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


From   Kirimi Sindi <sindijul@msu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
Date   Thu, 26 Feb 2009 16:24:01 -0500

Malik,

Running models is okay but you have to ask yourself what question you want to answer first. Then the next question is the type of data you have to enable you answer the question. Then the assumption you make about the data. Does the data have unobserved heterogeneity and is this heterogeneity corrected with the X's or not. That helps you choose between RE of FE. I guess within does not tell you much. But I guess you have started well by running a pooled model. Then look at the results and ask yourself what could be going on? Is it an artifact of the data. Do you have data problems.

Then move on.

Kirimi

Muhammad Billal Malik wrote:
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
-------------+------------------------------           Adj R-squared =  0.8454
       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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--
*******************************
Imagination is more important than knowledge. For while knowledge defines all we currently know and understand, imagination points to all we might yet discover and create.
*******************************

Kirimi Sindi
PhD Candidate
Department of Agricultural,
Food, and Resource Economics
Room 20 Cook Hall
Michigan State University
East Lansing,  MI  48824
Telephone: +1-517-353-5320
Home Tel : +1-517-355-8151	
Fax: +1-517-432-1800

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