Hausman test

Eline Meijer

Join Date: Dec 2022

Posts: 7
#1

Hausman test

13 Dec 2022, 13:55

Hi,

For my thesis I am doing a panel data analyses, and I am trying to perform an Haussmen test to determine random or fixed effects model.
However, with the outcome of the haussman test I get the following output.
How can I best solve this problem? (I already tried the sigmamore test, but this still does not work)

hausman fe re, sigmamore

Note: the rank of the differenced variance matrix (0) does not equal the number of coefficients
being tested (4); be sure this is what you expect, or there may be problems computing the
test. Examine the output of your estimators for anything unexpected and possibly consider
scaling your variables so that the coefficients are on a similar scale.

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference Std. err.
-------------+----------------------------------------------------------------
sacd | .0009592 .0009592 0 0
meanvaluee~c | 915.4605 915.4605 0 0
industrydu~y | -9.789869 -9.789869 0 0
firmsizeco~l | -3.293249 -3.293249 0 0
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Thankyou!
Tags: None
Andrew Musau

Join Date: Oct 2014

Posts: 10084
#2

13 Dec 2022, 14:18

Either there is an issue with your data or you stored estimates from the same model twice. Can you show the full set of commands that you ran and the exact Stata output? Place these within CODE delimiters

Code:

as I do here
1 like
Comment

Eline Meijer

Join Date: Dec 2022
Posts: 7

13 Dec 2022, 14:28

Hi Andrew,

Thankyou for your reply.
Hopefully I used the Code delimiters correctly. :

Code:

xtreg salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol ind
> ustrydummy, fe
note: meanvalueenvironmentalmunificenc omitted because of collinearity.
note: meanvaluedynamism omitted because of collinearity.
note: industrydummy omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =        254
Group variable: gvkey                           Number of groups  =        117

R-squared:                                      Obs per group:
     Within  = 0.0001                                         min =          1
     Between = 0.0038                                         avg =        2.2
     Overall = 0.0141                                         max =          6

                                                F(2,135)          =       0.00
corr(u_i, Xb) = 0.1174                          Prob > F          =     0.9963

--------------------------------------------------------------------------------------------------
                salesgrowth1year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------------------------+----------------------------------------------------------------
                            sacd |  -1.37e-06   .0000264    -0.05   0.959    -.0000535    .0000508
meanvalueenvironmentalmunificenc |          0  (omitted)
               meanvaluedynamism |          0  (omitted)
                 firmsizecontrol |  -.0243331   .4024349    -0.06   0.952    -.8202255    .7715592
                   industrydummy |          0  (omitted)
                           _cons |   .4410763   2.960823     0.15   0.882    -5.414521    6.296674
---------------------------------+----------------------------------------------------------------
                         sigma_u |   .7035624
                         sigma_e |  1.5188745
                             rho |  .17666081   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------
F test that all u_i=0: F(116, 135) = 0.71                    Prob > F = 0.9689

. xtreg salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol    
>   industrydummy, re
note: meanvaluedynamism omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =        254
Group variable: gvkey                           Number of groups  =        117

R-squared:                                      Obs per group:
     Within  = 0.0000                                         min =          1
     Between = 0.0739                                         avg =        2.2
     Overall = 0.0570                                         max =          6

                                                Wald chi2(4)      =      15.06
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0046

--------------------------------------------------------------------------------------------------
                salesgrowth1year | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------------------------+----------------------------------------------------------------
                            sacd |   2.08e-08   .0000189     0.00   0.999     -.000037     .000037
meanvalueenvironmentalmunificenc |   19.73189   11.16671     1.77   0.077    -2.154466    41.61825
               meanvaluedynamism |          0  (omitted)
                 firmsizecontrol |  -.0184656   .0373252    -0.49   0.621    -.0916216    .0546904
                   industrydummy |   -.137256    .125126    -1.10   0.273    -.3824984    .1079865
                           _cons |   1.032992   .7884602     1.31   0.190    -.5123619    2.578345
---------------------------------+----------------------------------------------------------------
                         sigma_u |          0
                         sigma_e |  1.5188745
                             rho |          0   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------  estimate store re

. estimate store fe

. hausman fe re

Note: the rank of the differenced variance matrix (0) does not equal the number of coefficients
        being tested (4); be sure this is what you expect, or there may be problems computing the
        test.  Examine the output of your estimators for anything unexpected and possibly consider
        scaling your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference       Std. err.
-------------+----------------------------------------------------------------
        sacd |    2.08e-08     2.08e-08               0               0
meanvaluee~c |    19.73189     19.73189               0               0
firmsizeco~l |   -.0184656    -.0184656               0               0
industrydu~y |    -.137256     -.137256               0               0
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

    chi2(0) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            = 0.00
Prob > chi2 =    .
(V_b-V_B is not positive definite)

Comment

Andrew Musau

Join Date: Oct 2014

Posts: 10084
#4

13 Dec 2022, 14:38

Originally posted by Eline Meijer View Post

Hopefully I used the Code delimiters correctly. :

Yes, thank you. You did store the same model twice. You need

Code:

xtreg salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol industrydummy, fe est sto fe xtreg salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol industrydummy, re est sto re hausman fe re

Some Notes:

1. Rescale the sacd variable. Its coefficients are too small.

Code:

*Express the variable in millions replace sacd= sacd/1e+6

2. If you have 30+ firms, you should calculate cluster robust standard errors to take care of heteroscedasticity and arbitrary forms of serial correlation
3. If you do so, look at the community contributed command xtoverid from SSC to help you choose between FE and RE

Code:

ssc install xtoverid, replace help xtoverid

Last edited by Andrew Musau; 13 Dec 2022, 14:43.
Comment

Eline Meijer

Join Date: Dec 2022
Posts: 7

13 Dec 2022, 15:29

Hi Andrew,

Thanks for your reply!
Unfortunately, I still get the same notificitation after conducting these steps.
In addition, do you maybe know how I can assure that variable 'environmental dynamism' is also taken into account in the analyses?

Code:

 replace sacd= sacd/1e+6
variable sacd was long now double
(263 real changes made)
 ssc install xtoverid, replace
checking xtoverid consistency and verifying not already installed...
installing into C:\Users\Eline\ado\plus\...
installation complete.

. help xtoverid

. xtreg salesgrowth3year sacd meanvaluedynamism meanvalueenvironmentalmunificenc firmsizecontrol industryd
> ummy, fe
note: meanvaluedynamism omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
     Within  = 0.0087                                         min =          1
     Between = 0.0365                                         avg =       50.0
     Overall = 0.0076                                         max =      1,826

                                                F(4,2595)         =       5.72
corr(u_i, Xb) = -0.3950                         Prob > F          =     0.0001

--------------------------------------------------------------------------------------------------
                salesgrowth3year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------------------------+----------------------------------------------------------------
                            sacd |  -13560.93    2041686    -0.01   0.995     -4017060     3989938
               meanvaluedynamism |          0  (omitted)
meanvalueenvironmentalmunificenc |   932.2239   410.1642     2.27   0.023     127.9418    1736.506
                 firmsizecontrol |  -3.524774   1.969087    -1.79   0.074    -7.385914    .3363665
                   industrydummy |  -10.18236   4.587859    -2.22   0.027    -19.17859   -1.186123
                           _cons |   74.62328   47.16309     1.58   0.114    -17.85781    167.1044
---------------------------------+----------------------------------------------------------------
                         sigma_u |  64.481602
                         sigma_e |  252.86382
                             rho |  .06105727   (fraction of variance due to u_i)



.  xtreg salesgrowth3year sacd meanvaluedynamism meanvalueenvironmentalmunificenc firmsizecontrol industry
> dummy, re
note: meanvaluedynamism omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
Within  = 0.0087                                         min =          1
Between = 0.1521                                         avg =       50.0
Overall = 0.0086                                         max =      1,826

Wald chi2(4)      =      23.08
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0001


salesgrowth3year  Coefficient  Std. err.      z    P>z     [95% conf. interval]

sacd    959.2338   8060.533     0.12   0.905    -14839.12    16757.59
meanvaluedynamism           0  (omitted)
meanvalueenvironmentalmunificenc    915.4605    402.338     2.28   0.023     126.8925    1704.028
firmsizecontrol   -3.293249   1.877834    -1.75   0.079    -6.973736    .3872383
industrydummy   -9.789869   4.461124    -2.19   0.028    -18.53351   -1.046227
_cons    71.09942   29.58207     2.40   0.016     13.11962    129.0792

sigma_u           0
sigma_e   252.86382
rho           0   (fraction of variance due to u_i)


. est store fe

. est store re

. hausman fe re

Note: the rank of the differenced variance matrix (0) does not equal the number of coefficients being
tested (4); be sure this is what you expect, or there may be problems computing the test.  Examine
the output of your estimators for anything unexpected and possibly consider scaling your variables
so that the coefficients are on a similar scale.

Coefficients ----
(b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
fe           re         Difference       Std. err.

sacd     959.2338     959.2338               0               0
meanvaluee~c     915.4605     915.4605               0               0
firmsizeco~l    -3.293249    -3.293249               0               0
industrydu~y    -9.789869    -9.789869               0               0

b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

chi2(0) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 0.00
Prob > chi2 =    .
(V_b-V_B is not positive definite)

.

Thanks a lot in advance!
Eline

Comment

Andrew Musau

Join Date: Oct 2014

Posts: 10084
#6

13 Dec 2022, 15:59

Look at what I do in #4. I first run the fixed effects regression, store its estimates and then run the random effects regression and store its estimates. This is not what you do in #5. For the suggestion to cluster standard errors and use xtoverid, you need:

Code:

xtreg salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol industrydummy, re robust xtoverid

A significant Sargan-Hansen statistic implies that the random effects estimator is inconsistent and therefore you should choose fixed effects.
Comment
Eline Meijer

Join Date: Dec 2022

Posts: 7
#7

13 Dec 2022, 16:06

This helps, thanks a lot!
Comment
Andrew Musau

Join Date: Oct 2014

Posts: 10084
#8

13 Dec 2022, 16:34

Originally posted by Eline Meijer View Post

In addition, do you maybe know how I can assure that variable 'environmental dynamism' is also taken into account in the analyses?

The output indicates that this variable is collinear with some other variable(s) in the regression. If it is a control variable, don't worry about it and proceed as its effect is already accounted for. If it is an important variable and you need to study its effect, then you need to find what other variables it is collinear with and then decide how you want to reformulate the model (e.g., including this variable and dropping the other one(s)). Start by looking at simple correlation coefficients for variables in your model.

Code:

correlate salesgrowth1year sacd meanvalueenvironmentalmunificenc meanvaluedynamism firmsizecontrol industrydummy
Comment

Eline Meijer

Join Date: Dec 2022
Posts: 7

14 Dec 2022, 01:23

Hi Andrew,

Thanks for your reply.
I tried this, and accordingly to exclude the correlated variables, but I still get this notification.
Since environmental dynamism and environmental munificence are my moderating variables, I cannot exclude this variable in the analyses.

Code:

. correlate salesgrowth3year sacd meanvalueenvironmentalmunificenc meanvaluedynamism industrydummy dummyva
> riable firmsizecontrol
(obs=2,652)

             | sa~3year     sacd meanva~c meanva~m indust~y dummyv~e firmsi~l
-------------+---------------------------------------------------------------
salesg~3year |   1.0000
        sacd |  -0.0009   1.0000
meanvaluee~c |   0.0782  -0.0065   1.0000
meanvalued~m |  -0.0328  -0.0136   0.2314   1.0000
industrydu~y |  -0.0683   0.0145  -0.4477   0.2871   1.0000
dummyvaria~e |  -0.0247   0.0387   0.0000  -0.0000   0.0000   1.0000
firmsizeco~l |  -0.0400   0.0629  -0.1711  -0.2774  -0.0738   0.0791   1.0000


. xtreg salesgrowth3year sacd meanvaluedynamism firmsizecontrol industrydummy dummyvariable, fe
note: meanvaluedynamism omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
     Within  = 0.0074                                         min =          1
     Between = 0.0004                                         avg =       50.0
     Overall = 0.0042                                         max =      1,826

                                                F(4,2595)         =       4.87
corr(u_i, Xb) = -0.6825                         Prob > F          =     0.0007

-----------------------------------------------------------------------------------
 salesgrowth3year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
------------------+----------------------------------------------------------------
             sacd |   33461.99    2043313     0.02   0.987     -3973226     4040150
meanvaluedynamism |          0  (omitted)
  firmsizecontrol |  -4.589953   1.916176    -2.40   0.017    -8.347341    -.832565
    industrydummy |  -15.37596   4.065132    -3.78   0.000    -23.34719   -7.404727
    dummyvariable |  -4.258121   3.188154    -1.34   0.182     -10.5097    1.993462
            _cons |   129.7785   45.49229     2.85   0.004     40.57366    218.9834
------------------+----------------------------------------------------------------
          sigma_u |  138.67703
          sigma_e |  253.02842
              rho |  .23099378   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
F test that all u_i=0: F(52, 2595) = 0.02                    Prob > F = 1.0000

. xtreg salesgrowth3year sacd meanvaluedynamism industrydummy dummyvariable, fe
note: meanvaluedynamism omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
     Within  = 0.0053                                         min =          1
     Between = 0.0006                                         avg =       50.0
     Overall = 0.0011                                         max =      1,826

                                                F(3,2596)         =       4.57
corr(u_i, Xb) = -0.8899                         Prob > F          =     0.0034

-----------------------------------------------------------------------------------
 salesgrowth3year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
------------------+----------------------------------------------------------------
             sacd |    60172.8    2045146     0.03   0.977     -3950109     4070455
meanvaluedynamism |          0  (omitted)
    industrydummy |  -14.27493   4.042746    -3.53   0.000    -22.20226   -6.347598
    dummyvariable |  -4.192154   3.190943    -1.31   0.189     -10.4492    2.064896
            _cons |   96.27985   43.32892     2.22   0.026     11.31711    181.2426
------------------+----------------------------------------------------------------
          sigma_u |  254.02055
          sigma_e |   253.2592
              rho |  .50150084   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
F test that all u_i=0: F(52, 2596) = 0.01                    Prob > F = 1.0000

.  correlate salesgrowth3year sacd meanvalueenvironmentalmunificenc meanvaluedynamism dummyvariable
(obs=2,652)

             | sa~3year     sacd meanva~c meanva~m dummyv~e
-------------+---------------------------------------------
salesg~3year |   1.0000
        sacd |  -0.0009   1.0000
meanvaluee~c |   0.0782  -0.0065   1.0000
meanvalued~m |  -0.0328  -0.0136   0.2314   1.0000
dummyvaria~e |  -0.0247   0.0387   0.0000  -0.0000   1.0000


.  xtreg salesgrowth3year sacd meanvalueenvironmentalmunificenc meanvaluedynamism dummyvariable, fe
note: meanvaluedynamism omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
     Within  = 0.0067                                         min =          1
     Between = 0.0000                                         avg =       50.0
     Overall = 0.0030                                         max =      1,826

                                                F(3,2596)         =       5.85
corr(u_i, Xb) = -0.7407                         Prob > F          =     0.0006

--------------------------------------------------------------------------------------------------
                salesgrowth3year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------------------------+----------------------------------------------------------------
                            sacd |   38222.36    2043624     0.02   0.985     -3969076     4045520
meanvalueenvironmentalmunificenc |   1448.301   358.4444     4.04   0.000      745.435    2151.167
               meanvaluedynamism |          0  (omitted)
                   dummyvariable |  -3.900198   3.184474    -1.22   0.221    -10.14456    2.344168
                           _cons |   9.266159   37.63718     0.25   0.806    -64.53577    83.06809
---------------------------------+----------------------------------------------------------------
                         sigma_u |  162.15972
                         sigma_e |  253.07213
                             rho |  .29107155   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------
F test that all u_i=0: F(52, 2596) = 0.01                    Prob > F = 1.0000

.  xtreg salesgrowth3year sacd meanvaluedynamism dummyvariable, fe
note: meanvaluedynamism omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =      2,652
Group variable: sabd                            Number of groups  =         53

R-squared:                                      Obs per group:
     Within  = 0.0005                                         min =          1
     Between = 0.0017                                         avg =       50.0
     Overall = 0.0000                                         max =      1,826

                                                F(2,2597)         =       0.61
corr(u_i, Xb) = -0.9585                         Prob > F          =     0.5411

-----------------------------------------------------------------------------------
 salesgrowth3year | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
------------------+----------------------------------------------------------------
             sacd |   36219.58    2049645     0.02   0.986     -3982884     4055324
meanvaluedynamism |          0  (omitted)
    dummyvariable |  -3.538488   3.192594    -1.11   0.268    -9.798776    2.721799
            _cons |   20.06457   37.65279     0.53   0.594    -53.76795    93.89709
------------------+----------------------------------------------------------------
          sigma_u |  153.24704
          sigma_e |  253.81776
              rho |  .26715003   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
F test that all u_i=0: F(52, 2597) = 0.00                    Prob > F = 1.0000

Comment

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17673

#10

14 Dec 2022, 02:04

Eline:
as an aside to Andrew's excellent advice:
1) if your -meanvaluedynamism- is panel-specific and time-invariant, as expected the -fe- estimator will wipe it out;
2) your within R-sq is negligible. This result should warn you about the lack of a panel-wise effect (that is also echoed by the lack of statistical significance of the F-test on u_i);
3) the panel-specific number of observations is totally unbalanced, as they range from 1 to 1826. I would be really queasy about running a panel data regression on a similar dataset and probably switch to a pooled OLS. In addition, even assuming the existence of a panel-wise effect, the relevance of the T dimension would make me to switch from -xtreg,fe- to -xtregar,fe-;
4) I would check the correctness of the functional form of the regresssand via the following approach, that mimicks -linktest-;

Code:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age i.year, fe

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

R-squared:                                      Obs per group:
     Within  = 0.1162                                         min =          1
     Between = 0.1078                                         avg =        6.1
     Overall = 0.0932                                         max =         15

                                                F(16,23784)       =     195.45
corr(u_i, Xb) = 0.0613                          Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0728746   .0107894     6.75   0.000     .0517267    .0940224
             |
 c.age#c.age |  -.0010113    .000061   -16.57   0.000    -.0011309   -.0008917
             |
        year |
         69  |   .0647054   .0158222     4.09   0.000     .0336928     .095718
         70  |   .0284423   .0234621     1.21   0.225     -.017545    .0744295
         71  |   .0579959   .0326524     1.78   0.076    -.0060048    .1219967
         72  |   .0510671   .0422995     1.21   0.227    -.0318426    .1339769
         73  |   .0424104    .052118     0.81   0.416    -.0597442    .1445651
         75  |   .0151376   .0717194     0.21   0.833    -.1254371    .1557123
         77  |   .0340933   .0918106     0.37   0.710    -.1458613    .2140478
         78  |   .0537334   .1023339     0.53   0.600    -.1468475    .2543143
         80  |   .0369475   .1221806     0.30   0.762    -.2025343    .2764293
         82  |   .0391687   .1423573     0.28   0.783    -.2398606     .318198
         83  |    .058766   .1523743     0.39   0.700    -.2398974    .3574294
         85  |   .1042758   .1726431     0.60   0.546    -.2341157    .4426673
         87  |   .1242272   .1930108     0.64   0.520    -.2540863    .5025406
         88  |   .1904977   .2068016     0.92   0.357    -.2148466     .595842
             |
       _cons |   .3937532   .2001741     1.97   0.049     .0013992    .7861072
-------------+----------------------------------------------------------------
     sigma_u |  .40275174
     sigma_e |  .30127563
         rho |  .64120306   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23784) = 8.75                 Prob > F = 0.0000

. predict fitted, xb
(24 missing values generated)

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

. xtreg ln_wage fitted sq_fitted, fe

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

R-squared:                                      Obs per group:
     Within  = 0.1164                                         min =          1
     Between = 0.1094                                         avg =        6.1
     Overall = 0.0941                                         max =         15

                                                F(2,23798)        =    1568.17
corr(u_i, Xb) = 0.0619                          Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   2.012332   .3976379     5.06   0.000     1.232936    2.791727
   sq_fitted |  -.3040363   .1193029    -2.55   0.011    -.5378776   -.0701949
       _cons |  -.8379964   .3301923    -2.54   0.011    -1.485194   -.1907985
-------------+----------------------------------------------------------------
     sigma_u |  .40239556
     sigma_e |  .30114591
         rho |  .64099409   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.75                 Prob > F = 0.0000

. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1, 23798) =    6.49
            Prob > F =    0.0108

.

In the previous toy-example the model is clearly misspecified as the -test- outcome on -sq_fitted- reaches statistical significance;

5) as Andrew already advised you about, you should go -robust- standard errors.

Kind regards,
Carlo
(Stata 19.0)

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Andrew Musau

Join Date: Oct 2014

Posts: 10084
#11

14 Dec 2022, 03:39

Carlo Lazzaro is more attentive than I am, and I naturally agree with all of his excellent points.
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Carlo Lazzaro

Join Date: Apr 2014

Posts: 17673
#12

14 Dec 2022, 03:44

Andrew Musau : I simply took shameless advantage from your excellent assist!

Kind regards,
Carlo
(Stata 19.0)
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Eline Meijer

Join Date: Dec 2022

Posts: 7
#13

15 Dec 2022, 07:06

Andrew and Carlo,
Thankyou very much for the responses!
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