st: sureg problem - how many parameters can be estimated with a given number of observations

[Alex Olssen <alex.olssen@gmail.com>]

Hi everyone,  I asked a related question earlier, but this time I have
included 2 examples using -sysuse auto-.

I want to know how many parameters SUR can estimate for a given number
of observations.

I have done some exploration with -sysuse auto- below.

sysuse auto clear,
keep in 1/5   /*we now have only 5 observations*/
sureg (weight length = price mpg)
ereturn list

The above estimation works and -ereturn list- tells us e(N) = 5 and e(k) = 6.
I.e., we have estimated 6 parameters with 5 observations.
Does this work because we estimate 3 parameters per equation and have
5 observations per equation?

But now consider

sysuse auto clear,
keep in 1/5
sureg (weight length = price mpg trunk)

This estimation does not work - Stata returns an error saying the
covariance matrix is singular.

Why is it that Stata can sureg estimate 6 parameters with 5
observations and 2 equations but it cannot estimate 8 parameters with
5 observations and 2 equations?

Is there something obvious I am missing?

Any help would be highly appreciated.

Kind regards,

Alex Olssen
Motu Economic Research
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