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

 From "Martin Weiss" To Subject AW: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test Date Tue, 3 Mar 2009 15:35:16 +0100

```<>

" My results for the coefficiants of the random effects
model and fixed effects model are very different,"

That is exactly the kind of question adressed by the -hausman- test. A huge
difference between parameter estimates is always hard to determine exactly.
What is huge in statistical terms can only be determined with reference to
the varcov of the estimates, and the -hausman- test works that out for you.
So run the test as seen in the xmpl of -help xtreg postestimation- and come
back with the results...

HTH
Martin

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Muhammad Billal
Malik
Gesendet: Montag, 2. März 2009 22:00
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test

1st Questtion if I have carrried out a Breusch-pagan LM test and my
model has obtained a value greater than 0.06 therefore I accept the
random effects model, right?

2nd Question: My results for the coefficiants of the random effects
model and fixed effects model are very different, with very different
coefficiants and p values. Is this a problem? But the test has passed
the Breusch Pagan Test for RE model, if I am right about Question 1.

Random-effects GLS regression                   Number of obs      =
43
Group variable (i): region                      Number of groups   =
7

R-sq:  within  = 0.4110                         Obs per group: min =
2
between = 0.9912                                        avg =
6.1
overall = 0.9550                                        max =
8

Random effects u_i ~ Gaussian                   Wald chi2(6)       =
763.37
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =
0.0000

----------------------------------------------------------------------------
--
lny |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
lx1 |   .1301386   .0466017     2.79   0.005      .038801
.2214762
lx2 |   .1708776   .0772652     2.21   0.027     .0194406
.3223145
lx3 |    3.27485   .6616212     4.95   0.000     1.978097
4.571604
lx4 |   .6025669   .1123974     5.36   0.000     .3822721
.8228617
lx5 |   4.753912   1.088747     4.37   0.000     2.620007
6.887817
lx6 |   .9487478   .2355224     4.03   0.000     .4871324
1.410363
_cons |  -36.19591   5.482063    -6.60   0.000    -46.94055
-25.45126
-------------+--------------------------------------------------------------
--
sigma_u |          0
sigma_e |  .03410935
rho |          0   (fraction of variance due to u_i)
----------------------------------------------------------------------------
--

. xtreg lny lx1 lx2 lx3 lx4 lx5 lx6, fe

Fixed-effects (within) regression               Number of obs      =
43
Group variable (i): region                      Number of groups   =
7

R-sq:  within  = 0.8302                         Obs per group: min =
2
between = 0.7280                                        avg =
6.1
overall = 0.6779                                        max =
8

F(6,30)            =
24.45
corr(u_i, Xb)  = 0.6968                         Prob > F           =
0.0000

----------------------------------------------------------------------------
--
lny |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
lx1 |  -.0021639   .0069926    -0.31   0.759    -.0164448
.0121169
lx2 |   .1352655   .0220522     6.13   0.000      .090229
.1803021
lx3 |   .2685463   .1091373     2.46   0.020     .0456582
.4914345
lx4 |   .1267882   .0500629     2.53   0.017     .0245461
.2290303
lx5 |   .8111474   .1926396     4.21   0.000      .417725
1.20457
lx6 |  -.0138814   .0480629    -0.29   0.775     -.112039
.0842761
_cons |   -.683041   1.127701    -0.61   0.549    -2.986114
1.620032
-------------+--------------------------------------------------------------
--
sigma_u |  1.0104691
sigma_e |  .03410935
rho |  .99886183   (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0:     F(6, 30) =   369.90               Prob > F =
0.0000

On Fri, Feb 27, 2009 at 7:42 PM, David Greenberg <dg4@nyu.edu> wrote:
> No, it is not difficult to understand and estimate these models. Look at
these papers:
>   Nathaniel Beck and Jonathan N. Katz, ?What To Do (and Not To Do)With
Time-Series Cross-Section Data,? American Political Science Review 89.3
(Sept. 1995): 634-47.
> _____, ?Time-Series-Cross-Section Data: What Have We Learned in the Past
Few Year,? Annual Review of Political Science 4 (2001):271-93.
>  The models can be estimated in Stata using the xtpcse keyword.    - David
Greenberg, Sociology Department, New York University
>
> ----- Original Message -----
> Date: Friday, February 27, 2009 7:54 am
> Subject: Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
> To: statalist@hsphsun2.harvard.edu
>
>
>> I am sorry David, but I have not been taught that in my Basic
>> Econometric course, will it be easy to understand and run?
>>
>> On Thu, Feb 26, 2009 at 9:26 PM, David Greenberg <dg4@nyu.edu> wrote:
>> > 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 -----
>> > 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
>> 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
>> >>
>> >> *
>> >> *   For searches and help try:
>> >> *   http://www.stata.com/help.cgi?search
>> >> *   http://www.stata.com/support/statalist/faq
>> >> *   http://www.ats.ucla.edu/stat/stata/
>> > *
>> > *   For searches and help try:
>> > *   http://www.stata.com/help.cgi?search
>> > *   http://www.stata.com/support/statalist/faq
>> > *   http://www.ats.ucla.edu/stat/stata/
>> >
>>
>>
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```