F-test for Fixed Effect With Robust SE

[Samuel Renhoar]

Hi everyone,

A few days ago i made a post and some of my questions answered very well.
But there's still a lil bit of confusion in Fixed Effect Model particularly F-test for Individual Effect Dummies (testparm) with Fixed Effect Robust Standard Error.
So here it is:

After using vce(robust) option for xtreg, fe command, i couldn't get my F-test (joint test) for my individual effect dummies (u_i) that i included in my model. I know that stata omits it because someone explained it to me. But, i still want to report it on my paper, because i think it could be necesarry (or it couldn't) to report F test for u_i, to provide the reasons why i included it in my model.
I don't know is it a right assumption or not, but i assumed that we could choose to pooled or not to pooled the data, to include or not to include individiual and time effect based on these F test (F test, for u_i (time invariant effect) and δ_t (for time variant effect)).

So my question is:
How to conduct F test (that omits) for individual effect (u_i) in fixed effect with robust standard error (xtreg, fe vce(robust))?

here is how i did fixed effect model with robust SE. i still could do F test for time effect (that i assumed as δ_t or dummy variables for time effect) by doing testparm over my year dummy variables.

. xtreg Y X1 X2 i.year, fe vce(robust)

Fixed-effects (within) regression               Number of obs     =        222
Group variable: year                            Number of groups  =         74

R-sq:                                           Obs per group:
     within  = 0.5916                                         min =          3
     between = 0.6470                                         avg =        3.0
     overall = 0.6243                                         max =          3

                                                F(4,73)           =     100.72
corr(u_i, Xb)  = 0.1511                         Prob > F          =     0.0000

                                  (Std. Err. adjusted for 74 clusters in id)
------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          X1 |   .8808422   .1626354     5.42   0.000     .5567103    1.204974
          X2 |   16.65939   13.84521     1.20   0.233    -10.93408    44.25285
             |
       year |
       2017  |  -.5542752   .3520155    -1.57   0.120    -1.255841    .1472906
       2018  |  -2.224763    .567658    -3.92   0.000    -3.356104   -1.093422
             |
       _cons |  -.1550369   1.315367    -0.12   0.906    -2.776559    2.466485
-------------+----------------------------------------------------------------
     sigma_u |  2.9370361
     sigma_e |  2.7763652
         rho |  .52809954   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. testparm i.year

 ( 1)  2017.year = 0
 ( 2)  2018.year = 0

       F(  2,    73) =    7.83
            Prob > F =    0.0008

i've got an idea about using the reg command with addition of individual and time dummies. But because i read that in reg. command, robust and cluster(id) options using a different method, so if anybody could confirm which one should i choose and is it a right (or wrong) thing to do?

. reg Y X1 X2 i.id i.year, vce(robust)

Linear regression                               Number of obs     =        222
                                                F(77, 144)        =      44.20
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8589
                                                Root MSE          =     2.7764

------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          X1 |   .8808422    .166491     5.29   0.000     .5517603    1.209924
          X2 |   16.65939   12.42937     1.34   0.182    -7.908193    41.22696
             |
        id |
       APLN  |   .2947118   1.225192     0.24   0.810    -2.126972    2.716396
       ASDM  |   1.050584   1.462409     0.72   0.474    -1.839978    3.941145
       ASII  |     2.8694   2.413574     1.19   0.236     -1.90121     7.64001
       ASJT  |    2.31474   1.607534     1.44   0.152    -.8626728    5.492152
       ASMI  |   4.015512   1.669058     2.41   0.017      .716494    7.314531
       ASRI  |  -3.831059   .9604417    -3.99   0.000    -5.729445   -1.932674
       ASRM  |   2.211627   1.556897     1.42   0.158    -.8656974    5.288952
       BACA  |  -.0261848   .7748567    -0.03   0.973    -1.557747    1.505378
       BAPA  |   1.378856   1.827293     0.75   0.452    -2.232926    4.990638
       BBCA  |   .0173037   .6407342     0.03   0.978    -1.249156    1.283763
       BBMD  |   .3834314    .738184     0.52   0.604    -1.075645    1.842507
       BBNI  |   .2716186   .7533377     0.36   0.719     -1.21741    1.760647
       BBRI  |   .2827238   .6037333     0.47   0.640    -.9106003    1.476048
       BBTN  |   -.077315   .8124557    -0.10   0.924    -1.683195    1.528565
       BCIP  |   2.590771   1.405957     1.84   0.067    -.1882089    5.369752
       BDMN  |   .4528766   .9091776     0.50   0.619    -1.344181    2.249934
       BEST  |  -2.037454   1.330063    -1.53   0.128    -4.666422    .5915147
       BINA  |  -.1135588   .7325616    -0.16   0.877    -1.561522    1.334404
       BJBR  |    .561522    .830212     0.68   0.500    -1.079454    2.202498
       BJTM  |   .7062759   .9025418     0.78   0.435    -1.077666    2.490217
       BKSL  |  -1.372539   .6198285    -2.21   0.028    -2.597676   -.1474013
       BMRI  |   .3669541   .8332335     0.44   0.660    -1.279994    2.013903
       BNBA  |   .3175581   .7390014     0.43   0.668    -1.143134     1.77825
       BNGA  |   .2506866   .7081542     0.35   0.724    -1.149033    1.650406
       BNII  |  -.0686958   .7415254    -0.09   0.926    -1.534376    1.396985
       BOLT  |   2.443337   4.159148     0.59   0.558    -5.777531    10.66421
       BRAM  |   2.319903    1.84863     1.25   0.212    -1.334053    5.973858
       BSDE  |   1.708504   1.436532     1.19   0.236    -1.130908    4.547917
       COWL  |  -4.949813   1.340089    -3.69   0.000    -7.598599   -2.301026
       CTRA  |  -.0605993   .8110554    -0.07   0.941    -1.663711    1.542513
       DART  |  -1.910334   .9455116    -2.02   0.045    -3.779209   -.0414595
       DILD  |   .4385749    .690611     0.64   0.526    -.9264696    1.803619
       DMAS  |  -.8064493   1.466592    -0.55   0.583    -3.705279     2.09238
       DUTI  |   2.279153   .8200434     2.78   0.006     .6582761    3.900031
       FMII  |  -5.050991   3.634907    -1.39   0.167    -12.23566    2.133676
       GMTD  |   1.609945   .7361016     2.19   0.030      .154985    3.064905
       GPRA  |   .7070048   .9660833     0.73   0.465    -1.202531    2.616541
       INDS  |   .3487059   2.395833     0.15   0.884    -4.386837    5.084249
       JRPT  |    4.44845   1.494431     2.98   0.003     1.494595    7.402305
       JTPE  |    .834028   3.572804     0.23   0.816    -6.227887    7.895942
       KIJA  |  -2.493057   1.432208    -1.74   0.084    -5.323924    .3378107
       LINK  |   5.043667   4.371182     1.15   0.250    -3.596301    13.68364
       LPCK  |   6.240876   6.955493     0.90   0.371    -7.507178    19.98893
       LPGI  |   1.179102   .8410096     1.40   0.163    -.4832171     2.84142
       LPKR  |   .7737229   1.459914     0.53   0.597    -2.111906    3.659352
       MARI  |   4.511691     6.4431     0.70   0.485     -8.22358    17.24696
       MDIA  |   3.637022   4.998187     0.73   0.468    -6.242271    13.51631
       MDLN  |  -5.018098   2.952339    -1.70   0.091    -10.85362    .8174219
       MEGA  |   3.629563   3.339883     1.09   0.279    -2.971967    10.23109
       MKPI  |   5.926182   2.035153     2.91   0.004     1.903549    9.948814
       MMLP  |   .8126784    2.50436     0.32   0.746    -4.137377    5.762734
       MNCN  |     1.6835   2.823976     0.60   0.552    -3.898301    7.265301
       MREI  |   2.293249   1.157294     1.98   0.049     .0057712    4.580727
       MTLA  |   3.542054   1.936665     1.83   0.069    -.2859105    7.370019
       MYRX  |  -2.469469   .7999408    -3.09   0.002    -4.050612   -.8883258
       NISP  |   .0944043   .7654037     0.12   0.902    -1.418474    1.607282
       PLIN  |   1.818417   3.990349     0.46   0.649    -6.068808    9.705643
       PNBN  |  -.5133411   .6766237    -0.76   0.449    -1.850739    .8240564
       PNIN  |   1.555931   .8908233     1.75   0.083    -.2048478     3.31671
       PPRO  |  -7.645823    1.93914    -3.94   0.000    -11.47868   -3.812969
       PWON  |    .827668   1.376719     0.60   0.549     -1.89352    3.548856
       RDTX  |   1.647971   1.343093     1.23   0.222    -1.006753    4.302695
       RODA  |   .2733828   1.023854     0.27   0.790    -1.750341    2.297106
       SCBD  |   2.449009   .9853489     2.49   0.014     .5013928    4.396625
       SCMA  |   11.37837   6.599241     1.72   0.087     -1.66552    24.42227
       SDRA  |  -.2775776   .5947717    -0.47   0.641    -1.453188    .8980333
       SMDM  |  -.2651635   .9403621    -0.28   0.778     -2.12386    1.593533
       SMRA  |  -.8117748   .9704148    -0.84   0.404    -2.729872    1.106323
       SMSM  |   7.956638    7.70801     1.03   0.304    -7.278821     23.1921
       TARA  |  -1.243613   1.169836    -1.06   0.290    -3.555881    1.068655
       TLKM  |   4.399757   4.520706     0.97   0.332    -4.535757    13.33527
       VINS  |   2.005052   1.621869     1.24   0.218    -1.200693    5.210797
       VIVA  |  -4.834313    4.09723    -1.18   0.240     -12.9328    3.264169
             |
       year |
       2017  |  -.5542752   .4074146    -1.36   0.176    -1.359561    .2510102
       2018  |  -2.224763   .5223219    -4.26   0.000    -3.257171   -1.192354
             |
       _cons |  -1.037165   .6538399    -1.59   0.115    -2.329528    .2551992
------------------------------------------------------------------------------

. testparm i.id

 ( 1)  2.id = 0
 ( 2)  3.id = 0
 ( 3)  4.id= 0
.
. (to save the space)
.
 (71)  72.id = 0
 (72)  73.id = 0
 (73)  74.id = 0

       F( 73,   144) =   10.22
            Prob > F =    0.0000

. testparm i.year

 ( 1)  2017.year = 0
 ( 2)  2018.year = 0

       F(  2,   144) =    9.39
            Prob > F =    0.0001

Thank you.

[Phil Bromiley]

I don't think I would worry much about this. You get strong results with robust standard errors with regression and if you look at the xtreg you will see that half of the variance is in the fixed effects. For fixed effects not to matter, the variance of fixed effects should be very small. I'm sure this varies by area, but in my area we don't normally bother testing the significance of fixed effects.
One of the big issues between fixed effect and conventional regression is that you are running a very different model. Xtreg with fixed effects basically use only the within panel variance. Regression without panel dummies mixes within panel variance and cross panel variance. Part of the question is what is your theoretical stance – if you want to understand within panel behavior over time, fixed effects makes sense no matter what. If on the other hand you want to understand cross panel variance, then a different estimator like the Mundlak or xthybrid estimators makes sense.

[Carlo Lazzaro]

Samuel:
I do share Phil's comments.
At the top of that, my guess is that you -regress- model may suffer from quasi-extreme multicolinearity, as you have a significan R-sq but most of your coefficients do not reach statistical significance and 95% CIs are really wide.
I would run -estat vif- after -regress-.
Besides, unlike in -xtreg-, -cluster- and -robust- options do a different job under -regress-. Usually, the first option is used when you detect heteroskedastcity amd -cluster()- is the way to go when you detect autocorrelation. If you have both heteroskedasticity and autocorrelation, the advice is to go -cluster()-.

[Samuel Renhoar]

Phil:
When you said "if you look at the xtreg you will see that half of the variance is in the fixed effects", did you referring to rho number under the xtreg command?
Correct me if i'm wrong, i assumed that when i'm using fixed effect model and include the fixed and time dummies, my goal is to only control the parameter of my predictor (to have a better estimation), that is to say that the main purpose of my research is only to find the parameter of my predictor, so i don't really need to worry about the variance. Is that a correct assumption?

To be honest i don't understand your last words about variance but i only assumed that my goal is as i mentioned before.
Anyway, thank you phil i think i don't have to worry about it anymore.

[Samuel Renhoar]

Carlo:

in order to do -estat vif- which command do you mean to run before estat vif?
regress Y X1 X2 i.id i.year, vce (robust)
or
xtreg Y X1 X2 i.year, fe vce(robust)

I'm sorry Carlo, i don't get this words, "Usually, the first option is used when you detect heteroskedastcity amd -cluster()- is the way to go when you detect autocorrelation. If you have both heteroskedasticity and autocorrelation, the advice is to go -cluster()-"
what do you mean by "first option","heteroskedasticity amd", and what is difference between tw?

[Samuel Renhoar]

Carlo:

this a complete sentence for my last questions (this bug doesn't let me to complete my words)
what do you mean by "first option","heteroskedasticity amd", and what is difference between these two cases, because it seems like both cases ended with the same cluster command?

[Carlo Lazzaro]

Samuel:
under -regress- , -robust- option takes heteroskedasticity only into account: hence, if you have heteroskedasticity only, you are safe with -robust-.
If you have serial correlation only, you should go -cluster(), which is Always robust to heteroskedasticity if you detect both these nuisances at the same time.

[Carlo Lazzaro]

Samuel:

regress Y X1 X2 i.id i.year, vce (robust)
estat vif

or

regress Y X1 X2 i.id i.year, vce (robust)
estat vce, corr

xtreg Y X1 X2 i.year, fe vce(robust)

estat vce, corr

[Samuel Renhoar]

Carlo:

for #7, Thank you carlo now its crystal clear.

for#8 let me show all of those result

this for code number 1

. reg Y X1 X2 i.id i.year, vce (robust)

Linear regression                               Number of obs     =        222
                                                F(77, 144)        =      44.20
                                                Prob > F          =     0.0000
                                                R-squared         =     0.8589
                                                Root MSE          =     2.7764

------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          X1 |   .8808422    .166491     5.29   0.000     .5517603    1.209924
          X2 |   16.65939   12.42937     1.34   0.182    -7.908193    41.22696
             |
          id |
       APLN  |   .2947118   1.225192     0.24   0.810    -2.126972    2.716396
       ASDM  |   1.050584   1.462409     0.72   0.474    -1.839978    3.941145
       ASII  |     2.8694   2.413574     1.19   0.236     -1.90121     7.64001
       ASJT  |    2.31474   1.607534     1.44   0.152    -.8626728    5.492152
       ASMI  |   4.015512   1.669058     2.41   0.017      .716494    7.314531
       ASRI  |  -3.831059   .9604417    -3.99   0.000    -5.729445   -1.932674
       ASRM  |   2.211627   1.556897     1.42   0.158    -.8656974    5.288952
       BACA  |  -.0261848   .7748567    -0.03   0.973    -1.557747    1.505378
       BAPA  |   1.378856   1.827293     0.75   0.452    -2.232926    4.990638
       BBCA  |   .0173037   .6407342     0.03   0.978    -1.249156    1.283763
       BBMD  |   .3834314    .738184     0.52   0.604    -1.075645    1.842507
       BBNI  |   .2716186   .7533377     0.36   0.719     -1.21741    1.760647
       BBRI  |   .2827238   .6037333     0.47   0.640    -.9106003    1.476048
       BBTN  |   -.077315   .8124557    -0.10   0.924    -1.683195    1.528565
       BCIP  |   2.590771   1.405957     1.84   0.067    -.1882089    5.369752
       BDMN  |   .4528766   .9091776     0.50   0.619    -1.344181    2.249934
       BEST  |  -2.037454   1.330063    -1.53   0.128    -4.666422    .5915147
       BINA  |  -.1135588   .7325616    -0.16   0.877    -1.561522    1.334404
       BJBR  |    .561522    .830212     0.68   0.500    -1.079454    2.202498
       BJTM  |   .7062759   .9025418     0.78   0.435    -1.077666    2.490217
       BKSL  |  -1.372539   .6198285    -2.21   0.028    -2.597676   -.1474013
       BMRI  |   .3669541   .8332335     0.44   0.660    -1.279994    2.013903
       BNBA  |   .3175581   .7390014     0.43   0.668    -1.143134     1.77825
       BNGA  |   .2506866   .7081542     0.35   0.724    -1.149033    1.650406
       BNII  |  -.0686958   .7415254    -0.09   0.926    -1.534376    1.396985
       BOLT  |   2.443337   4.159148     0.59   0.558    -5.777531    10.66421
       BRAM  |   2.319903    1.84863     1.25   0.212    -1.334053    5.973858
       BSDE  |   1.708504   1.436532     1.19   0.236    -1.130908    4.547917
       COWL  |  -4.949813   1.340089    -3.69   0.000    -7.598599   -2.301026
       CTRA  |  -.0605993   .8110554    -0.07   0.941    -1.663711    1.542513
       DART  |  -1.910334   .9455116    -2.02   0.045    -3.779209   -.0414595
       DILD  |   .4385749    .690611     0.64   0.526    -.9264696    1.803619
       DMAS  |  -.8064493   1.466592    -0.55   0.583    -3.705279     2.09238
       DUTI  |   2.279153   .8200434     2.78   0.006     .6582761    3.900031
       FMII  |  -5.050991   3.634907    -1.39   0.167    -12.23566    2.133676
       GMTD  |   1.609945   .7361016     2.19   0.030      .154985    3.064905
       GPRA  |   .7070048   .9660833     0.73   0.465    -1.202531    2.616541
       INDS  |   .3487059   2.395833     0.15   0.884    -4.386837    5.084249
       JRPT  |    4.44845   1.494431     2.98   0.003     1.494595    7.402305
       JTPE  |    .834028   3.572804     0.23   0.816    -6.227887    7.895942
       KIJA  |  -2.493057   1.432208    -1.74   0.084    -5.323924    .3378107
       LINK  |   5.043667   4.371182     1.15   0.250    -3.596301    13.68364
       LPCK  |   6.240876   6.955493     0.90   0.371    -7.507178    19.98893
       LPGI  |   1.179102   .8410096     1.40   0.163    -.4832171     2.84142
       LPKR  |   .7737229   1.459914     0.53   0.597    -2.111906    3.659352
       MARI  |   4.511691     6.4431     0.70   0.485     -8.22358    17.24696
       MDIA  |   3.637022   4.998187     0.73   0.468    -6.242271    13.51631
       MDLN  |  -5.018098   2.952339    -1.70   0.091    -10.85362    .8174219
       MEGA  |   3.629563   3.339883     1.09   0.279    -2.971967    10.23109
       MKPI  |   5.926182   2.035153     2.91   0.004     1.903549    9.948814
       MMLP  |   .8126784    2.50436     0.32   0.746    -4.137377    5.762734
       MNCN  |     1.6835   2.823976     0.60   0.552    -3.898301    7.265301
       MREI  |   2.293249   1.157294     1.98   0.049     .0057712    4.580727
       MTLA  |   3.542054   1.936665     1.83   0.069    -.2859105    7.370019
       MYRX  |  -2.469469   .7999408    -3.09   0.002    -4.050612   -.8883258
       NISP  |   .0944043   .7654037     0.12   0.902    -1.418474    1.607282
       PLIN  |   1.818417   3.990349     0.46   0.649    -6.068808    9.705643
       PNBN  |  -.5133411   .6766237    -0.76   0.449    -1.850739    .8240564
       PNIN  |   1.555931   .8908233     1.75   0.083    -.2048478     3.31671
       PPRO  |  -7.645823    1.93914    -3.94   0.000    -11.47868   -3.812969
       PWON  |    .827668   1.376719     0.60   0.549     -1.89352    3.548856
       RDTX  |   1.647971   1.343093     1.23   0.222    -1.006753    4.302695
       RODA  |   .2733828   1.023854     0.27   0.790    -1.750341    2.297106
       SCBD  |   2.449009   .9853489     2.49   0.014     .5013928    4.396625
       SCMA  |   11.37837   6.599241     1.72   0.087     -1.66552    24.42227
       SDRA  |  -.2775776   .5947717    -0.47   0.641    -1.453188    .8980333
       SMDM  |  -.2651635   .9403621    -0.28   0.778     -2.12386    1.593533
       SMRA  |  -.8117748   .9704148    -0.84   0.404    -2.729872    1.106323
       SMSM  |   7.956638    7.70801     1.03   0.304    -7.278821     23.1921
       TARA  |  -1.243613   1.169836    -1.06   0.290    -3.555881    1.068655
       TLKM  |   4.399757   4.520706     0.97   0.332    -4.535757    13.33527
       VINS  |   2.005052   1.621869     1.24   0.218    -1.200693    5.210797
       VIVA  |  -4.834313    4.09723    -1.18   0.240     -12.9328    3.264169
             |
        year |
       2017  |  -.5542752   .4074146    -1.36   0.176    -1.359561    .2510102
       2018  |  -2.224763   .5223219    -4.26   0.000    -3.257171   -1.192354
             |
       _cons |  -1.037165   .6538399    -1.59   0.115    -2.329528    .2551992
------------------------------------------------------------------------------

. estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
          X1 |      4.05    0.247167
          X2 |     18.70    0.053486
          id |
          2  |      2.04    0.491325
          3  |      2.17    0.461177
          4  |      2.51    0.398404
          5  |      2.22    0.451449
          6  |      2.12    0.471656
          7  |      2.10    0.476757
          8  |      2.17    0.461579
          9  |      1.97    0.506810
         10  |      2.04    0.489476
         11  |      1.99    0.503765
         12  |      1.98    0.504301
         13  |      1.98    0.506045
         14  |      1.98    0.503804
         15  |      1.97    0.506787
         16  |      2.12    0.471037
         17  |      1.99    0.501544
         18  |      2.09    0.477395
         19  |      1.98    0.506209
         20  |      1.98    0.504364
         21  |      1.99    0.502469
         22  |      2.00    0.499891
         23  |      1.98    0.505835
         24  |      1.98    0.505452
         25  |      1.97    0.506372
         26  |      1.97    0.506686
         27  |      3.57    0.279836
         28  |      2.24    0.446401
         29  |      2.02    0.494005
         30  |      2.10    0.476913
         31  |      2.02    0.494865
         32  |      1.99    0.503436
         33  |      1.99    0.503010
         34  |      2.10    0.477297
         35  |      2.02    0.494321
         36  |      2.47    0.404489
         37  |      2.01    0.497430
         38  |      2.01    0.497165
         39  |      2.38    0.421015
         40  |      2.12    0.471457
         41  |      3.20    0.312271
         42  |      2.01    0.496527
         43  |      3.86    0.259255
         44  |      2.12    0.472456
         45  |      2.02    0.495334
         46  |      2.10    0.475651
         47  |      4.80    0.208144
         48  |      3.52    0.284123
         49  |      2.49    0.402010
         50  |      1.98    0.505512
         51  |      2.37    0.421144
         52  |      2.04    0.490043
         53  |      2.73    0.366918
         54  |      2.02    0.494357
         55  |      2.21    0.452832
         56  |      1.99    0.503404
         57  |      1.97    0.506605
         58  |      2.25    0.444504
         59  |      1.97    0.506440
         60  |      2.05    0.487498
         61  |      2.42    0.413355
         62  |      2.17    0.461584
         63  |      2.13    0.469281
         64  |      1.98    0.505502
         65  |      2.02    0.495296
         66  |      5.72    0.174788
         67  |      1.98    0.506075
         68  |      2.01    0.498242
         69  |      2.04    0.489250
         70  |      6.24    0.160248
         71  |      1.98    0.505786
         72  |      3.86    0.259237
         73  |      2.01    0.497687
         74  |      3.04    0.329145
        year |
       2017  |      1.36    0.737741
       2018  |      1.39    0.720815
-------------+----------------------
    Mean VIF |      2.56

code 2 is really long result, i'm sorry (it made me exceeds word limit)

code number 3

. xtreg Y X1 X2 i.year, fe vce(robust)

Fixed-effects (within) regression               Number of obs     =        222
Group variable: id                              Number of groups  =         74

R-sq:                                           Obs per group:
     within  = 0.5916                                         min =          3
     between = 0.6470                                         avg =        3.0
     overall = 0.6243                                         max =          3

                                                F(4,73)           =     100.72
corr(u_i, Xb)  = 0.1511                         Prob > F          =     0.0000

                                    (Std. Err. adjusted for 74 clusters in id)
------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          X1 |   .8808422   .1626354     5.42   0.000     .5567103    1.204974
          X2 |   16.65939   13.84521     1.20   0.233    -10.93408    44.25285
             |
        year |
       2017  |  -.5542752   .3520155    -1.57   0.120    -1.255841    .1472906
       2018  |  -2.224763    .567658    -3.92   0.000    -3.356104   -1.093422
             |
       _cons |  -.1550369   1.315367    -0.12   0.906    -2.776559    2.466485
-------------+----------------------------------------------------------------
     sigma_u |  2.9370361
     sigma_e |  2.7763652
         rho |  .52809954   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of xtreg model

             |                         2017.     2018.          
        e(V) |       X1        X2      year      year     _cons 
-------------+--------------------------------------------------
          X1 |   1.0000                                         
          X2 |  -0.8060    1.0000                               
   2017.year |   0.2298   -0.1837    1.0000                     
   2018.year |   0.3493    0.0553    0.5206    1.0000           
       _cons |   0.4471   -0.8797   -0.0472   -0.4620    1.0000

what does it tell carlo? and what should i do about it

[Jeff Wooldridge]

Samuel: A few additional comments.

1. Let me just emphasize what Carlo pointed out: vce(robust) works very different with regress and xtreg. In the latter case it is the same as vce(cluster id).
2. It is impossible to use standard errors clustered for serial correlation to test u(i) = 0. The test is not well defined. In fact, if you were to try

regress Y X1 X2 i.id i.year, vce (cluster id)

you will see that the standard errors for the id fixed effects are all over the place. They are not well defined. I won't go into details about why one cannot compute cluster-robust standard errors for the fixed effects, but you can't. And that means the F statistic is meaningless, too.

3. I'll disagree with Carlo about using VIFs in this context. The reason for the very high R-squared is because you are putting in all of those fixed effects. Those are doing a lot of work, and you shouldn't get credit for that. As Phil noted, you are using the within variation to estimate the effects of X1 and X2 on y. That's why you shouldn't be using reg to begin with because the goodness-of-fit is very misleading. The within R-squared reported with xtreg is much more telling -- and it's about .60 in your case.

So ignore vifs and don't worry about the correlation of the covariates, either. And under no circumstances do you care about the vifs of the fixed effects -- unit or time. Your X1 variance is very significant, X2 is not. The end, unless you have more variables to try, or want to add lags, interactions, and so on.

[Samuel Renhoar]

Jeff:

Thank you Jeff,
1. Yes i got this point and read this idea in stata manual, particulary the point that cluster (id) and robust option works in the same way for xtreg command (so thank you for confirming this point).
2. Okay jeff if you say so, i won't bother to use it anymore.
3. (Correct me if i'm wrong) When i'm trying to explain the goodness-of-fit for my model, does it mean that i should use within R-square for my model?

Okay, i think shouldn't worry about it anymore. I think explain the relationship between my dependent and independent variabel is all i wanted in my research.
Thank you jeff, you're really helpful.

Best Regards,
Samuel.

[Carlo Lazzaro]

Thanks Jeff Wooldridge for diasagreing with me: this one of the best way for me to learn!

[Jeff Wooldridge]

Samuel: In case you are still wondering about the F test, this is an example I use in my courses. You can see the standard errors are essentially zero in some cases, and the F statistic drops all but two of the constraints. The standard errors on ez and the year dummies are fine, subject to small sample (N = 22) concerns. But all standard errors and tests involving the city effects are meaningless.

. reg luclms ez i.year c2-c22, vce(cluster city)

Linear regression                               Number of obs     =        198
                                                F(8, 21)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9332
                                                Root MSE          =     .20051

                                  (Std. Err. adjusted for 22 clusters in city)
------------------------------------------------------------------------------
             |               Robust
      luclms |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          ez |  -.1044148   .0772488    -1.35   0.191    -.2650624    .0562328
             |
        year |
       1981  |  -.3216319   .0500958    -6.42   0.000    -.4258118    -.217452
       1982  |   .1354957   .0605516     2.24   0.036     .0095717    .2614197
       1983  |  -.2192554   .0898156    -2.44   0.024    -.4060372   -.0324736
       1984  |  -.5791517   .1048188    -5.53   0.000    -.7971344   -.3611691
       1985  |  -.5917868   .0964101    -6.14   0.000    -.7922827    -.391291
       1986  |  -.6212648   .0830494    -7.48   0.000    -.7939754   -.4485541
       1987  |  -.8889486    .088801   -10.01   0.000     -1.07362   -.7042769
       1988  |  -1.227633   .1017089   -12.07   0.000    -1.439148   -1.016118
             |
          c2 |   -.193488    .042916    -4.51   0.000    -.2827366   -.1042393
          c3 |  -.3789381    .042916    -8.83   0.000    -.4681868   -.2896894
          c4 |  -.5411763    .042916   -12.61   0.000     -.630425   -.4519276
          c5 |   .0110321   .0085832     1.29   0.213    -.0068176    .0288819
          c6 |   .5545758   1.28e-14  4.3e+13   0.000     .5545758    .5545758
          c7 |   .7500629   1.28e-14  5.9e+13   0.000     .7500629    .7500629
          c8 |  -.0587597   .0085832    -6.85   0.000    -.0766094   -.0409099
          c9 |   .3534239   .0085832    41.18   0.000     .3355741    .3712736
         c10 |    1.64501    .042916    38.33   0.000     1.555761    1.734259
         c11 |  -.1303174    .042916    -3.04   0.006    -.2195661   -.0410687
         c12 |  -.0349802    .042916    -0.82   0.424    -.1242289    .0542685
         c13 |  -.8325769    .042916   -19.40   0.000    -.9218256   -.7433282
         c14 |  -.8736305   .0085832  -101.78   0.000    -.8914802   -.8557808
         c15 |  -.2354225    .042916    -5.49   0.000    -.3246712   -.1461738
         c16 |   .4357443    .042916    10.15   0.000     .3464957     .524993
         c17 |   -.445226   1.27e-14 -3.5e+13   0.000     -.445226    -.445226
         c18 |  -.0428939    .042916    -1.00   0.329    -.1321425    .0463548
         c19 |   .0934068    .042916     2.18   0.041     .0041582    .1826555
         c20 |  -.3509774   1.28e-14 -2.8e+13   0.000    -.3509774   -.3509774
         c21 |   .4577897   1.28e-14  3.6e+13   0.000     .4577897    .4577897
         c22 |   .2186381    .042916     5.09   0.000     .1293894    .3078867
       _cons |   11.67615   .0665544   175.44   0.000     11.53775    11.81456
------------------------------------------------------------------------------

. testparm c2-c22

 ( 1)  c2 = 0
 ( 2)  c3 = 0
 ( 3)  c4 = 0
 ( 4)  c5 = 0
 ( 5)  c6 = 0
 ( 6)  c7 = 0
 ( 7)  c8 = 0
 ( 8)  c9 = 0
 ( 9)  c10 = 0
 (10)  c11 = 0
 (11)  c12 = 0
 (12)  c13 = 0
 (13)  c14 = 0
 (14)  c15 = 0
 (15)  c16 = 0
 (16)  c17 = 0
 (17)  c18 = 0
 (18)  c19 = 0
 (19)  c20 = 0
 (20)  c21 = 0
 (21)  c22 = 0
       Constraint 1 dropped
       Constraint 2 dropped
       Constraint 3 dropped
       Constraint 4 dropped
       Constraint 5 dropped
       Constraint 6 dropped
       Constraint 7 dropped
       Constraint 8 dropped
       Constraint 9 dropped
       Constraint 11 dropped
       Constraint 12 dropped
       Constraint 13 dropped
       Constraint 14 dropped
       Constraint 15 dropped
       Constraint 16 dropped
       Constraint 17 dropped
       Constraint 18 dropped
       Constraint 19 dropped
       Constraint 20 dropped
       Constraint 21 dropped

       F(  1,    21) =    9.22
            Prob > F =    0.0063

[Samuel Renhoar]

Jeff:

Thank you Jeff for even providing a good example.
Best regards.