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


From   David Greenberg <dg4@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Panel Data-FIXED, RANDOM EFFECTS and Hausman Test
Date   Fri, 27 Feb 2009 14:42:12 -0500

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 -----
From: Muhammad Billal Malik <m18mlk@googlemail.com>
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 -----
> > 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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> 
> 
> *
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