however, I ran both -xtoverid-, and -rhausman- command. While -xtoverid- with p-value of 0,0000 implies I should go with Fixed Effects, -rhausman- with a p-value of 0,96 contradicts this and depicts RE is the way to go.

Which one should be followed and what's the difference between them?


Many thanks in advance!

[Carlo Lazzaro]

Indy:
welcome to this forum.
As per FAQ please share via CODE delimiters what you typed and what Stata gives you back. Thanks.
That said, some comments about you post:
- -estat hettest- is not supported by -xtreg- (if the latter is actually the command that you used to run your panel data regression);
- unlike the community-contributed programme -xtoverid-, -hausman- does not support non-default standard errors: hence, I fail to get its use in your case.

[Joro Kolev]

Carlo gives good guidance.

My view is that there is a bit of a trade-off in using user written canned commands, on one hand they make getting output very easy, on the other figuring out what this output means, how to apply the command, and what exactly the command does, is difficult.

Here is a thread by the author of -xtoverid- that you might find useful: https://www.stata.com/statalist/arch.../msg01069.html

If I were you, I would test what you want through the Mundlak devise, see this thread here
https://www.stata.com/statalist/arch.../msg01069.html

and in particular my post in #10, and Eric's post in #11.

[Indy Reynders]

Thanks for the fast responses! This is my Stata output, Carlo.

. xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Grootte, fe robust

Fixed-effects (within) regression               Number of obs      =       270
Group variable: Id                              Number of groups   =        54

R-sq:  within  = 0.2700                         Obs per group: min =         5
       between = 0.0020                                        avg =       5.0
       overall = 0.0114                                        max =         5

                                                F(8,53)            =         .
corr(u_i, Xb)  = -0.3796                        Prob > F           =         .

                                      (Std. Err. adjusted for 54 clusters in Id)
--------------------------------------------------------------------------------
               |               Robust
 Schuldenratio |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
CEOextraversie |   .0506618   .0162008     3.13   0.003      .018167    .0831565
      Leeftijd |   .0029279   .0037137     0.79   0.434    -.0045208    .0103767
      Geslacht |    .122094   .0363564     3.36   0.001     .0491724    .1950156
  Ambtsperiode |  -.0030655   .0027168    -1.13   0.264    -.0085148    .0023838
   CEOeducatie |  -.0631688   .0306594    -2.06   0.044    -.1246637   -.0016739
   CEOervaring |   .0061025   .0416662     0.15   0.884    -.0774694    .0896744
  CEOdualiteit |   .1625837   .0675521     2.41   0.020     .0270913     .298076
           ROA |  -.1709866   .0301336    -5.67   0.000    -.2314271   -.1105462
       Grootte |  -.0000716   .0000656    -1.09   0.280    -.0002031    .0000599
         _cons |   .1010751   .1390782     0.73   0.471    -.1778806    .3800307
---------------+----------------------------------------------------------------
       sigma_u |  .26517523
       sigma_e |   .0880263
           rho |  .90074327   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimate store fe

. xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Grootte, re robust

Random-effects GLS regression                   Number of obs      =       270
Group variable: Id                              Number of groups   =        54

R-sq:  within  = 0.2491                         Obs per group: min =         5
       between = 0.0946                                        avg =       5.0
       overall = 0.1107                                        max =         5

                                                Wald chi2(9)       =     52.15
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

                                      (Std. Err. adjusted for 54 clusters in Id)
--------------------------------------------------------------------------------
               |               Robust
 Schuldenratio |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
CEOextraversie |   .0448348   .0110767     4.05   0.000     .0231248    .0665448
      Leeftijd |   .0021191    .003066     0.69   0.489    -.0038901    .0081283
      Geslacht |   .0707765   .0496508     1.43   0.154    -.0265372    .1680902
  Ambtsperiode |  -.0043701   .0029916    -1.46   0.144    -.0102336    .0014933
   CEOeducatie |  -.0529977   .0210933    -2.51   0.012    -.0943398   -.0116555
   CEOervaring |  -.0267776   .0401245    -0.67   0.505    -.1054201    .0518649
  CEOdualiteit |   .1188195   .0770983     1.54   0.123    -.0322903    .2699293
           ROA |  -.1581985    .035614    -4.44   0.000    -.2280006   -.0883963
       Grootte |   .0000191   .0000355     0.54   0.591    -.0000505    .0000887
         _cons |   .2047551   .1494075     1.37   0.171    -.0880782    .4975884
---------------+----------------------------------------------------------------
       sigma_u |  .20599524
       sigma_e |   .0880263
           rho |  .84559153   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimate store re

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(Id)
Sargan-Hansen statistic  42.860  Chi-sq(9)    P-value = 0.0000

. xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Grootte, fe robust

Fixed-effects (within) regression               Number of obs      =       270
Group variable: Id                              Number of groups   =        54

R-sq:  within  = 0.2700                         Obs per group: min =         5
       between = 0.0020                                        avg =       5.0
       overall = 0.0114                                        max =         5

                                                F(8,53)            =         .
corr(u_i, Xb)  = -0.3796                        Prob > F           =         .

                                      (Std. Err. adjusted for 54 clusters in Id)
--------------------------------------------------------------------------------
               |               Robust
 Schuldenratio |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
CEOextraversie |   .0506618   .0162008     3.13   0.003      .018167    .0831565
      Leeftijd |   .0029279   .0037137     0.79   0.434    -.0045208    .0103767
      Geslacht |    .122094   .0363564     3.36   0.001     .0491724    .1950156
  Ambtsperiode |  -.0030655   .0027168    -1.13   0.264    -.0085148    .0023838
   CEOeducatie |  -.0631688   .0306594    -2.06   0.044    -.1246637   -.0016739
   CEOervaring |   .0061025   .0416662     0.15   0.884    -.0774694    .0896744
  CEOdualiteit |   .1625837   .0675521     2.41   0.020     .0270913     .298076
           ROA |  -.1709866   .0301336    -5.67   0.000    -.2314271   -.1105462
       Grootte |  -.0000716   .0000656    -1.09   0.280    -.0002031    .0000599
         _cons |   .1010751   .1390782     0.73   0.471    -.1778806    .3800307
---------------+----------------------------------------------------------------
       sigma_u |  .26517523
       sigma_e |   .0880263
           rho |  .90074327   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimate store fe

. xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Grootte, re robust

Random-effects GLS regression                   Number of obs      =       270
Group variable: Id                              Number of groups   =        54

R-sq:  within  = 0.2491                         Obs per group: min =         5
       between = 0.0946                                        avg =       5.0
       overall = 0.1107                                        max =         5

                                                Wald chi2(9)       =     52.15
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

                                      (Std. Err. adjusted for 54 clusters in Id)
--------------------------------------------------------------------------------
               |               Robust
 Schuldenratio |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
CEOextraversie |   .0448348   .0110767     4.05   0.000     .0231248    .0665448
      Leeftijd |   .0021191    .003066     0.69   0.489    -.0038901    .0081283
      Geslacht |   .0707765   .0496508     1.43   0.154    -.0265372    .1680902
  Ambtsperiode |  -.0043701   .0029916    -1.46   0.144    -.0102336    .0014933
   CEOeducatie |  -.0529977   .0210933    -2.51   0.012    -.0943398   -.0116555
   CEOervaring |  -.0267776   .0401245    -0.67   0.505    -.1054201    .0518649
  CEOdualiteit |   .1188195   .0770983     1.54   0.123    -.0322903    .2699293
           ROA |  -.1581985    .035614    -4.44   0.000    -.2280006   -.0883963
       Grootte |   .0000191   .0000355     0.54   0.591    -.0000505    .0000887
         _cons |   .2047551   .1494075     1.37   0.171    -.0880782    .4975884
---------------+----------------------------------------------------------------
       sigma_u |  .20599524
       sigma_e |   .0880263
           rho |  .84559153   (fraction of variance due to u_i)
--------------------------------------------------------------------------------

. estimate store re

. rhausman fe re, cluster
bootstrap in progress
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100
--------------------------------------------------------------------------------
Cluster-Robust Hausman Test
(based on 100 bootstrap repetitions)

b1: obtained from xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Gr
> ootte, fe robust
b2: obtained from xtreg Schuldenratio CEOextraversie Leeftijd Geslacht Ambtsperiode CEOeducatie CEOervaring CEOdualiteit ROA Gr
> ootte, re robust

    Test:  Ho:  difference in coefficients not systematic

                  chi2(9) = (b1-b2)' * [V_bootstrapped(b1-b2)]^(-1) * (b1-b2)
                          =        3.79
                Prob>chi2 =      0.9245

-estat hettest- was used after -regress-, not -xtreg-. However, I'm guessing I'm making the wrong assumptions about heteroscedasticity in my FEM. I think I should run -xttest3- if I want to test for heteroscedasticity in FEM, right? But as I'd like to report results of both POLS and FE, should I also report results of both White-test and Wald-test in my research paper?

I'm sorry if these questions sound silly, I'm an economic student working on my master thesis, and I'm not really familiar with statistical analyzing!

[Carlo Lazzaro]

Indy:
what if you add -i.timevar- to the set of your predictors?
Besides:
-xttest3- is the way to go to check for heteroskedasticity after -xtreg,fe-.
However, with 270 panels, the cluster robust standard errors (that take heteroskedasticity and serial correlation into account) shoud be invoked anyhow.
I do not follow you about the need to present POLS in your master thesis if there's a panel-wise effect.
Just out of curiosity: what does your supervisor say about you're research strategy?

[Indy Reynders]

We haven't talked about my analysis yet! I'm not sure why I want to include POLS-regression results. I know it's not common to discuss both FE and POLS, but I read a paper with fairly simular hypotheses to mine doing this, although not really explaining why (see http://dx.doi.org/10.1016/j.sbspro.2015.06.276). I thought it won't do any harm, but the more research I'm doing, the more I feel like there is no good use reporting both. So maybe I shouldn't. Like I said, I'm completely new to "advanced statistics", so it's kind of a trial and error process!