# st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test

 From Muhammad Billal Malik To statalist@hsphsun2.harvard.edu Subject st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test Date Thu, 26 Feb 2009 18:41:58 +0000

```I am having some problems with my econometrics based dissertation. I
doing a panel data on 12 sub-saharan african nations, with 6 variables
over a 17 year time period.

I am using a simple log log model to test to see if one of my
variables lx2 (tourism receipts) has a positive affect on GDP. I have
run a pooled regression, then fixed effects between and within, and
finally a random effects. I have then carried out a Hausman test and
achieved a negative value, which has confused me more. I was wondering
what do I do, as in what model shall I choose? I have attached my
STATA output so you can see if I have gone through the right steps.

I will really appreciate if you can help me,

Kind Regards,

Mohammud

Carrying out a pooled data regression
. regress ly lx1 lx2 lx3 lx4 lx5 lx6

Source |       SS       df       MS              Number of obs =      57
-------------+------------------------------           F(  6,    50) =   52.04
Model |  59.1406489     6  9.85677481           Prob > F      =  0.0000
Residual |  9.47031674    50  .189406335           R-squared     =  0.8620
Total |  68.6109656    56  1.22519581           Root MSE      =  .43521

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |    .173204   .0545574     3.17   0.003     .0636223    .2827857
lx2 |   .0816157   .0737985     1.11   0.274    -.0666129    .2298442
lx3 |   1.207415   .7336368     1.65   0.106    -.2661382    2.680968
lx4 |   .8167941   .0985049     8.29   0.000     .6189412    1.014647
lx5 |   4.014936   1.263028     3.18   0.003     1.478069    6.551803
lx6 |   .2619006   .2371792     1.10   0.275    -.2144879     .738289
_cons |   -20.5465   5.498655    -3.74   0.000    -31.59087   -9.502123
------------------------------------------------------------------------------

. gen country = region
Setting up a panel
. tsset country year, yearly
panel variable:  country (strongly balanced)
time variable:  year, 1990 to 2006

Carrying out a fixed effects within regression on panel data
. xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, fe

Fixed-effects (within) regression               Number of obs      =        57
Group variable (i): country                     Number of groups   =        10

R-sq:  within  = 0.7640                         Obs per group: min =         2
between = 0.5507                                        avg =       5.7
overall = 0.5374                                        max =         8

F(6,41)            =     22.12
corr(u_i, Xb)  = 0.5835                         Prob > F           =    0.0000

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |  -.0075411   .0061342    -1.23   0.226    -.0199293    .0048472
lx2 |   .1397473   .0208394     6.71   0.000     .0976612    .1818334
lx3 |  -.0471179   .0766965    -0.61   0.542    -.2020095    .1077738
lx4 |   .0883038   .0510516     1.73   0.091    -.0147971    .1914046
lx5 |   .4423916   .1609951     2.75   0.009     .1172554    .7675278
lx6 |  -.0635172   .0380633    -1.67   0.103    -.1403876    .0133532
_cons |   2.404044   .8235133     2.92   0.006     .7409252    4.067163
-------------+----------------------------------------------------------------
sigma_u |  .95115353
sigma_e |  .03719725
rho |  .99847294   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(9, 41) =   755.95               Prob > F = 0.0000

. xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, be

Carrying out a fixed effects between regression on panel data

Between regression (regression on group means)  Number of obs      =        57
Group variable (i): country                     Number of groups   =        10

R-sq:  within  = 0.0790                         Obs per group: min =         2
between = 0.9488                                        avg =       5.7
overall = 0.7682                                        max =         8

F(6,3)             =      9.26
sd(u_i + avg(e_i.))=  .4441503                  Prob > F           =    0.0477

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |   .5188441   .2315068     2.24   0.111    -.2179138    1.255602
lx2 |  -.0061883   .4172493    -0.01   0.989    -1.334062    1.321685
lx3 |   .1313838   4.684306     0.03   0.979    -14.77617    15.03894
lx4 |   .9508895   .2441334     3.89   0.030      .173948    1.727831
lx5 |   7.621178   7.059213     1.08   0.359    -14.84439    30.08674
lx6 |   -.672947   1.417266    -0.47   0.667    -5.183319    3.837425
_cons |  -26.37744   19.85242    -1.33   0.276     -89.5567    36.80181
------------------------------------------------------------------------------

. xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re

Carrying out a random effects regression on panel data

Random-effects GLS regression                   Number of obs      =        57
Group variable (i): country                     Number of groups   =        10

R-sq:  within  = 0.7556                         Obs per group: min =         2
between = 0.6683                                        avg =       5.7
overall = 0.6327                                        max =         8

Random effects u_i ~ Gaussian                   Wald chi2(6)       =     94.90
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |  -.0065896   .0077505    -0.85   0.395    -.0217803    .0086011
lx2 |   .1253869   .0257565     4.87   0.000     .0749051    .1758687
lx3 |  -.0363082   .0969763    -0.37   0.708    -.2263783    .1537619
lx4 |   .1554292    .061983     2.51   0.012     .0339448    .2769135
lx5 |   .4387479   .2031582     2.16   0.031     .0405652    .8369306
lx6 |  -.0456517   .0477556    -0.96   0.339    -.1392509    .0479475
_cons |   2.241371   1.053202     2.13   0.033     .1771336    4.305609
-------------+----------------------------------------------------------------
sigma_u |  .44383293
sigma_e |  .03719725
rho |  .99302502   (fraction of variance due to u_i)
------------------------------------------------------------------------------
Fixed-effects (within) regression               Number of obs      =        57
Group variable (i): country                     Number of groups   =        10

R-sq:  within  = 0.7640                         Obs per group: min =         2
between = 0.5507                                        avg =       5.7
overall = 0.5374                                        max =         8

F(6,41)            =     22.12
corr(u_i, Xb)  = 0.5835                         Prob > F           =    0.0000

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |  -.0075411   .0061342    -1.23   0.226    -.0199293    .0048472
lx2 |   .1397473   .0208394     6.71   0.000     .0976612    .1818334
lx3 |  -.0471179   .0766965    -0.61   0.542    -.2020095    .1077738
lx4 |   .0883038   .0510516     1.73   0.091    -.0147971    .1914046
lx5 |   .4423916   .1609951     2.75   0.009     .1172554    .7675278
lx6 |  -.0635172   .0380633    -1.67   0.103    -.1403876    .0133532
_cons |   2.404044   .8235133     2.92   0.006     .7409252    4.067163
-------------+----------------------------------------------------------------
sigma_u |  .95115353
sigma_e |  .03719725
rho |  .99847294   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(9, 41) =   755.95               Prob > F = 0.0000

. estimates store fixed

. xtreg ly lx1 lx2 lx3 lx4 lx5 lx6, re

Random-effects GLS regression                   Number of obs      =        57
Group variable (i): country                     Number of groups   =        10

R-sq:  within  = 0.7556                         Obs per group: min =         2
between = 0.6683                                        avg =       5.7
overall = 0.6327                                        max =         8

Random effects u_i ~ Gaussian                   Wald chi2(6)       =     94.90
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

------------------------------------------------------------------------------
ly |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 |  -.0065896   .0077505    -0.85   0.395    -.0217803    .0086011
lx2 |   .1253869   .0257565     4.87   0.000     .0749051    .1758687
lx3 |  -.0363082   .0969763    -0.37   0.708    -.2263783    .1537619
lx4 |   .1554292    .061983     2.51   0.012     .0339448    .2769135
lx5 |   .4387479   .2031582     2.16   0.031     .0405652    .8369306
lx6 |  -.0456517   .0477556    -0.96   0.339    -.1392509    .0479475
_cons |   2.241371   1.053202     2.13   0.033     .1771336    4.305609
-------------+----------------------------------------------------------------
sigma_u |  .44383293
sigma_e |  .03719725
rho |  .99302502   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store random

Carrying out a HAUSMAN TEST

. hausman fixed random

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
lx1 |   -.0075411    -.0065896       -.0009515               .
lx2 |    .1397473     .1253869        .0143604               .
lx3 |   -.0471179    -.0363082       -.0108097               .
lx4 |    .0883038     .1554292       -.0671254               .
lx5 |    .4423916     .4387479        .0036437               .
lx6 |   -.0635172    -.0456517       -.0178655               .
------------------------------------------------------------------------------
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(6) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=    -4.12    chi2<0 ==> model fitted on these
data fails to meet the asymptotic
assumptions of the Hausman test;
see suest for a generalized test

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```