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Re: st: (Feasible) generalized least squares


From   "Clive Nicholas" <[email protected]>
To   [email protected]
Subject   Re: st: (Feasible) generalized least squares
Date   Tue, 16 Jan 2007 21:33:55 -0000 (GMT)

Herbert Smith wrote:

> For a garden-variety, cross-sectional regression, an estimator of
>
> var(b)
>
> is
>
> var(b)=invsym(X'*W*X)
>
> where X is the design matrix and W is a diagonalized weight matrix.
>
> Is there a way in Stata to get the FGLS estimated var-cov in a single
> command?  By which I mean:
>
> -regress depvar indvars [pweight=w]-
>
> gives the GLS estimates for b
>
> b=invsym(X'*W*X)*(X'*W*y)
>
> but the standard errors are computed as though
>
> -regress depvar indvars [pweight=w], vce(robust)-
>
> and are close to the FGLS estimates, but are not the same....

Isn't this satisfactory?

. webuse grunfeld, clear

. tsset company year
       panel variable:  company (strongly balanced)
        time variable:  year, 1935 to 1954

. xtgls invest mvalue kstock time

Cross-sectional time-series FGLS regression

Coefficients:  generalized least squares
Panels:        homoskedastic
Correlation:   no autocorrelation

Estimated covariances      =         1        Number of obs      =       200
Estimated autocorrelations =         0        Number of groups   =        10
Estimated coefficients     =         4        Time periods       =        20
                                              Wald chi2(3)       =    867.82
Log likelihood             = -1191.645        Prob > chi2        =    0.0000

----------------------------------------------------------------------------
    invest |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------+----------------------------------------------------------------
    mvalue |   .1163783   .0059669    19.50   0.000     .1046834    .1280732
    kstock |   .2213351   .0302499     7.32   0.000     .1620463    .2806239
      time |   .7737904   1.377808     0.56   0.574    -1.926665    3.474245
     _cons |  -49.14306   14.83261    -3.31   0.001    -78.21443   -20.07169
----------------------------------------------------------------------------

. matrix list e(V)

symmetric e(V)[4,4]
            mvalue      kstock        time       _cons
mvalue    .0000356
kstock  -.00009563   .00091506
  time   .00200231  -.02292234   1.8983561
 _cons  -.03314052   .09155466  -15.771641   220.00619

Or am I missing something? :)

CLIVE NICHOLAS        |t: 0(044)7903 397793
Politics              |e: [email protected]
Newcastle University  |http://www.ncl.ac.uk/geps

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