Significance of the F-test in a FE model

[Onur Tekel]

Dear list members,

I have an unbalanced panel data (max. T=21, quarterly) composed of bank-specific variables (i.e. mostly financial ratios) for 28 banks. My dependent variable is non-stationary, and all independent variables are stationary according to Fisher-type unit root test. Therefore, I performed a first-difference transformation for the dependent variable and continue for the analyses.
I perform FE and RE models (i.e. various models including different variables and different lag orders) respectively, and F-test results in some of the models indicate "no u_i effects". Further, the Hausman test rejects the null in favor of the FE model. On the other hand, when I run the same model without transformation I obtain significant F-test results.
I did not perform cointegration tests, because only the dependent variable has a unit root. My question is what should be a proper next step?: To test the poolability, to continue with the RE model or use untransformed dependent variable in the analyses?

Best Regards,

Onur

[Carlo Lazzaro]

Onuk:
welcome to this forum.
From your description (that can be be remakably improved with sharing what you typed and what Stata gave you back via CODE delimiters, as per FAQ) it seems that you have used -xtreg-.
However, as your N and T dimensions are both long, you should consider -xtgls- and -xtregar-.

[Onur Tekel]

Dear Carlo,

Thank you for your reply and kind welcome. Below you can see two of the models that I estimate for the same lag structure. First the FE model and next the RE model:

. xtreg D.NPL_Gross L.(D.NPL_Gross) L.(CosttoIncome EA Diversification ROE AbsoluteSize LSV), fe

Fixed-effects (within) regression               Number of obs      =       515
Group variable: bank                            Number of groups   =        28

R-sq:  within  = 0.1301                         Obs per group: min =         2
       between = 0.2579                                        avg =      18.4
       overall = 0.0218                                        max =        19

                                                F(7,480)           =     10.26
corr(u_i, Xb)  = -0.7402                        Prob > F           =    0.0000

---------------------------------------------------------------------------------
    D.NPL_Gross |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      NPL_Gross |
            LD. |  -.3497388   .0431137    -8.11   0.000    -.4344537   -.2650239
                |
   CosttoIncome |
            L1. |  -.0000866   .0000861    -1.01   0.315    -.0002557    .0000825
                |
             EA |
            L1. |  -.1440745   .0601065    -2.40   0.017    -.2621789   -.0259701
                |
Diversification |
            L1. |  -.0022121   .0075998    -0.29   0.771     -.017145    .0127209
                |
            ROE |
            L1. |  -.0028489   .0380603    -0.07   0.940    -.0776342    .0719365
                |
   AbsoluteSize |
            L1. |  -.0002535   .0082527    -0.03   0.976    -.0164694    .0159625
                |
            LSV |
            L1. |   .0745034   .1028754     0.72   0.469    -.1276383    .2766451
                |
          _cons |   .0238524   .1406159     0.17   0.865    -.2524463    .3001511
----------------+----------------------------------------------------------------
        sigma_u |  .02583369
        sigma_e |  .03950041
            rho |  .29958747   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0:     F(27, 480) =     1.14             Prob > F = 0.2919

. xtreg D.NPL_Gross L.(D.NPL_Gross) L.(CosttoIncome EA Diversification ROE AbsoluteSize LSV), re

Random-effects GLS regression                   Number of obs      =       515
Group variable: bank                            Number of groups   =        28

R-sq:  within  = 0.1088                         Obs per group: min =         2
       between = 0.0009                                        avg =      18.4
       overall = 0.1004                                        max =        19

                                                Wald chi2(7)       =     56.60
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

---------------------------------------------------------------------------------
    D.NPL_Gross |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
      NPL_Gross |
            LD. |  -.3081634   .0425825    -7.24   0.000    -.3916236   -.2247032
                |
   CosttoIncome |
            L1. |  -.0000943   .0000839    -1.12   0.261    -.0002587    .0000702
                |
             EA |
            L1. |   .0303691   .0211455     1.44   0.151    -.0110753    .0718136
                |
Diversification |
            L1. |   .0002925   .0058996     0.05   0.960    -.0112706    .0118556
                |
            ROE |
            L1. |   .0162871   .0234697     0.69   0.488    -.0297127    .0622869
                |
   AbsoluteSize |
            L1. |   .0000743     .00132     0.06   0.955    -.0025129    .0026616
                |
            LSV |
            L1. |   .0966939    .101085     0.96   0.339     -.101429    .2948168
                |
          _cons |  -.0104245    .023547    -0.44   0.658    -.0565759    .0357268
----------------+----------------------------------------------------------------
        sigma_u |          0
        sigma_e |  .03950041
            rho |          0   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

and also below you can find the Hausman test results:

. hausman fe

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           .          Difference          S.E.
-------------+----------------------------------------------------------------
LD.NPL_Gross |   -.3497388    -.3081634       -.0415753        .0067469
L.CosttoIn~e |   -.0000866    -.0000943        7.63e-06         .000019
        L.EA |   -.1440745     .0303691       -.1744436        .0562642
L.Diversi~on |   -.0022121     .0002925       -.0025045        .0047907
       L.ROE |   -.0028489     .0162871        -.019136        .0299626
L.Absolute~e |   -.0002535     .0000743       -.0003278        .0081465
       L.LSV |    .0745034     .0966939       -.0221905        .0191093
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       43.41
                Prob>chi2 =      0.0000
                (V_b-V_B is not positive definite)

[Carlo Lazzaro]

Onur:
what does -xttets0- tell you after -xtreg,re-?
Probably that there's no evidence of panel-wise random effect.
Hence, I think you should switch to a pooled OLS.

[Onur Tekel]

Onur:
what does -xttets0- tell you after -xtreg,re-?

Well, I get a "not sorted" error when I perform the BP Lagrange Multiplier test. According to what I read from the other entries this error arises when the estimation is performed with "L" operator. As a workaround, generating the laggged variables instead of using the lag operator is suggested. I tried it, but the error persists.

[Carlo Lazzaro]

Onur:
set aside -xttest0- for a while, both the F-test after -xtreg,fe- and the u_i in -xtreg,re- does not seem to show any evidence of a panel-wise effect.
In my opinion, you should switch to a pooled OLS.

[Onur Tekel]

I think you are right. I performed poolability test after your comment (thanks a lot, by the way). The code and the result are as follows:

regress D.NPL_Gross L.(D.NPL_Gross) L.(CosttoIncome EA Diversification ROE AbsoluteSize LSV)
regress D.NPL_Gross L.(D.NPL_Gross) L.(CosttoIncome EA Diversification ROE AbsoluteSize LSV) i.bank
testparm i.bank

F( 27,   480) =    1.14
            Prob > F =    0.2919

So this means "No bank related effects".

[Carlo Lazzaro]

Onur:
pooled OLS seems to be the way to go, then.