I have been conducting further analyses of the reciprocal
causation case and the notion of correlated errors.  I'm
leaning now to the view that the covariance component C(u,v)
between X3 and X4 is not a distinct parameter, but being a
function of other parameters of the model, is taken into
account by them.  So freeing up s(u,v) does not allow one
to take C(u,v) into account.

That undermines my previous argument for freeing up s(u,v).

The nonrecursive case is fraught with complexities.

Stan Mulaik