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st: RE: Hausman Query


From   DE SOUZA Eric <eric.de_souza@coleurope.eu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Hausman Query
Date   Wed, 5 Jan 2011 11:14:46 +0100

First of all, the Hausman test makes no sense if you robustify (vce(robust)).

Second, even if you do not robustify, the Hausman test is valid under rather restrictive assumptions.

Use instead the user written program, xtoverid, courtesy of Mark Schaffer and Steven Stillman.

To see what it does type -ssc describe xtoverid- from within Stata
To download and install it type -ssc install xtoverid-

Eric


Eric de Souza
College of Europe
Brugge (Bruges), Belgium
http://www.coleurope.eu


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Ross, Andrew
Sent: 05 January 2011 09:50
To: statalist@hsphsun2.harvard.edu
Subject: st: Hausman Query

Hello
 
I am currently using Stata to investigate new firm formation for 32 Scottish regions over a 10 year period. I was wondering, if you might offer your opinion on a Stata related matter, that I have encountered?
 
As you can see from the attached output I've run a fixed and random effects model and followed this by the hausman test. However, the hausman highlights a 'note', as you will see from the attached output.
 
I was wondering, if you could shed any light on this note and what is means? I have asked four other people and they do not know. One suggested it may be a result of over parameterisation given the small size of the panel, but they are not sure.
 
Many thanks.
 
Andrew

xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ_b
> s Pop_density Gov_sector Small_bus, fe vce (robust)

Fixed-effects (within) regression               Number of obs      =       320
Group variable: Region                          Number of groups   =        32

R-sq:  within  = 0.2061                         Obs per group: min =        10
       between = 0.0019                                        avg =      10.0
       overall = 0.0030                                        max =        10

                                                F(11,277)          =      3.10
corr(u_i, Xb)  = -0.9507                        Prob > F           =    0.0006

                                 (Std. Err. adjusted for clustering on Region)
------------------------------------------------------------------------------
             |               Robust
      Lab_TP |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
    Wge_grow |  -.0265289   .0270548    -0.98   0.328     -.079788    .0267303
    Pop_grow |   .4054536   .5845519     0.69   0.489    -.7452749    1.556182
Log_unempl~d |   4.109563   4.222209     0.97   0.331     -4.20213    12.42126
    NVQ4_pop |  -.0295052   .0431429    -0.68   0.495    -.1144348    .0554243
 House_price |   .0000483   .0000121     3.99   0.000     .0000245    .0000722
    LQ_agric |   .1687096   .4963323     0.34   0.734    -.8083529    1.145772
      LQ_man |  -.1523606   .4695697    -0.32   0.746    -1.076739    .7720178
       LQ_bs |   2.506032   1.647939     1.52   0.129    -.7380422    5.750107
 Pop_density |   .0236083   .0110802     2.13   0.034     .0017962    .0454204
  Gov_sector |  -.0001643   .0309392    -0.01   0.996    -.0610701    .0607415
   Small_bus |   .3920981   .4383467     0.89   0.372     -.470816    1.255012
       _cons |   -32.9382   42.48215    -0.78   0.439    -116.5671    50.69067
-------------+----------------------------------------------------------
-------------+------
     sigma_u |  17.794849
     sigma_e |   2.771809
         rho |   .9763121   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store fixed

. xtreg Lab_TP Wge_grow Pop_grow Log_unemployed NVQ4_pop House_price LQ_agric LQ_man LQ
> _bs Pop_density Gov_sector Small_bus, re vce (robust)

Random-effects GLS regression                   Number of obs      =       320
Group variable: Region                          Number of groups   =        32

R-sq:  within  = 0.1667                         Obs per group: min =        10
       between = 0.6091                                        avg =      10.0
       overall = 0.4986                                        max =        10

Random effects u_i ~ Gaussian                   Wald chi2(12)      =   3152.08
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0000

                                 (Std. Err. adjusted for clustering on Region)
------------------------------------------------------------------------------
             |               Robust
      Lab_TP |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
    Wge_grow |  -.0254291   .0298964    -0.85   0.395     -.084025    .0331667
    Pop_grow |   .8175778   .5211693     1.57   0.117    -.2038953    1.839051
Log_unempl~d |  -4.643811   2.993296    -1.55   0.121    -10.51056    1.222941
    NVQ4_pop |    .008423   .0484623     0.17   0.862    -.0865613    .1034074
 House_price |   .0000265   .0000108     2.46   0.014     5.39e-06    .0000476
    LQ_agric |   .7014816   .4126435     1.70   0.089    -.1072848    1.510248
      LQ_man |   .2703715   .5041589     0.54   0.592    -.7177617    1.258505
       LQ_bs |   4.506697   1.720704     2.62   0.009      1.13418    7.879214
 Pop_density |   .0023373   .0006452     3.62   0.000     .0010727    .0036018
  Gov_sector |  -.0345817    .034529    -1.00   0.317    -.1022574    .0330939
   Small_bus |   .6680098   .1846674     3.62   0.000     .3060683    1.029951
       _cons |   -42.7439   17.37493    -2.46   0.014    -76.79813   -8.689662
-------------+----------------------------------------------------------
-------------+------
     sigma_u |  2.2647466
     sigma_e |   2.771809
         rho |  .40033378   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store random

. hausman fixed random

Note: the rank of the differenced variance matrix (10) does not equal the number of
        coefficients being tested (11); be sure this is what you expect, or there may
        be problems computing the test.  Examine the output of your estimators for
        anything unexpected and possibly consider scaling your variables so that the
        coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------
-------------+------
    Wge_grow |   -.0265289    -.0254291       -.0010997               .
    Pop_grow |    .4054536     .8175778       -.4121243        .2647328
Log_unempl~d |    4.109563    -4.643811        8.753374        2.977789
    NVQ4_pop |   -.0295052      .008423       -.0379283               .
 House_price |    .0000483     .0000265        .0000218        5.53e-06
    LQ_agric |    .1687096     .7014816       -.5327721        .2758099
      LQ_man |   -.1523606     .2703715       -.4227322               .
       LQ_bs |    2.506032     4.506697       -2.000664               .
 Pop_density |    .0236083     .0023373         .021271        .0110614
  Gov_sector |   -.0001643    -.0345817        .0344174               .
   Small_bus |    .3920981     .6680098       -.2759117        .3975498
------------------------------------------------------------------------------
                           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(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =        5.58
                Prob>chi2 =      0.8493
                (V_b-V_B is not positive definite)


Andrew Ross
PhD Candidate
School of Accounting, Economics & Statistics Napier University Business School Craiglockhart Campus Room 1/38
EH14 IDJ
Email: a.ross2@napier.ac.uk







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