Mundlak test interpretation

[Jeremiah Anderson]

I have seen from previous discussions that the Mundlak regression can be used as a sort of Hausman test. I have run the regression however not sure how to interpret the results i.e. tell if the coefficients are significant which would make them endogeneous. Do I just use the single reported p value?

[Carlo Lazzaro]

Jeremiah:
as per FAQ, please post what you typed and what Stata gave you back to increase your chances of getting helpful replies.

[Marcos Almeida]

@ Jeremiah: in addition to the suggestion Carlo very appropriately pointed out, I wish to remind that the Mundlak test is a user-written command.

If you type

. help mundlak

You will get this general information:

The command mundlak estimates random-effects regression models
(xtreg, re) adding group-means of variables in indepvars which
vary within groups. This technique was proposed by Mundlak (1978)
as a way to relax the assumption in the random-effects estimator
that the observed variables are uncorrelated with the unobserved
variables. Additionally, the degree of statistical significance
of the estimated coefficients on the group means can be used to
test whether such assumption holds for individual regressors. See
also Chapter 10 in Wooldridge (2010) and Chapter 11 in Greene
(2011).

And have access to download the commands.

Please keep also in mind that you're supposed to perform e(sample) after a fixed-effects model in other to perform the Mundlak test.

Best,

Marcos

[Marcos Almeida]

@ Jeremiah:

Indeed, as Carlo already underlined (by the way, it is also well stated in FAQ #10 and #12), when you said you've "run a regression", I don't know if it was -xtreg-, for example, or something else.

Trying to hazard a guess: when you say you are not sure on how to

tell if the coefficients are significant which would make them endogeneous

I wonder if you have used -xtivreg- when running your regression. If so, to my modest knowledge (and maybe I'm wrong), there is no option yet to perform the Mundlak test under such conditions.


Best,

Marcos

[Jeremiah Anderson]

Apologies for not making myself more clear. I downloaded the Mundlak package and then run my regression using the command 'mundlak' in the beginning. STATA then reported a table with two columns for RE and Mundlak which I assume to be the variable coefficients? The bottom of table then had other information such as p value, chi squared, sigm_u and sigma_e.
@Marcos I was unaware that I had to perform the e(sample). I have looked in the Woolridge textbook but haven't been able to a step by step instruction on how to conduct this test. Would you be able to briefly explain the steps?

After I've confirmed the procedure I will then post my results for interpretation help.

[Sebastian Kripfganz]

I had a brief look at the user-written mundlak command. The p-value at the bottom of the table seems to refer to the Wald chi2 test for the joint significance of all regressors in the model, not just the additional time averages. It is thus not helpful in this context.

After running the mundlak command you can type
estimates replay Mundlak
to display the full regression results for the augmented model. There you can directly have a look at the significance of the included time averages, or subsequently test for their joint significance with the postestimation command test.

Alternatively, without using the mundlak command, you can also construct the time averages by yourself and run the Mundlak regression (alternative name: correlated random effects regression) with the xtreg, re command, as explained for example in my post #9 in the following thread:
http://www.statalist.org/forums/foru...701#post376701

[Jeremiah Anderson]

Thank you so much sebastian, exactly what I needed to know.

[Sophia Kan]

Sebastian Kripfganz: Thank you for your post. I just followed the instructions you gave on post #9 of post376701. Here, I was able to keep my instrument (I used the xtivreg command). Is this basically the work around for a Mundlak with IV?

foreach variable of varlist $e $x {
by newid: egen `variable'_mean = mean(`variable')
}

eststo clear
eststo: quietly xtivreg $e $x $i , fe
eststo: quietly xtivreg $e $x $i *_mean, re
esttab

Output

Thank you in advance!

[Rocio Aguilar]

Dear all,
I would like to share with you a doubt. I have a dynamic model estimated by xtabond2:

. xtabond2 zROA_EST_w99 l.zROA_EST_w99 ZMunificence_KH ZDynamism_KH zSIZE_FIRM_IMP i.ORIGIN_DICH i.DUALITY zSIZE_BOARD zSIZE_TMT zAGETMT LEVEL_KW  i.PARTIAL_CHANGE_MISSION zCOG_YEARS_COWORKINGw_95   zPEOI, gmm(zROA_EST_w99, lag(2 3)) gmm(zSIZE_FIRM_IMP , lag(2 4)) gmm( zSIZE_BOARD, lag(3 4)) gmm(zSIZE_TMT, lag(2 3))  iv(ZMunificence_KH ZDynamism_KH i.ORIGIN_DICH i.DUALITY zAGETMT LEVEL_KW  i.PARTIAL_CHANGE_MISSION zCOG_YEARS_COWORKINGw_95   zPEOI ) twostep robust  arte(3)

Under the theoretical approach of my topic, size's variables as size of firm, size of board and size of tmt should be treat as endogenous variables. However, the rest of variables with regard with the output of xtabond2 iv(var) could be treat as exogenous taking in account the Hansen test=0.450 and the Difference test=0.767

iv(ZMunificence_KH ZDynamism_KH 0b.ORIGIN_DICH 1.ORIGIN_DICH 0b.DUALITY 1.DUALITY zAGETMT LEVEL_KW 0b.PARTIAL_CHANGE_MISSION 1.PARTIAL_CHANGE_MISSION zCOG_YEARS_COWORKINGw_95 zPEOI)
    Hansen test excluding group:     chi2(79)   =  79.93  Prob > chi2 =  0.450
    Difference (null H = exogenous): chi2(9)    =   5.72  Prob > chi2 =  0.767

I wonder if I previously run the Mundlak test, It would improve the addres of the endogeneity issue of the model

 . mundlak zROA_EST_w99 ZMunificence_KH ZDynamism_KH zSIZE_FIRM_IMP ORIGIN_DICH DUALITY zSIZE_BOARD zSIZE_TMT zAGETMT LEVEL_KW PARTIAL_CHANGE_MISSION zCOG_YEARS_COWORKINGw_95 zPEOI

+------------------------------------------------+
|             Variable |     RE     |  Mundlak   |
|----------------------+------------+------------|
|      ZMunificence_KH |     -0.074 |     -0.064 |
|         ZDynamism_KH |      0.085 |      0.082 |
|       zSIZE_FIRM_IMP |      0.114 |     -0.004 |
|          ORIGIN_DICH |     -0.129 |     -0.138 |
|              DUALITY |      0.313 |      0.594 |
|          zSIZE_BOARD |      0.112 |      0.058 |
|            zSIZE_TMT |     -0.083 |     -0.065 |
|              zAGETMT |     -0.069 |     -0.037 |
|             LEVEL_KW |      0.005 |      0.081 |
| PARTIAL_CHANGE_MIS~N |     -0.077 |     -0.051 |
| zCOG_YEARS_COWORK~95 |      0.045 |     -0.004 |
|                zPEOI |     -0.072 |     -0.054 |
| mean__ZMunificence~H |            |     -0.046 |
|   mean__ZDynamism_KH |            |      0.014 |
| mean__zSIZE_FIRM_IMP |            |      0.129 |
|        mean__DUALITY |            |     -0.636 |
|    mean__zSIZE_BOARD |            |      0.133 |
|      mean__zSIZE_TMT |            |     -0.005 |
|        mean__zAGETMT |            |     -0.033 |
|       mean__LEVEL_KW |            |     -0.175 |
| mean__PARTIAL_CHAN~N |            |     -0.485 |
| mean__zCOG_YEARS_~95 |            |      0.072 |
|          mean__zPEOI |            |     -0.043 |
|                _cons |      0.041 |      0.368 |
|----------------------+------------+------------|
|                    N |        799 |        799 |
|                  N_g |    121.000 |    121.000 |
|                g_min |      2.000 |      2.000 |
|                g_avg |      6.603 |      6.603 |
|                g_max |     10.000 |     10.000 |
|                  rho |      0.298 |      0.298 |
|                 rmse |      0.723 |      0.720 |
|                 chi2 |     37.375 |     54.936 |
|                    p |      0.000 |      0.000 |
|                 df_m |     12.000 |     23.000 |
|                sigma |      0.857 |      0.857 |
|              sigma_u |      0.468 |      0.468 |
|              sigma_e |      0.718 |      0.718 |
|                 r2_w |      0.029 |      0.040 |
|                 r2_o |      0.069 |      0.108 |
|                 r2_b |      0.139 |      0.201 |
+------------------------------------------------+

. estimates replay Mundlak

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Model Mundlak
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Random-effects GLS regression                   Number of obs     =        799
Group variable: N_COMPANY                       Number of groups  =        121

R-sq:                                           Obs per group:
     within  = 0.0405                                         min =          2
     between = 0.2005                                         avg =        6.6
     overall = 0.1083                                         max =         10

                                                Wald chi2(23)     =      54.94
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0002

------------------------------------------------------------------------------------------------
                  zROA_EST_w99 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------------------+----------------------------------------------------------------
               ZMunificence_KH |  -.0641728   .0334043    -1.92   0.055     -.129644    .0012985
                  ZDynamism_KH |   .0819554   .0420622     1.95   0.051     -.000485    .1643958
                zSIZE_FIRM_IMP |  -.0043049   .0842493    -0.05   0.959    -.1694306    .1608208
                   ORIGIN_DICH |  -.1378076   .1122247    -1.23   0.219     -.357764    .0821488
                       DUALITY |   .5937757   .1418436     4.19   0.000     .3157674    .8717839
                   zSIZE_BOARD |   .0579195   .0679891     0.85   0.394    -.0753366    .1911756
                     zSIZE_TMT |  -.0653475   .0650647    -1.00   0.315    -.1928719     .062177
                       zAGETMT |  -.0374435   .0567624    -0.66   0.509    -.1486957    .0738087
                      LEVEL_KW |   .0813778   .1071567     0.76   0.448    -.1286455    .2914011
        PARTIAL_CHANGE_MISSION |  -.0511701    .122346    -0.42   0.676    -.2909638    .1886236
      zCOG_YEARS_COWORKINGw_95 |   -.003673   .0573224    -0.06   0.949    -.1160228    .1086769
                         zPEOI |  -.0543144   .0564798    -0.96   0.336    -.1650128    .0563841
         mean__ZMunificence_KH |  -.0459581    .225841    -0.20   0.839    -.4885982    .3966821
            mean__ZDynamism_KH |   .0138254   .2221559     0.06   0.950    -.4215922    .4492431
          mean__zSIZE_FIRM_IMP |   .1292623   .1016339     1.27   0.203    -.0699365     .328461
                 mean__DUALITY |   -.635596   .2398822    -2.65   0.008    -1.105757   -.1654354
             mean__zSIZE_BOARD |   .1329851   .1212469     1.10   0.273    -.1046544    .3706246
               mean__zSIZE_TMT |  -.0050497   .1160224    -0.04   0.965    -.2324495      .22235
                 mean__zAGETMT |  -.0328052    .084568    -0.39   0.698    -.1985555     .132945
                mean__LEVEL_KW |  -.1750052   .1545016    -1.13   0.257    -.4778227    .1278124
  mean__PARTIAL_CHANGE_MISSION |  -.4849598   .5769533    -0.84   0.401    -1.615767    .6458478
mean__zCOG_YEARS_COWORKINGw_95 |   .0717855   .0818186     0.88   0.380     -.088576    .2321471
                   mean__zPEOI |  -.0433404   .0945906    -0.46   0.647    -.2287346    .1420537
                         _cons |   .3684413   .3048514     1.21   0.227    -.2290564     .965939
-------------------------------+----------------------------------------------------------------
                       sigma_u |  .46774649
                       sigma_e |  .71849948
                           rho |  .29765764   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------------

Thanks in advance,
Rocio Aguilar