Wald chi2 & Prob > chi2 value did not show in my xtreg re vce(robust) output

[Saadatu Asema]

My thesis supervisor is making a big deal out of this and I am considering using PCSE or FGLS regression because the above values come up with PCSE and FGLS.

 xtreg roa npl stdta de ltdr avinf_npl avinf_stdta avinf_de avinf_ltdr, re vce(robust)

Random-effects GLS regression                   Number of obs      =        80
Group variable: id                              Number of groups   =         8

R-sq:  within  = 0.6739                         Obs per group: min =        10
       between = 0.5108                                        avg =      10.0
       overall = 0.6129                                        max =        10

                                                Wald chi2(7)       =         .
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =         .

                                     (Std. Err. adjusted for 8 clusters in id)
------------------------------------------------------------------------------
             |               Robust
         roa |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         npl |  -.2263572   .0303436    -7.46   0.000    -.2858296   -.1668848
       stdta |   .1056417    .035604     2.97   0.003     .0358592    .1754242
          de |  -.8938725   .3424584    -2.61   0.009    -1.565079   -.2226665
        ltdr |  -.0258621   .0233812    -1.11   0.269    -.0716884    .0199641
   avinf_npl |   .0141532   .0024576     5.76   0.000     .0093365    .0189699
 avinf_stdta |  -.0106536   .0021378    -4.98   0.000    -.0148436   -.0064636
    avinf_de |   .0718727   .0279978     2.57   0.010      .016998    .1267474
  avinf_ltdr |   .0012853   .0011808     1.09   0.276    -.0010289    .0035996
       _cons |   3.839852   1.845138     2.08   0.037     .2234476    7.456256
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  .85396652
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------


Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of roa

         chi2(1)      =    83.82
         Prob > chi2  =   0.0000

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,       7) =      0.000
           Prob > F =      0.9851

[Clyde Schechter]

Your adviser probably needs to learn some basic statistics about how robust standard errors work. There is nothing wrong here. You have 8 id-defined groups. So the number of degrees of freedom in the model is based on the number of groups, i.e. it is 8-1 = 7. It is not based on the sample size. Now, look at how many explanatory variables are in your model: 9 (including _cons). You cannot test a 9-dimensional hypothesis with 7 degrees of freedom. So there is no chi square statistic for the entire model. Nevertheless, the individual coefficient standard error calculations are fine, as each involves only 1 degree of freedom.

Now, let's remember what the overall model chi square statistic is about. It's a test of the omnibus hypothesis that all 9 of the coefficients in your model (including the constant term) are zero. Unless that specific hypothesis test is an answer to one of your research questions, it is completely irrelevant. Even if you had a value for that chi square and p-value, the only thing you would appropriately do with it is ignore it.

If that omnibus hypothesis test is in fact an answer to one of your research questions, then you are not able to answer that question with this model and you would need to do something different.

By the way, -xtreg, re- is a GLS estimator. Whether PCSE would make sense in your data depends on what these variables are and whether that implies that the error terms really are (or should be expected to be) correlated contemporaneously across panels. Picking a model just because it produces a desired result is not appropriate. You should use a model that is a reasonably good match to the real world data generating process you are modeling, as best we understand it.