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Re: st: fixed vs random effect model


From   Clive Nicholas <clivelists@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: fixed vs random effect model
Date   Mon, 5 Jul 2010 01:32:14 +0100

Martin Weiss replied:

> What`s your rule of thumb then, Steve, for the RE model to be considered? In
> this case, you have -.15, do you still use RE? If you -bootstrap- the thing,
> the CI covers 0 comfortably...
>
>
> ***********
> webuse grunfeld, clear
> xtset company year
> bs e(corr), reps(200) seed(32456): xtreg invest mvalue kstock, i(company) fe
> ***********

For me -- speaking as an idiot non-econometrican -- the key, as I
implied earlier, would be to use both -hausman- and that indicator in
-xtreg, fe- together:

. webuse grunfeld, clear

. xtreg invest mvalue kstock, i(company) fe

Fixed-effects (within) regression               Number of obs      =       200
Group variable (i): company                     Number of groups   =        10

R-sq:  within  = 0.7668                         Obs per group: min =        20
       between = 0.8194                                        avg =      20.0
       overall = 0.8060                                        max =        20

                                                F(2,188)           =    309.01
corr(u_i, Xb)  = -0.1517                        Prob > F           =    0.0000
                      ^^^^^^^^^
------------------------------------------------------------------------------
      invest |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      mvalue |   .1101238   .0118567     9.29   0.000     .0867345    .1335131
      kstock |   .3100653   .0173545    17.87   0.000     .2758308    .3442999
       _cons |  -58.74393   12.45369    -4.72   0.000    -83.31086     -34.177
-------------+----------------------------------------------------------------
     sigma_u |  85.732501
     sigma_e |  52.767964
         rho |  .72525012   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(9, 188) =    49.18              Prob > F = 0.0000

. est store fixed

. qui xtreg invest mvalue kstock, re

. est store random

. hausman fixed .

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed        random       Difference          S.E.
-------------+----------------------------------------------------------------
      mvalue |    .1101238     .1097811        .0003427        .0055213
      kstock |    .3100653      .308113        .0019524        .0024516
------------------------------------------------------------------------------
                           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(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =        2.33
                Prob>chi2 =      0.3119
                                       ^^^^^^^^^

Here, the two statistics reinforce the same conclusion: an RE model
could be fit to this data. But lucky is the researcher who has such
data to play with; certainly not me.

An alternative example (although one could say this is a selective
model, but imagine it was the only data we had):

. webuse nlswork

. xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work,
i(idcode) fe

Fixed-effects (within) regression               Number of obs      =     13550
Group variable (i): idcode                      Number of groups   =      4001

R-sq:  within  = 0.1325                         Obs per group: min =         1
       between = 0.2106                                        avg =       3.4
       overall = 0.1744                                        max =        11

                                                F(8,9541)          =    182.14
corr(u_i, Xb)  = 0.1774                         Prob > F           =    0.0000
                      ^^^^^^^^
------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0046006   .0006602     6.97   0.000     .0033066    .0058947
     nev_mar |  -.0295329   .0118592    -2.49   0.013    -.0527794   -.0062863
       south |  -.0514096   .0169021    -3.04   0.002    -.0845412    -.018278
       union |   .1249207   .0089688    13.93   0.000     .1073399    .1425015
      tenure |   .0206019    .001053    19.56   0.000     .0185378    .0226661
       hours |  -.0015052   .0003538    -4.25   0.000    -.0021987   -.0008117
      wks_ue |  -.0001856   .0004326    -0.43   0.668    -.0010336    .0006624
    wks_work |   .0011162   .0001514     7.37   0.000     .0008193     .001413
       _cons |   1.500244   .0237174    63.26   0.000     1.453753    1.546735
-------------+----------------------------------------------------------------
     sigma_u |  .39638065
     sigma_e |  .26223304
         rho |  .69556838   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(4000, 9541) =     5.85          Prob > F = 0.0000

. est store fixed

. qui xtreg ln_wage age nev_mar south union tenure hours wks_ue wks_work, re

. hausman fixed .

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |     fixed          .          Difference          S.E.
-------------+----------------------------------------------------------------
         age |    .0046006     .0029873        .0016134        .0002999
     nev_mar |   -.0295329      -.01738       -.0121529        .0066411
       south |   -.0514096    -.1348857        .0834761        .0135749
       union |    .1249207     .1377239       -.0128032        .0039118
      tenure |    .0206019     .0254651       -.0048631        .0004508
       hours |   -.0015052    -.0001432        -.001362        .0001495
      wks_ue |   -.0001856    -.0008195        .0006339        .0001434
    wks_work |    .0011162     .0016362         -.00052        .0000481
------------------------------------------------------------------------------
                           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(8) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      440.74
                Prob>chi2 =      0.0000
                                       ^^^^^^^^^

There's not much more difference in -corr(u_i, Xb)- than that observed
in the Grunfeld data, and yet the Hausman test suggests a
statistically significant difference between the two models fit to
this data, this time favouring FE. No doubt the specialist
econometricians will have more to say about this if they feel more
needs to be said, which they probably will.

-- 
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]

"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson.
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