Hausman test for panel data

[Abdelmoneam Khaled]

I am performing a Hausman test to decide whether to use fixed effects or random effects model. The results I get are as follows:

. *Huasman test

. 
.  xtreg  lnTotal lnINS lnINFO EX Fopen  DCC  DDiff lnINF lnliquid lnreserve GDP  DC, fe

Fixed-effects (within) regression               Number of obs     =        166
Group variable: Country1                        Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.0961                                         min =         14
     between = 0.0023                                         avg =       16.6
     overall = 0.0000                                         max =         19

                                                F(11,145)         =       1.40
corr(u_i, Xb)  = -0.1736                        Prob > F          =     0.1782

------------------------------------------------------------------------------
     lnTotal |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lnINS |  -.0185582   .0639773    -0.29   0.772    -.1450068    .1078903
      lnINFO |  -.0898688   .0363678    -2.47   0.015    -.1617483   -.0179893
          EX |   .0006407   .0026112     0.25   0.807    -.0045203    .0058016
       Fopen |  -.0000704    .006281    -0.01   0.991    -.0124846    .0123438
         DCC |   .0696891   .0565816     1.23   0.220    -.0421421    .1815203
       DDiff |   -.000171   .0003266    -0.52   0.601    -.0008164    .0004744
       lnINF |  -.0024146   .0038216    -0.63   0.528    -.0099678    .0051386
    lnliquid |   .0069447   .0162551     0.43   0.670    -.0251829    .0390722
   lnreserve |  -.0000648   .0094526    -0.01   0.995    -.0187476    .0186179
         GDP |  -2.41e-07   8.55e-07    -0.28   0.779    -1.93e-06    1.45e-06
          DC |    .000066   .0001659     0.40   0.691    -.0002619    .0003938
       _cons |    2.41544   .2245863    10.76   0.000     1.971554    2.859326
-------------+----------------------------------------------------------------
     sigma_u |  .10458566
     sigma_e |  .03365599
         rho |  .90616053   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 145) = 39.74                     Prob > F = 0.0000

. 
. . est store fe

. 
.  xtreg  lnTotal lnINS lnINFO EX Fopen  DCC  DDiff lnINF lnliquid lnreserve GDP  DC, re

Random-effects GLS regression                   Number of obs     =        166
Group variable: Country1                        Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.0333                                         min =         14
     between = 0.8975                                         avg =       16.6
     overall = 0.7080                                         max =         19

                                                Wald chi2(11)     =     373.44
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     lnTotal |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lnINS |  -.2017622   .0624443    -3.23   0.001    -.3241509   -.0793735
      lnINFO |  -.3138742   .0415717    -7.55   0.000    -.3953532   -.2323952
          EX |   .0198729   .0019662    10.11   0.000     .0160192    .0237266
       Fopen |   .0489099   .0037879    12.91   0.000     .0414857    .0563341
         DCC |   .1402536   .1003481     1.40   0.162     -.056425    .3369322
       DDiff |  -.0001883    .000587    -0.32   0.748    -.0013388    .0009622
       lnINF |  -.0174453   .0056082    -3.11   0.002    -.0284372   -.0064533
    lnliquid |   .1004124   .0197108     5.09   0.000       .06178    .1390448
   lnreserve |   .0142735   .0091647     1.56   0.119     -.003689     .032236
         GDP |   2.92e-06   3.19e-07     9.17   0.000     2.30e-06    3.55e-06
          DC |  -.0002536   .0002279    -1.11   0.266    -.0007003    .0001932
       _cons |   3.094598   .2414919    12.81   0.000     2.621283    3.567914
-------------+----------------------------------------------------------------
     sigma_u |          0
     sigma_e |  .03365599
         rho |          0   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. 
. . est store re

. 
. . hausman fe re,sigmamore

Note: the rank of the differenced variance matrix (9) does not equal the number of coefficients being tested
        (11); be sure this is what you expect, or there may be problems computing the test.  Examine the output
        of your estimators for anything unexpected and possibly consider scaling your variables so that the
        coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference          S.E.
-------------+----------------------------------------------------------------
       lnINS |   -.0185582    -.2017622         .183204        .0972626
      lnINFO |   -.0898688    -.3138742        .2240054        .0508787
          EX |    .0006407     .0198729       -.0192322        .0042882
       Fopen |   -.0000704     .0489099       -.0489803        .0106965
         DCC |    .0696891     .1402536       -.0705645        .0194799
       DDiff |    -.000171    -.0001883        .0000172         .000059
       lnINF |   -.0024146    -.0174453        .0150307        .0040267
    lnliquid |    .0069447     .1004124       -.0934677        .0217691
   lnreserve |   -.0000648     .0142735       -.0143383        .0144098
         GDP |   -2.41e-07     2.92e-06       -3.16e-06        1.51e-06
          DC |     .000066    -.0002536        .0003195        .0001946
------------------------------------------------------------------------------
                           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(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      109.57
                Prob>chi2 =      0.0000
                (V_b-V_B is not positive definite)

. 
. *Breusch Pagan  LM test for random effects VS OLS

. 
. . quietly xtreg Total INS INFO Fopen Topen Diff INF    liquid reserve DC, re

. 
. xttest0

Breusch and Pagan Lagrangian multiplier test for random effects

        Total[Country1,t] = Xb + u[Country1] + e[Country1,t]

        Estimated results:
                         |       Var     sd = sqrt(Var)
                ---------+-----------------------------
                   Total |    .473289         .68796
                       e |   .0465037       .2156472
                       u |          0              0

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

. 
. ** Test FE or RE STD**

. 
. xtoverid
Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS
r(198);

How do I go about interpreting the results?

[Carlo Lazzaro]

Abdelmoneam:
I would repeat -hausman- with the -sigmamore- option.
The -xttest0- should be performed before (and not after) -hausman-.
That said, I'm under the impression that the -fe- specification fits your data better than the -re- one.

[Abdelmoneam Khaled]

Thank you,

I did the xttest0 before hausman and it gives me the same results

[Carlo Lazzaro]

Abdelmonean:
have you add the -sigmamore- option to -hausman-?

[Abdelmoneam Khaled]

Yes, I have

[Carlo Lazzaro]

Abdelmonean:
I would go -fe-.

[Ferra Nazanin]

Can we apply hausman for a regression clustered by company ID over two years? And is there any easy legend explaining step by step about whether endogeneity exists and so on?

[Carlo Lazzaro]

Ferra:
welcome to this forum.
1),no, you should switch to the community-contributed command -xtoverid- (assuming that you refer to -xtreg-);
2) there's no hard and fast rule about endogeneity detection. Take a look at the reference quoted in -xtivreg- and -ivregress-.