Is it possible to make the Hausman specification test by comparing two-way error component models?

[Lucas Bordure]

Good morning.
I would like to know if the comparison between the two-way effect random effects error component model and the two-way effect fixed effects error component model is possible to run in the Hausman specification test.
Here is my command:

*Two-way random effects error component model | Two-way fixed effects error component model Hausman test
xtreg firm_performance intangible_assets enterprise_value market_capitalization leverage stock_growth dividend_payout_ratio stock_volatility i.year i.industry_n, re
estimates store random
xtreg firm_performance intangible_assets enterprise_value market_capitalization leverage stock_growth dividend_payout_ratio stock_volatility i.year i.industry_n, fe
estimates store fixed
hausman fixed random

[Andrew Musau]

Is your data at the firm level? It is a common misconception that you can add additional random effects using dummies. This applies only to fixed effects. xtreg can estimate a two level (random-intercept) model, but nothing more than that. If you want to estimate a two-way random effects model, then you have to reach for mixed. Then you can use the Hausman test to compare both sets of results. However, you are making very strong assumptions by not clustering your standard errors. You need to justify these assumptions.

[Joro Kolev]

Stata does not have a two way random effects model in the -xtreg- set. I guess -xtmixed- can do it, but I am not an expert on the latter command so you will have to read the manual yourself to figure out how.

Otherwise yes, I see no reason why it should be impossible to use Hausman test on two way models.

[Lucas Bordure]

I've got this error:

"no coefficients in common; specify equations(matchlist)
for problems with different equation names."

when i run this command:

*Two-way random effects model
mixed firm_performance intangible_assets enterprise_value market_capitalization leverage stock_growth dividend_payout_ratio stock_volatility || industry_n:
estimates store random
*Two-way fixed effects model
xtreg firm_performance intangible_assets enterprise_value market_capitalization leverage stock_growth dividend_payout_ratio stock_volatility i.year i.industry_n
estimates store fixed
hausman fixed random

[Jeff Wooldridge]

I'd recommend against this sort of test, but before commenting further it would be very helpful to know the sizes of N and T. I also wonder how your "mixed" command is accounting for year to be treated as a "random effect."

[Lucas Bordure]

Dear Jeff Wooldridge,
My N=120
My T=11

I also wonder how your "mixed" command is accounting for year to be treated as a "random effect."

For me, year is time effect. And time effect was part of the two-way error component random effect model.

[Andrew Musau]

*TWO-WAY RE

mixed firm_performance intangible_assets - stock_volatility || _all: R.industry_n || _all: R.year, mle

With your data dimensions, it still remains a hard sell not clustering your standard errors.

[Jeff Wooldridge]

Agree with Andrew on clustering. And with that data structure, I don't see how you can get away with using time dummies for the year effects. The random effects assumption for the time effects is essentially assuming that none of your x variables or y trends over time -- whether up, down, or U shape, or some other complicated pattern. It's really a non-starter. Put in year dummies and then you might want to compare RE and FE. However, FE is the way to go unless your estimates are so imprecise as to be useless. If you show the results I'd be happy to weigh in.

Are some firms changing industry over time? If not, putting in the industry dummies is redundant with firm FE.

The default should be

xtset firm_n
xtreg firm_performance intangible_assets enterprise_value market_capitalization leverage stock_growth dividend_payout_ratio stock_volatility i.year, fe vce(cluster firm_n)

Nothing else is as convincing, no matter what a Hausman test shows.

[Lucas Bordure]

If I understand, I don't put time dummies in the random effect model?
If I understand, I put time dummies in fixed effect model?

I believed that in two-way error component models (random or fixed), time dummies and individual dummies were used both.

My firms don't change of industry over time.

[Jeff Wooldridge]

You put time dummies into both RE and FE. The interesting question is whether the heterogeneity is correlated with the Xs. That's what the Hausman test is meant to do. But the degrees-of-freedom will be wrong because of the time dummies. They shouldn't count. Only the variables that change across i and t count.

[Allan Angeli]

Stata does not have a two way random effects model in the -xtreg- set. I guess -xtmixed- can do it, but I am not an expert on the latter command so you will have to read the manual yourself to figure out how.

Otherwise yes, I see no reason why it should be impossible to use Hausman test on two way models.

Dear all,

I am working with panel data.

I did the tests and they suggest fixed effect adjustment. However, analyzing the model and context, I cannot safely discard the variable effect.

1) With these tests, is it possible to safely say that I only have a fixed effect?

2) How is the code to see the mixed effect (fixed and random effect at the same time)? So how do I do xtreg fe and re, what is the "xtreg" for the mixed effect? xtmixed?

I appreciate any help. Thanks a lot!

Banco = Bank = id
Data = date/time (semesters)
$dependente = dependent
$explicativas = independent variables

xtreg $dependente $explicativas, fe

Fixed-effects (within) regression               Number of obs      =      3534
Group variable: banco                           Number of groups   =       186

R-sq:  within  = 0.5596                         Obs per group: min =         1
       between = 0.5303                                        avg =      19.0
       overall = 0.5155                                        max =        38

                                                F(22,3326)         =    192.07
corr(u_i, Xb)  = -0.1482                        Prob > F           =    0.0000

         rho |  .67080754   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(185, 3326) =    15.88           Prob > F = 0.0000

xtreg $dependente $explicativas, re theta

Random-effects GLS regression                   Number of obs      =      3534
Group variable: banco                           Number of groups   =       186

R-sq:  within  = 0.5572                         Obs per group: min =         1
       between = 0.7092                                        avg =      19.0
       overall = 0.6631                                        max =        38

                                                Wald chi2(22)      =   4680.29
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

------------------- theta --------------------
  min      5%       median        95%      max
0.2381   0.3606     0.7094     0.8126   0.8126

 rho |  .41958416   (fraction of variance due to u_i)

quietly xtreg $dependente $explicativas, re

xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        inter[banco,t] = Xb + u[banco] + e[banco,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                   inter |   480.5217        21.9208
                       e |   84.10534       9.170897
                       u |   60.79998       7.797434

        Test:   Var(u) = 0
                             chibar2(01) =  5715.62
                          Prob > chibar2 =   0.0000

 quietly xtreg $dependente $explicativas, fe
estimates store fixed
quietly xtreg $dependente $explicativas, re
estimates store random

Note: the rank of the differenced variance matrix (19) does not equal the number of coefficients being tested (22); 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.

                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =  -992.36    chi2<0 ==> model fitted on these
                                        data fails to meet the asymptotic
                                        assumptions of the Hausman test;
                                        see suest for a generalized test

hausman fixed random, sigmamore

 b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      123.82
                Prob>chi2 =      0.0000

hausman fixed random, sigmaless

 b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      127.54
                Prob>chi2 =      0.0000

xi: xtreg $dependente $explicativas, re

xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re   
Sargan-Hansen statistic 127.820  Chi-sq(22)   P-value = 0.0000

Testing for time-fixed effects

xtreg $dependente $explicativas i.data, fe

Fixed-effects (within) regression               Number of obs      =      3534
Group variable: banco                           Number of groups   =       186

R-sq:  within  = 0.5679                         Obs per group: min =         1
       between = 0.5260                                        avg =      19.0
       overall = 0.5098                                        max =        38

                                                F(57,3291)         =     75.87
corr(u_i, Xb)  = -0.1572                        Prob > F           =    0.0000

 rho |  .67554064   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(185, 3291) =    15.95           Prob > F = 0.0000


testparm i.data

F( 36,  3291) =    2.46
            Prob > F =    0.0000

Wald test

xttest3

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

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

chi2 (186)  =   1.5e+32
Prob>chi2 =      0.0000

Wooldridge test

xtserial $dependente $explicativas, output

Linear regression                                      Number of obs =    3294
                                                       F( 21,   177) =   44.75
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.5291
                                                       Root MSE      =  7.7268

                                (Std. Err. adjusted for 178 clusters in banco)

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,     170) =     14.070
           Prob > F =      0.0002

. 
. 
. 
. xtserial $dependente $explicativas

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,     170) =     14.070
           Prob > F =      0.0002

Trying MIXED EFFECT MODEL

 xtmixed $dependente $explicativas|| banco:

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log likelihood = -13101.186  
Iteration 1:   log likelihood = -13101.186  

Computing standard errors:

Mixed-effects ML regression                     Number of obs      =      3534
Group variable: banco                           Number of groups   =       186

                                                Obs per group: min =         1
                                                               avg =      19.0
                                                               max =        38


                                                Wald chi2(22)      =   4628.55
Log likelihood = -13101.186                     Prob > chi2        =    0.0000


------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
banco: Identity              |
                   sd(_cons) |   9.789867   .5879408       8.70276    11.01277
-----------------------------+------------------------------------------------
                sd(Residual) |   9.159925   .1122329      8.942573     9.38256
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =  1512.54 Prob >= chibar2 = 0.0000

. 
. 
. 
. estat ic

-----------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
           . |   3534           .   -13101.19     25     26252.37    26406.63
-----------------------------------------------------------------------------
               Note:  N=Obs used in calculating BIC; see [R] BIC note

[Jeff Wooldridge]

Allan: Just use fixed effects and cluster your standard errors to account for serial correlation. Admittedly, it's hard to give you other advice because you don't show the output that matters: the estimated coefficients and confidence intervals. Running all of those tests is noise once you know you have to use fixed effects.

[Allan Angeli]

Allan: Just use fixed effects and cluster your standard errors to account for serial correlation. Admittedly, it's hard to give you other advice because you don't show the output that matters: the estimated coefficients and confidence intervals. Running all of those tests is noise once you know you have to use fixed effects.

Dear, Jeff Wooldridge
Thankyou for your answer!

Here is the completed code

Subtitle:
Banco = Bank = id
Data = date/time (semesters)
$dependente = dependent
$explicativas = independent variables

*========================= ESTIMADOR DE EFEITOS FIXOS =========================
. *teste de CHOW
.
. xtreg $dependente $explicativas, fe
 
Fixed-effects (within) regression               Number of obs      =      3534
Group variable: banco                           Number of groups   =       186
 
R-sq:  within  = 0.5596                         Obs per group: min =         1
       between = 0.5303                                        avg =      19.0
       overall = 0.5155                                        max =        38
 
                                                F(22,3326)         =    192.07
corr(u_i, Xb)  = -0.1482                        Prob > F           =    0.0000
 
------------------------------------------------------------------------------
       inter |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          v1 |  -6.934438   2.117205    -3.28   0.001    -11.08559   -2.783283
          v2 |   4.882984   2.542846     1.92   0.055     -.102716    9.868684
          v3 |   67.64443   2.049863    33.00   0.000     63.62531    71.66355
          v4 |   .3831291   .0621725     6.16   0.000     .2612289    .5050294
          v5 |   8.788123   11.82267     0.74   0.457    -14.39232    31.96856
          v6 |  -1.352919   1.006036    -1.34   0.179    -3.325431    .6195925
          v7 |  -.0002855   .0002561    -1.11   0.265    -.0007876    .0002167
          v8 |  -21.53611   1.895777   -11.36   0.000    -25.25312    -17.8191
          v9 |  -.0009577   .0005602    -1.71   0.087    -.0020561    .0001407
         v10 |  -.2887443   .0960853    -3.01   0.003    -.4771366    -.100352
         v11 |   1.103769   1.168471     0.94   0.345    -1.187225    3.394764
         v12 |   .7773185   .2449676     3.17   0.002     .2970161    1.257621
         v14 |  -5.217405   1.470318    -3.55   0.000    -8.100224   -2.334586
         v15 |   2.981397   1.862894     1.60   0.110    -.6711373    6.633931
         v16 |   3.773943   6.038419     0.62   0.532    -8.065449    15.61333
         v17 |    .535882    .436962     1.23   0.220    -.3208595    1.392624
         v18 |   37.72751   9.948457     3.79   0.000      18.2218    57.23323
         v19 |  -45.12017   3.779811   -11.94   0.000    -52.53116   -37.70918
         v21 |   45.17704   2.063937    21.89   0.000     41.13033    49.22376
         v22 |   -.067528   .0483883    -1.40   0.163    -.1624019    .0273458
         v23 |   48.02018   9.599176     5.00   0.000     29.19929    66.84107
         v24 |   1.23e-08   1.71e-09     7.21   0.000     8.96e-09    1.57e-08
       _cons |   5.691604   14.38328     0.40   0.692    -22.50936    33.89257
-------------+----------------------------------------------------------------
     sigma_u |  13.091392
     sigma_e |  9.1708966
         rho |  .67080754   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(185, 3326) =    15.88           Prob > F = 0.0000

*========================= ESTIMADOR DE EFEITOS ALEATÓRIOS =========================
. xtreg $dependente $explicativas, re theta
 
Random-effects GLS regression                   Number of obs      =      3534
Group variable: banco                           Number of groups   =       186
 
R-sq:  within  = 0.5572                         Obs per group: min =         1
       between = 0.7092                                        avg =      19.0
       overall = 0.6631                                        max =        38
 
                                                Wald chi2(22)      =   4680.29
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000
 
------------------- theta --------------------
  min      5%       median        95%      max
0.2381   0.3606     0.7094     0.8126   0.8126
 
------------------------------------------------------------------------------
       inter |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          v1 |  -5.125656    1.97626    -2.59   0.009    -8.999054   -1.252258
          v2 |   4.829306   2.512329     1.92   0.055    -.0947693    9.753381
          v3 |   66.35121   1.914631    34.65   0.000     62.59861    70.10382
          v4 |   .5113285   .0573408     8.92   0.000     .3989427    .6237143
          v5 |   6.348042   11.84897     0.54   0.592    -16.87551    29.57159
          v6 |  -1.369849   1.004979    -1.36   0.173    -3.339571    .5998729
          v7 |  -.0002238   .0002561    -0.87   0.382    -.0007256    .0002781
          v8 |  -19.12462   1.827927   -10.46   0.000    -22.70729   -15.54194
          v9 |  -.0005529   .0005259    -1.05   0.293    -.0015837     .000478
         v10 |  -.2899256   .0933122    -3.11   0.002    -.4728141   -.1070371
         v11 |   1.689392   1.151047     1.47   0.142    -.5666185    3.945402
         v12 |   .9701752   .2413045     4.02   0.000      .497227    1.443123
         v14 |  -6.311447   1.451728    -4.35   0.000    -9.156781   -3.466113
         v15 |   5.509521    .900591     6.12   0.000     3.744395    7.274647
         v16 |   12.36448   .8036462    15.39   0.000     10.78936     13.9396
         v17 |   .4697527   .4404013     1.07   0.286    -.3934179    1.332923
         v18 |   40.78611   10.00732     4.08   0.000     21.17212     60.4001
         v19 |  -48.28812   3.699366   -13.05   0.000    -55.53874   -41.03749
         v21 |   44.81132   1.998229    22.43   0.000     40.89486    48.72778
         v22 |  -.0568349    .048768    -1.17   0.244    -.1524186    .0387487
         v23 |   51.57671   9.493769     5.43   0.000     32.96927    70.18416
         v24 |   1.27e-08   1.64e-09     7.75   0.000     9.51e-09    1.60e-08
       _cons |  -19.04766   3.598371    -5.29   0.000    -26.10034   -11.99499
-------------+----------------------------------------------------------------
     sigma_u |  7.7974341
     sigma_e |  9.1708966

         rho |  .41958416   (fraction of variance due to u_i)

*========================= BREUSCH-PAGAN LM (multiplicador de lagrange)=========================
. *test for random effects versus OLS(pooled)
.
. *rodar o modelo random
. quietly xtreg $dependente $explicativas, re
 
.
. *comando para rodar a comparação entre o random e o OLS
. xttest0
 
Breusch and Pagan Lagrangian multiplier test for random effects
 
        inter[banco,t] = Xb + u[banco] + e[banco,t]
 
        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                   inter |   480.5217        21.9208
                       e |   84.10534       9.170897
                       u |   60.79998       7.797434
 
        Test:   Var(u) = 0
                             chibar2(01) =  5715.62
                          Prob > chibar2 =   0.0000

*============= TESTE DE HAUSMAN (for fixed versus random effects model) =============
. quietly xtreg $dependente $explicativas, fe
. estimates store fixed
. quietly xtreg $dependente $explicativas, re
. estimates store random
 
. hausman fixed random
 
Note: the rank of the differenced variance matrix (19) does not equal the number of coefficients being tested (22); 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))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
          v1 |   -6.934438    -5.125656       -1.808783        .7595746
          v2 |    4.882984     4.829306        .0536783        .3927654
          v3 |    67.64443     66.35121        1.293218        .7322054
          v4 |    .3831291     .5113285       -.1281994        .0240304
          v5 |    8.788123     6.348042        2.440081               .
          v6 |   -1.352919    -1.369849        .0169298        .0461086
          v7 |   -.0002855    -.0002238       -.0000617        5.22e-06
          v8 |   -21.53611    -19.12462       -2.411493        .5026465
          v9 |   -.0009577    -.0005529       -.0004048         .000193
         v10 |   -.2887443    -.2899256        .0011813        .0229177
         v11 |    1.103769     1.689392       -.5856226        .2010341
         v12 |    .7773185     .9701752       -.1928567        .0422046
         v14 |   -5.217405    -6.311447        1.094042        .2330702
         v15 |    2.981397     5.509521       -2.528124        1.630739
         v16 |    3.773943     12.36448       -8.590535        5.984702
         v17 |     .535882     .4697527        .0661293               .
         v18 |    37.72751     40.78611       -3.058592               .
         v19 |   -45.12017    -48.28812        3.167951         .775672
         v21 |    45.17704     44.81132        .3657229        .5166412
         v22 |    -.067528    -.0568349       -.0106931               .
         v23 |    48.02018     51.57671       -3.556535        1.418635
         v24 |    1.23e-08     1.27e-08       -4.24e-10        4.65e-10
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg
 
    Test:  Ho:  difference in coefficients not systematic
 
                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =  -992.36    chi2<0 ==> model fitted on these
                                        data fails to meet the asymptotic
                                        assumptions of the Hausman test;
                                        see suest for a generalized test

hausman fixed random, sigmamore
 
Note: the rank of the differenced variance matrix (19) does not equal the number of coefficients being tested (22); 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))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
          v1 |   -6.934438    -5.125656       -1.808783        .8435136
          v2 |    4.882984     4.829306        .0536783        .5902281
          v3 |    67.64443     66.35121        1.293218        .8137951
          v4 |    .3831291     .5113285       -.1281994        .0263343
          v5 |    8.788123     6.348042        2.440081         1.89034
          v6 |   -1.352919    -1.369849        .0169298        .1803009
          v7 |   -.0002855    -.0002238       -.0000617        .0000447
          v8 |   -21.53611    -19.12462       -2.411493        .6004505
          v9 |   -.0009577    -.0005529       -.0004048         .000216
         v10 |   -.2887443    -.2899256        .0011813        .0283261
         v11 |    1.103769     1.689392       -.5856226        .2853074
         v12 |    .7773185     .9701752       -.1928567        .0598552
         v14 |   -5.217405    -6.311447        1.094042        .3452792
         v15 |    2.981397     5.509521       -2.528124        1.662374
         v16 |    3.773943     12.36448       -8.590535        6.075461
         v17 |     .535882     .4697527        .0661293        .0520976
         v18 |    37.72751     40.78611       -3.058592        1.340276
         v19 |   -45.12017    -48.28812        3.167951        1.015159
         v21 |    45.17704     44.81132        .3657229        .6283263
         v22 |    -.067528    -.0568349       -.0106931        .0057785
         v23 |    48.02018     51.57671       -3.556535        2.186001
         v24 |    1.23e-08     1.27e-08       -4.24e-10        5.51e-10
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg
 
    Test:  Ho:  difference in coefficients not systematic
 
                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      123.82
                Prob>chi2 =      0.0000

. hausman fixed random, sigmaless
 
Note: the rank of the differenced variance matrix (19) does not equal the number of coefficients being tested (22); 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))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
          v1 |   -6.934438    -5.125656       -1.808783         .831131
          v2 |    4.882984     4.829306        .0536783        .5815637
          v3 |    67.64443     66.35121        1.293218        .8018488
          v4 |    .3831291     .5113285       -.1281994        .0259477
          v5 |    8.788123     6.348042        2.440081         1.86259
          v6 |   -1.352919    -1.369849        .0169298        .1776542
          v7 |   -.0002855    -.0002238       -.0000617         .000044
          v8 |   -21.53611    -19.12462       -2.411493         .591636
          v9 |   -.0009577    -.0005529       -.0004048        .0002129
         v10 |   -.2887443    -.2899256        .0011813        .0279103
         v11 |    1.103769     1.689392       -.5856226        .2811192
         v12 |    .7773185     .9701752       -.1928567        .0589765
         v14 |   -5.217405    -6.311447        1.094042        .3402106
         v15 |    2.981397     5.509521       -2.528124        1.637971
         v16 |    3.773943     12.36448       -8.590535        5.986274
         v17 |     .535882     .4697527        .0661293        .0513328
         v18 |    37.72751     40.78611       -3.058592        1.320601
         v19 |   -45.12017    -48.28812        3.167951        1.000256
         v21 |    45.17704     44.81132        .3657229        .6191026
         v22 |    -.067528    -.0568349       -.0106931        .0056937
         v23 |    48.02018     51.57671       -3.556535        2.153911
         v24 |    1.23e-08     1.27e-08       -4.24e-10        5.43e-10
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg
 
    Test:  Ho:  difference in coefficients not systematic
 
                 chi2(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      127.54
                Prob>chi2 =      0.0000