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

 From David Greenberg To statalist@hsphsun2.harvard.edu Subject Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test Date Thu, 26 Feb 2009 16:26:26 -0500

```With a small number of nations and more years than nations you may be better off using panel-corrected standard errors than the approach you are taking. David Greenberg, Sociology Department, New York University

----- Original Message -----
From: Muhammad Billal Malik <m18mlk@googlemail.com>
Date: Thursday, February 26, 2009 2:20 pm
Subject: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
To: statalist@hsphsun2.harvard.edu

> 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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```

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