How to set the floating point precision beyond e-22?

You will have to find a different solution to the problem.  To machine 
precision, that matrix looks singular.  This usually indicates that it's 
not the right matrix to try to invert.

It might be a scaling issue though: If you're measuring age in days
and hormone concentrations in Molar, then you'll get that sort of
eigenvalue ratios in a fairly benign way.

I'm quite aware of that problem, but we have to deal with certain economic
variables which are usually given in a certain dimension. So it is difficult
to force all values to a certain order.

The other thing is, that i.e. EViews is able to perform 2SLS in the same
regression setup. Don't they have to invert the same matrices? If so, how do
they do it and how can we mimic their proceeding in R? Scaling and
Rescaling? What about the interpretation of the coefficients computed on a
scaled basis and given in the context of re-/unscaled data?

I'm not quite clear about it.

Thanks to all of you.