# [R] systemfit - SUR

Arne Henningsen ahenningsen at email.uni-kiel.de
Tue Nov 30 10:20:29 CET 2004

```On Tuesday 30 November 2004 09:34, contact at thomasalmer.com wrote:
> Arne Henningsen <ahenningsen at email.uni-kiel.de> schrieb am 29.11.2004,
>
> 17:02:12:
> > On Monday 29 November 2004 16:42, contact at thomasalmer.com wrote:
> > > Hello to everyone,
> > >
> > > I have 2 problems and would be very pleased if anyone can help me:
> > >
> > > 1) When I use the package "systemfit" for SUR regressions, I get two
> > > different variance-covariance matrices when I firstly do the SUR
> > > regression ("The covariance matrix of the residuals used for
> > > estimation") and secondly do the OLS regressions. In the manual for
> > > "systemfit" on page 14 I see however, that the variance-covariance
> > > matrix for SUR is obtained from OLS. How can this be explained?
> >
> > Hi Thomas,
> > I get identical residual covariance matrices:
> >
> > R> library(systemfit)
> > R> data( kmenta )
> > R> demand  supply  labels  system  fitols  fitols\$rcov
> >          [,1]     [,2]
> > [1,] 3.725391 4.136963
> > [2,] 4.136963 5.784441
> > R> fitsur  fitsur\$rcovest
> >          [,1]     [,2]
> > [1,] 3.725391 4.136963
> > [2,] 4.136963 5.784441
>
> It is a pity, but my matrices are not as nice :-(

Please show how you obtained these results.

This is what I did:
R> data( kmenta )
R> demand <- q ~ p + d
R> supply <- q ~ p + f + a
R> labels <- list( "demand", "supply" )
R> system <- list( demand, supply )
R>
R> # OLS estimation:
R> fitols <- systemfit("OLS", system, labels, data=kmenta )
R> # (non-iterated) SUR estimation
R> fitsur <- systemfit("SUR", system, labels, data=kmenta )
R> iterated SUR estimation
R> fitsurit <- systemfit("SUR", system, labels, data=kmenta, maxit=100 )
R>
R> fitols\$rcov
[,1]     [,2]
[1,] 3.725391 4.136963
[2,] 4.136963 5.784441
R> fitsur\$rcovest
[,1]     [,2]
[1,] 3.725391 4.136963
[2,] 4.136963 5.784441
R> fitsurit\$rcovest
[,1]     [,2]
[1,] 6.199071 7.493383
[2,] 7.493383 9.128547

> An excerpt:
> fitsur\$rcovest
>             [,1]         [,2]         [,3]       ...
>  [1,] 0.015097517  0.018005050
>  [2,] 0.018005050  0.276259834
>  ...
>
> fitols\$rcov
>                [,1]          [,2] 	[,3]	 ...
>  [1,]  1.010326e-02  0.0096103837
>  [2,]  9.610384e-03  0.2329884378
>  ...
>
> fitsur "The covariance matrix of the residuals used for estimation":
>     eq1         eq2        eq3         ...
> eq1 0.01317429  0.01504719 0.007981307
> eq2 0.01504719  0.25233860
> ...
>
> fitols "The covariance matrix of the residuals":
>     eq1          eq2          eq3      ...
> eq1 9.51154e-03  0.009137884  0.002648577
> eq2 9.13788e-03  0.220435063
> ...
>
> By the way: Why are the figures larger for SUR?

OLS minimizes the residuals and, thus, also the variance of the residuals
(=diagonal of the residual covariance matrix).
Iterated SUR is equivalent to a maximum likelihood estimation. Maximizing the
likelihood value is equivalent to minimizing the determinant of the residual
covariance matrix. Thus, the determinant of the residual covariance matrix
and not the residuals itself are minimized:

R> det(fitols\$rcov)
[1] 4.434845
R> det(fitsurit\$rcov)
[1] 0.4376941
R> det(fitsurit\$rcovest)
[1] 0.4377184

> > Did you do _iterated_ SUR?
>
> Yes:
> "systemfit results
> method: iterated SUR
> convergence achieved after 30 iterations"

If you use iterated SUR, the SUR estimations are iterated. In the first SUR
estimation the residual covariance matrix of the OLS estimation is used. In
all following iterations the residual covariance matrix of the previous step
SUR estimation is used.

> I do not know how to change that.

Please read the documentation. It says to set argument "maxit" to 1 - or do
not provide this argument, since 1 is the default.

> > Best wishes,
> > Arne
>
> THANKS A LOT FOR YOUR IMMEDIATE HELP!!!
>
> > > 2) Is there an easy possibility to test a) the OLS equations, and b)
> > > the SUR system for SUR structures? In other words: Is the LM-Test from
> > > Breusch and Pagan available in R?

I don't understand what you want to test. Does the hausman test what you are
looking for (see ?hausman.systemfit). If you have questions regarding this
test, you might ask my co-author of systemfit, Jeff Hamann.

Best wishes,
Arne

> > > Thanks for the attention!
> > >
> > > Best Regards,
> > > Thomas Almer
> > >
> > > ______________________________________________
> > > R-help at stat.math.ethz.ch mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide!
> > > http://www.R-project.org/posting-guide.html
> >
> > --
> > Arne Henningsen
> > Department of Agricultural Economics
> > University of Kiel
> > Olshausenstr. 40
> > D-24098 Kiel (Germany)
> > Tel: +49-431-880 4445
> > Fax: +49-431-880 1397
> > ahenningsen at agric-econ.uni-kiel.de
> > http://www.uni-kiel.de/agrarpol/ahenningsen/
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html

--
Arne Henningsen
Department of Agricultural Economics
University of Kiel
Olshausenstr. 40
D-24098 Kiel (Germany)
Tel: +49-431-880 4445
Fax: +49-431-880 1397
ahenningsen at agric-econ.uni-kiel.de
http://www.uni-kiel.de/agrarpol/ahenningsen/

```

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