Xtreg re or Pooled OLS

[Luke Brown]

Good morning,
I have a doubt regarding the choice between a pooled OLS and random effect model(FE has been rejected by hausman test). Since results are very similar, how can I know which is the best one?
Results are as follows

xtreg riskavers i.hhsex i.Age i.Educ i.Race logincome logwealth i.crisis, vce(cluster YY1)

Random-effects GLS regression                   Number of obs      =     28816
Group variable: YY1                             Number of groups   =      6512

R-sq:  within  = 0.2451                         Obs per group: min =         1
       between = 0.2561                                        avg =       4.4
       overall = 0.2470                                        max =         6

                                                Wald chi2(15)      =  11456.28
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

                                            (Std. Err. adjusted for 6512 clusters in YY1)
-----------------------------------------------------------------------------------------
                        |               Robust
              riskavers |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                2.hhsex |  -.0769613   .0080151    -9.60   0.000    -.0926706    -.061252
                        |
                    Age |
                 31-40  |  -.0825255   .0132473    -6.23   0.000    -.1084897   -.0565613
                 41-50  |  -.1479359   .0125065   -11.83   0.000    -.1724481   -.1234236
                 51-60  |  -.2032754   .0126981   -16.01   0.000    -.2281633   -.1783875
                 61-70  |  -.2907162   .0133807   -21.73   0.000     -.316942   -.2644904
                   >70  |  -.3951584   .0138086   -28.62   0.000    -.4222228    -.368094
                        |
                   Educ |
           High school  |   .1136211   .0211006     5.38   0.000     .0722647    .1549775
       College diploma  |   .2599014   .0219011    11.87   0.000     .2169761    .3028268
    Bachelor or higher  |   .3341337   .0217551    15.36   0.000     .2914946    .3767729
                        |
                   Race |
Black/African American  |  -.0271337   .0112309    -2.42   0.016    -.0491459   -.0051215
              Hispanic  |  -.1192264   .0130494    -9.14   0.000    -.1448028   -.0936501
       Asian and other  |  -.0571324   .0149053    -3.83   0.000    -.0863462   -.0279186
                        |
              logincome |   .0325405   .0031336    10.38   0.000     .0263988    .0386822
              logwealth |   .0478233   .0019773    24.19   0.000     .0439479    .0516987
               1.crisis |  -.0215324   .0057067    -3.77   0.000    -.0327172   -.0103476
                  _cons |    .735227   .0319558    23.01   0.000     .6725947    .7978593
------------------------+----------------------------------------------------------------
                sigma_u |  .06082281
                sigma_e |  .47364256
                    rho |  .01622289   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------

And for pooled:

reg riskavers i.hhsex i.Age i.Educ i.Race logincome logwealth i.crisis, vce(cluster YY1)

Linear regression                                      Number of obs =   28816
                                                       F( 15,  6511) =  763.13
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.2470
                                                       Root MSE      =  .47699

                                            (Std. Err. adjusted for 6512 clusters in YY1)
-----------------------------------------------------------------------------------------
                        |               Robust
              riskavers |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                2.hhsex |  -.0772738   .0080188    -9.64   0.000    -.0929934   -.0615543
                        |
                    Age |
                 31-40  |  -.0825552   .0132448    -6.23   0.000    -.1085194   -.0565911
                 41-50  |  -.1478768    .012499   -11.83   0.000    -.1723788   -.1233747
                 51-60  |  -.2032355   .0127015   -16.00   0.000    -.2281345   -.1783364
                 61-70  |  -.2903652   .0133909   -21.68   0.000    -.3166157   -.2641147
                   >70  |  -.3949107   .0138091   -28.60   0.000     -.421981   -.3678404
                        |
                   Educ |
           High school  |   .1140297   .0210833     5.41   0.000     .0726995      .15536
       College diploma  |   .2605843   .0218812    11.91   0.000       .21769    .3034786
    Bachelor or higher  |   .3346558   .0217346    15.40   0.000     .2920489    .3772627
                        |
                   Race |
Black/African American  |  -.0272847    .011225    -2.43   0.015    -.0492894   -.0052799
              Hispanic  |  -.1193019   .0130651    -9.13   0.000    -.1449137     -.09369
       Asian and other  |   -.056815   .0149023    -3.81   0.000    -.0860284   -.0276017
                        |
              logincome |   .0327228   .0031347    10.44   0.000     .0265778    .0388679
              logwealth |   .0477421    .001978    24.14   0.000     .0438646    .0516196
               1.crisis |  -.0215046   .0057056    -3.77   0.000    -.0326893   -.0103198
                  _cons |   .7335781    .031953    22.96   0.000     .6709398    .7962164

Thank you so much for your help

[Carlo Lazzaro]

Luke:
what does -xttest0- tells you?

[Luke Brown]

This is what I obtain when I run -xttest0- after the xtreg estimation:

xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        riskavers[YY1,t] = Xb + u[YY1] + e[YY1,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
               riskavers |   .3019869       .5495334
                       e |   .2243373       .4736426
                       u |   .0036994       .0608228

        Test:   Var(u) = 0
                             chibar2(01) =     7.81
                          Prob > chibar2 =   0.0026

[Carlo Lazzaro]

Luke:
then check with the user-written command -xtoverid- whether -re- specification is the way to go.
Please note that you cannot test fe vs re with -hausman- if you impose non-default standard errors (nor is correct to invoke them after -hausman- outcome with defauls standard errors).