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Re: st: RE: OLS, FE xtreg and the i() option


From   Robert Gaskell <robboh@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: OLS, FE xtreg and the i() option
Date   Wed, 2 Mar 2005 22:26:57 +0000

There are no dummies in the OLS regression; I am not expecting
identical results, but I am puzzled by the completely opposite results
(one positive coefficient, one negative) given by the standard OLS
estimation (a basic .reg var1 var2) and the FE estimations (.xtreg
var1 var2, fe i(x)), particularly as when looking at the data as a
whole (and theory) would seem to support the view of the OLS
estimation.  My question is in essence whether one estimation 'voids'
the other; obviously only one is 'true'.

Robert Gaskell


On Wed, 2 Mar 2005 12:34:08 -0600, Gustavo Sanchez <gsanchez@stata.com> wrote:
> Robert [robboh@gmail.com] asked:
>
> >I have been working on a panel dataset, looking at the relationship
> >between inflation and openness, but am slightly confused at to the
> >results I have been finding.  When running OLS and Fixed-Effects (FE)
> >estimations completely different results are found.  However, when the
> >i() option for the FE estimation is set to the year (which it
> >shouldn't be; it should be the country code), the panel data results
> >are almost exactly equal to OLS.
>
> >Am I making an error in my use of Stata, or is this a kind of
> >'pooling' (when setting i() to the year), implying that the 'correct'
> >value is as found by the 'correct' FE estimation.  I have not been
> >able to find any direct information on this in the Stata documentation
> >or the net in general - any comments that you can give will be much
> >appreciated.
>
> Fixed effects using -xtreg,fe- and OLS using -regress- including the
> dummy variables produce the same slope parameters for the explanatory
> variables (see the example below).
> Are you including the dummy variables in your OLS regression?
>
> Here is the example:
>
> . sysuse auto,clear
> (1978 Automobile Data)
>
> . xtreg price mpg weight,fe i(rep78)
>
> Fixed-effects (within) regression               Number of obs      =
> 69
> Group variable (i): rep78                       Number of groups   =
> 5
>
> R-sq:  within  = 0.3591                         Obs per group: min =
> 2
>       between = 0.0002                                        avg =
> 13.8
>       overall = 0.2994                                        max =
> 30
>
>                                                F(2,62)            =
> 17.37
> corr(u_i, Xb)  = -0.4414                        Prob > F           =
> 0.0000
> ----------------------------------------------------------------------------
> --
>       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+--------------------------------------------------------------
> --
>         mpg |   -63.0971   87.45276    -0.72   0.473    -237.9127
> 111.7185
>      weight |   2.093066    .636901     3.29   0.002     .8199193
> 3.366213
>       _cons |   1143.134   3565.726     0.32   0.750     -5984.65
> 8270.918
> -------------+--------------------------------------------------------------
> --
>     sigma_u |  1287.8103
>     sigma_e |   2424.057
>         rho |  .22011463   (fraction of variance due to u_i)
> ----------------------------------------------------------------------------
> --
> F test that all u_i=0:     F(4, 62) =     1.66               Prob > F =
> 0.1707
>
> . xi:regress price mpg weight i.rep78
> i.rep78           _Irep78_1-5         (naturally coded; _Irep78_1 omitted)
>
>      Source |       SS       df       MS              Number of obs =
> 69
> -------------+------------------------------           F(  6,    62) =
> 6.03
>       Model |   212481723     6  35413620.6           Prob > F      =
> 0.0001
>    Residual |   364315236    62  5876052.19           R-squared     =
> 0.3684
> -------------+------------------------------           Adj R-squared =
> 0.3073
>       Total |   576796959    68  8482308.22           Root MSE      =
> 2424.1
>
> ----------------------------------------------------------------------------
> --
>       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+--------------------------------------------------------------
> --
>         mpg |   -63.0971   87.45276    -0.72   0.473    -237.9127
> 111.7185
>      weight |   2.093066    .636901     3.29   0.002     .8199193
> 3.366213
>   _Irep78_2 |   753.7024   1919.763     0.39   0.696    -3083.849
> 4591.254
>   _Irep78_3 |   1349.361   1772.706     0.76   0.449    -2194.228
> 4892.95
>   _Irep78_4 |    2030.47    1810.09     1.12   0.266    -1587.848
> 5648.788
>   _Irep78_5 |    3376.91    1900.17     1.78   0.080    -421.4749
> 7175.296
>       _cons |  -598.9665   3960.904    -0.15   0.880    -8516.701
> 7318.768
> ----------------------------------------------------------------------------
> --
>
> Sincerely,
>
> --Gustavo
> gas@stata.com
>
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