Husman test

[hussein bataineh]

Hi please i have a question related to Husman test, when we run random effect model in the Husman test do we need to control for industry or this step we take it after the result of the Husman test support using Random effect. i give an example.


this example i did not add industry.

xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year , fe
estimate store fe
xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year , re
estimates store re
hausman fe re


This example i add industry as control variable in the random effect regression.

xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year , fe
estimate store fe
xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year I. industry , re
estimates store re
hausman fe re


What is the appropriate way??

[Carlo Lazzaro]

Hussein:
1) -hausman- pick up solely the coefficients shared by both codes; therefore, -i.industry- would be ruled out from -hausman- in both instances;
2) in your second code -I.industry- should be -i.industry-.

[hussein bataineh]

Thanks a lot professor Carlo

Please as i understand from your notes that (industry )should not be used in Husman test.
. please i would like to ask should (year) be use in both fixed effect and random effect in Husman test???. so mainly our Husman test


xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year , fe
estimate store fe
xtreg percacatagebondwh CSO FSIZE ROA SD_OCF LEV DIV BSIZE BIND ESG_combinedwh PSIZE DPP RPP DR MA i.year , re
estimates store re
hausman fe re

[Carlo Lazzaro]

Hussein:
you should use -i.year- in the right-hand side of yourb regression equations.
The only issue with -hausman- comparison between -fe- and -re- estimators, is the fact that only the regressors that are shared between the two regression equationbs will be taken into account (see -i.race- case in the following toy-example):

. . 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.race i.year, fe
note: 2.race omitted because of collinearity.
note: 3.race omitted because of collinearity.

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
             |
        race |
      Black  |          0  (omitted)
      Other  |          0  (omitted)
             |
        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

. estimates store fe

. xtreg ln_wage c.age##c.age i.race i.year, re

Random-effects GLS regression                   Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-squared:                                      Obs per group:
     Within  = 0.1161                                         min =          1
     Between = 0.1245                                         avg =        6.1
     Overall = 0.1116                                         max =         15

                                                Wald chi2(18)     =    3757.34
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0790911   .0039765    19.89   0.000     .0712973    .0868848
             |
 c.age#c.age |  -.0011036   .0000586   -18.84   0.000    -.0012184   -.0009888
             |
        race |
      Black  |  -.1251588   .0127093    -9.85   0.000    -.1500685   -.1002491
      Other  |   .0940173   .0529605     1.78   0.076    -.0097834    .1978181
             |
        year |
         69  |   .0648079   .0124419     5.21   0.000     .0404223    .0891936
         70  |   .0263438   .0120155     2.19   0.028     .0027938    .0498938
         71  |   .0537732   .0125423     4.29   0.000     .0291908    .0783556
         72  |   .0482933   .0136268     3.54   0.000     .0215853    .0750013
         73  |    .038056   .0144537     2.63   0.008     .0097272    .0663847
         75  |    .006932   .0169468     0.41   0.683    -.0262832    .0401472
         77  |   .0276061   .0199382     1.38   0.166    -.0114721    .0666842
         78  |   .0492717    .021678     2.27   0.023     .0067837    .0917597
         80  |   .0309794   .0248624     1.25   0.213    -.0177499    .0797087
         82  |   .0296793   .0279688     1.06   0.289    -.0251386    .0844972
         83  |   .0521756   .0296308     1.76   0.078    -.0058997    .1102509
         85  |   .0997798   .0329073     3.03   0.002     .0352827     .164277
         87  |   .1196681   .0363187     3.29   0.001     .0484848    .1908515
         88  |   .1842637   .0386857     4.76   0.000     .1084411    .2600862
             |
       _cons |   .3198597   .0604665     5.29   0.000     .2013475    .4383719
-------------+----------------------------------------------------------------
     sigma_u |  .35862524
     sigma_e |  .30127563
         rho |  .58625495   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. hausman fe re

Note: the rank of the differenced variance matrix (15) does not equal the number of coefficients being tested (16); 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.
-------------+----------------------------------------------------------------
         age |    .0728746     .0790911       -.0062165        .0100299
 c.age#c.age |   -.0010113    -.0011036        .0000922        .0000171
        year |
         69  |    .0647054     .0648079       -.0001025        .0097746
         70  |    .0284423     .0263438        .0020984        .0201519
         71  |    .0579959     .0537732        .0042228        .0301475
         72  |    .0510671     .0482933        .0027738        .0400445
         73  |    .0424104      .038056        .0043545        .0500737
         75  |    .0151376      .006932        .0082056        .0696885
         77  |    .0340933     .0276061        .0064872        .0896195
         78  |    .0537334     .0492717        .0044617        .1000114
         80  |    .0369475     .0309794        .0059681        .1196243
         82  |    .0391687     .0296793        .0094894        .1395827
         83  |     .058766     .0521756        .0065904        .1494656
         85  |    .1042758     .0997798         .004496        .1694779
         87  |    .1242272     .1196681         .004559         .189563
         88  |    .1904977     .1842637         .006234         .203151
------------------------------------------------------------------------------
                          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(15) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  89.25
Prob > chi2 = 0.0000

.

Se aside any comments on the correct model specification, -i.race- is nit included in the set of coefficients listed in -hausman- table, as it is a time-invariant regressor that cannot be estimated with -fe-.
More substantively, please call me Carlo, just like all on (and many more off) this list do. Thanks.