R help - Dec 2012 - Error message "cs_lu(A) failed: near-singular A (or out of memory)"

Hi there everyone,

I have the following model (this is naturally a simplified version just for
showing my problem, in case you're wondering this is a translog cost
function with the associated cost share equations):

C ~ á + â1 log X + â2 log Y + ã1 log Z + ã2 log XX
C1 ~ â1 + â2 log YY + ã1 log ZZ

Then I have some restrictions on the coefficients, namely that the sum of â
equal 1 and the some of ã equal zero
So, I've added the following equations to the model

C2 ~ 0 +  â1.Y1 + â2.Y2
C3 ~ 0 +  ã1.Y3 + ã2. Y4

I've created columns in my data frame with values of 0 for variable C3 and
values of 1 for Y1, Y2, Y3, Y4 and C2

I'm using the systemfit package to solve a multiple equation system using
the SURE method, and using a matrix to impose the restrictions on the
coefficients (i.e., that the â1 in all equations is the same value, and the
same for all the other coefficients).

When I try to run the model without the restricting equations (C2, C3) it
runs just fine, but when I add these two equations I get the error:

"Error in solve(xtOmegaInv %*% xMat2, xtOmegaInv %*% yVec, tol = solvetol)
:
  cs_lu(A) failed: near-singular A (or out of memory)"

Any ideas on what the problem might be?

All the best,
Rui Neiva

P.S.: I've also posted this question on the Matrix help forum, but since I
do not know how active that forum is I've decided to see if anyone in the
mailing list would be able to help.

	[[alternative HTML version deleted]]

Dear Rui

If you impose the homogeneity (adding-up) restrictions, your system
becomes singular, because the error terms of the share equations
always sum up to zero. Therefore, you can arbitrarily delete one of
the share equations and obtain the coefficients that were not directly
estimated by the homogeneity restrictions. Furthermore, you can impose
the homogeneity restriction at each single equation by normalization
with one input price (num?raire). Finally, I suggest to impose the
cross-equation restrictions by the argument "restrict.regMat" rather
than by argument "restrict.matrix", because the documentation says
"the advantage of imposing restrictions on the coefficients by
'restrict.regMat' is that the matrix, which has to be inverted during
the estimation, gets smaller by this procedure, while it gets larger
if the restrictions are imposed by 'restrict.matrix' and
'restrict.rhs'." I will send you my lecture notes on econometric
production analysis with R by private mail. Please do not forget to
cite R and the R packages that you use in your publications. If you
have further questions regarding system estimation, microeconomic
analysis, or stochastic frontier (efficiency) analysis with R, you can
use a forum at the R-Forge sites of the systemfit [1,2], micEcon
[3,4], or frontier [5] packages/projects, respectively.

[1] http://www.systemfit.org/
[2] http://r-forge.r-project.org/projects/systemfit/
[3] http://www.micEcon.org/
[4] http://r-forge.r-project.org/projects/micecon/
[5] http://r-forge.r-project.org/projects/frontier/

Best (holiday) wishes from Copenhagen,
Arne

On 9 December 2012 23:31, Rui Neiva <ruiqneiva at gmail.com>
wrote:
> Hi there everyone,
>
> I have the following model (this is naturally a simplified version just for
> showing my problem, in case you're wondering this is a translog cost
> function with the associated cost share equations):
>
> C ~ ? + ?1 log X + ?2 log Y + ?1 log Z + ?2 log XX
> C1 ~ ?1 + ?2 log YY + ?1 log ZZ
>
> Then I have some restrictions on the coefficients, namely that the sum of ?
> equal 1 and the some of ? equal zero
> So, I've added the following equations to the model
>
> C2 ~ 0 +  ?1.Y1 + ?2.Y2
> C3 ~ 0 +  ?1.Y3 + ?2. Y4
>
> I've created columns in my data frame with values of 0 for variable C3
and
> values of 1 for Y1, Y2, Y3, Y4 and C2
>
> I'm using the systemfit package to solve a multiple equation system
using
> the SURE method, and using a matrix to impose the restrictions on the
> coefficients (i.e., that the ?1 in all equations is the same value, and the
> same for all the other coefficients).
>
> When I try to run the model without the restricting equations (C2, C3) it
> runs just fine, but when I add these two equations I get the error:
>
> "Error in solve(xtOmegaInv %*% xMat2, xtOmegaInv %*% yVec, tol =
solvetol)
> :
>   cs_lu(A) failed: near-singular A (or out of memory)"
>
> Any ideas on what the problem might be?
>
> All the best,
> Rui Neiva
>
> P.S.: I've also posted this question on the Matrix help forum, but
since I
> do not know how active that forum is I've decided to see if anyone in
the
> mailing list would be able to help.
>
>         [[alternative HTML version deleted]]
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
Arne Henningsen
http://www.arne-henningsen.name