xttest0 test and hausman test

[Enza Testa]

Hi guys! I tested the presence of fixed invariant effect in my model with the hausman and I obtained a small p-value 0.0143 so I reject the null and consider the fixed effect model. Then I tested the ols against re with the xttest0 and I obtained a pvalue=1.000, so I need to reject the random effect model again. I need to prefer the fixed or the ols? thank you!!

xtreg price age nbh cbd intst rooms area land baths dist,fe
est store fe
xtreg price age nbh cbd intst rooms area land baths dist,re
est store re
hausman fe re

    Test:  Ho:  difference in coefficients not systematic

                  chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       17.62
                Prob>chi2 =      0.0138

xtreg price age nbh cbd intst rooms area land baths dist,re vce (cluster id)
xttest0

price[id,t] = Xb + u[id] + e[id,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                   price |   2.05e+09       45318.08
                       e |   1.15e+09       33875.28
                       u |          0              0

        Test:   Var(u) = 0
                             chibar2(01) =     0.00
                          Prob > chibar2 =   1.0000

[Carlo Lazzaro]

Enza:
you're reporting results of different models:
-those compared via -hausman- have defaulst standard errors;
-the last one has clustered standard errors.

That said, sticking with the first comparison, if the F.test at the foot of -xtreg, fe- outcome table does not reach satistical significance, pooled OLS outperforms -xtreg, fe-.

[Enza Testa]

I tested the Hausman without robust standard error since the test does not allow to do it. About the second point you are right, I tested the model with clustered standard errors but I also did it without cluster option and the results are the same (maybe it does not affect the result of the test, I'm just mking an hypotesis). So, also if I detected the presence of fixed effect you think that considering the results of the BP test I need to perform an OLS model?

[Carlo Lazzaro]

Enza:
not quite.
My previous suggestion was to look at the F-test at the foot of -xtreg, fe- outcome table does not reach satistical significance, pooled OLS outperforms -xtreg, fe-.
Put differently, if the null of -re- specification has been rejected by -hausman-, testing BP on -re- seems pointless.

[Enza Testa]

The results after xtreg fe is the following

 
xtreg price age nbh cbd intst rooms area land baths dist,fe vce (cluster id)

Fixed-effects (within) regression               Number of obs      =       284
Group variable: id                              Number of groups   =       142

R-sq:  within  = 0.6167                         Obs per group: min =         2
       between = 0.1052                                        avg =       2.0
       overall = 0.3563                                        max =         2

                                                F(9,141)           =     30.21
corr(u_i, Xb)  = -0.4356                        Prob > F           =    0.0000

                                   (Std. Err. adjusted for 142 clusters in id)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -344.8193   147.4296    -2.34   0.021    -636.2774   -53.36113
         nbh |    10712.8    3672.44     2.92   0.004     3452.637    17972.96
         cbd |   .7035692   3.136893     0.22   0.823    -5.497854    6.904992
       intst |  -2.795218   2.238024    -1.25   0.214    -7.219638    1.629202
       rooms |  -6389.045   3925.237    -1.63   0.106    -14148.97    1370.879
        area |   36.75132   6.139734     5.99   0.000     24.61349    48.88915
        land |    .130162   .1170249     1.11   0.268    -.1011881    .3615122
       baths |   19080.05   6318.069     3.02   0.003      6589.66    31570.44
        dist |   1.726177   1.383375     1.25   0.214    -1.008661    4.461014
       _cons |  -1464.453   24218.54    -0.06   0.952    -49342.84    46413.93
-------------+----------------------------------------------------------------
     sigma_u |  31135.824
     sigma_e |   33875.28
         rho |  .45793642   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Here the F test i significant.

I tested the with Hausman in order to detect the presence of FE and I rejected the null so I excluded RE. Then i tested with BP ols against RE just because the professor told me to do it but maybe it does not make sense.

[Carlo Lazzaro]

Enza:
I referred to the other F-test, that appears at the foot of -xtreg, fe- outcome (which is not calculated if the standrd errors are not in default mode).
Hence, you have to use your first two codes (I mean -fe- vs -re-).
See also on this topic any decent panel data econometrics textbook or, just to start off, -xtreg- entry in Stata .pdf manual.

[Enza Testa]

Ok, sorry for not understand but I'm a beginner. I didn't use the default standard, just robust error. If I consider default standard errors I obtain the following

. xtreg price age nbh cbd intst rooms area land baths dist,fe 

Fixed-effects (within) regression               Number of obs      =       284
Group variable: id                              Number of groups   =       142

R-sq:  within  = 0.6167                         Obs per group: min =         2
       between = 0.1052                                        avg =       2.0
       overall = 0.3563                                        max =         2

                                                F(9,133)           =     23.77
corr(u_i, Xb)  = -0.4356                        Prob > F           =    0.0000

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -344.8193   105.3651    -3.27   0.001    -553.2273   -136.4112
         nbh |    10712.8   4897.249     2.19   0.030      1026.23    20399.37
         cbd |   .7035692   4.421159     0.16   0.874    -8.041313    9.448451
       intst |  -2.795218   3.110046    -0.90   0.370    -8.946769    3.356332
       rooms |  -6389.045   4520.193    -1.41   0.160    -15329.81    2551.721
        area |   36.75132   6.473148     5.68   0.000     23.94768    49.55496
        land |    .130162   .0872943     1.49   0.138    -.0425028    .3028269
       baths |   19080.05   6314.962     3.02   0.003       6589.3     31570.8
        dist |   1.726177   1.824837     0.95   0.346     -1.88328    5.335633
       _cons |  -1464.453   25664.27    -0.06   0.955    -52227.38    49298.47
-------------+----------------------------------------------------------------
     sigma_u |  31135.824
     sigma_e |   33875.28
         rho |  .45793642   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(141, 133) =     0.61            Prob > F = 0.9983

In this case I fail to reject the null, so OLS outperforms fe? I can extend this result also at the case with robust standard errors?

[Marcos Almeida]

Carlo already point it out, in general terms in #2 and #4.

Specifically related to your question, as rephrased above: yes and yes.

[Enza Testa]

Thank you Carlo and Marcos!!

[Carlo Lazzaro]

Enza:
Nick Cox in one of his quite old post said something like: "...we are all beginners, some of us are only more experienced...".
Back to your query: if you impose cluster/robust standard errors you should compare -fe- and -re- via the user-written programme -xtoverid- (type -search xtoverid- from within Stata to install it).
As you did not include -fvvarlist- notation in your code, you will not face problems in running it.

[Enza Testa]

Thanks Carlo!