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


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
Date   Thu, 26 Feb 2009 22:32:10 -0000

Muhammad,

The "negative Hausman statistic" problem comes up from time to time on
Statalist.  A couple of my own responses:

http://www.stata.com/statalist/archive/2006-10/msg00599.html on how to
guarantee a postive Hausman stat in an FE vs RE test

http://www.stata.com/statalist/archive/2007-10/msg00819.html on an
add-in (-xtoverid-) that will do this automatically plus give you a
cluster-robust test statistic if you want it.

...but I think Kirimi and David make some fundamental points that are
probably more important than just this technical issue of getting a
positive test stat.

--Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html
 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> David Greenberg
> Sent: 26 February 2009 21:26
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
> 
> 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
> > 
> > *
> > *   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/
> 


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