Having supported the need for multi-sector models to address issues
raised by the TSS interpretation, I'd better put in some words of
support for Duncan on their usefulness in some respects. They are, for
example, useful when considering aggregate investment behaviour in a
Keynesian dynamic sense--and I've developed several such models.
Duncan's comments about the complexity of genuine multi-sectoral models
is also well taken.
I have developed one such, of an extremely simple economy (no technical
change or population growth, circulating capital only, with banks,
capitalists and workers) and it generated five vector and one scalar
equation of daunting complexity (at least to my eyes).
I also support the time-dynamics aspect of the TSS approach, and
granted, many useful insights can be gained from a one-sector rendition
of the same.
However, from my non-LTV point of view, a major impetus to the TSS
approach has been the desire to preserve the LTV, due to its failure to
survive when presented in a simultaneist guise (correct me if I'm wrong
on this).
Now the LTV *can* be maintained without contradiction in a single sector
simultaneist model (you simply assert that labor is the only source of
value, and derive the relevant statics). It can also, I'm sure, be
maintained in a single sector TSS model--and it will lead to the
prediction of looming catastrophe when the rate of profit inevitably
falls below the rate of depreciation at some future date.
But I doubt that the TSS interpretation will help the LTV survive the
same criticisms it has suffered in a simultaneist guise *when we move to
2 or more sectors with differing capital to labor ratios and/or
differing rates of technical change*. This is why I would like to see
the TSS (after you've presented it in 1-sector guise) presented in
multi-sectoral form.
The reason for my scepticism is the following. I am sure that a
multi-sector TSS could show a time path from input prices to output
values to input prices ... which was self-consistent over time. But I
doubt that the equilibrium of such a system would be sustainable--as
opposed to stable.
To explain this, a dynamic system can and probably will have an unstable
equilibrium--one which, if the system diverges even slightly from it, it
will never return to. But if a deterministic dynamic system starts at
its equilibrium, then by definition, it should remain there for all
time. I doubt that this will be the case when the TSS approach is
generalised to more than 1 sector--because I expect that the same
contradictions which bedevil the entirety of the simultaneist
interpretation of the LTV will likewise bedevil the equilibrium of the
TSS interpretation.
Working this out will involve a bit of math, which at present I haven't
the time for (other bits of math are taking priority). But this is a
challenge that I think the TSS school should subject itself to.
Cheers,
Steve Keen