From: clyder@GN.APC.ORG
Date: Fri Jun 13 2003 - 07:21:29 EDT
Ian suggested that Kalecki's accounting identities are based
on the conservation of money. I am not sure that this is really
the case, since in a general treatment involving the existence
of bank capital money is not conserved, but the Kaleckian
identities can be retained as constraints on the evolution
of the system.
Consider the following simple model. You have 5 categories of
agents:
1. Firms making commodities
2. Rentiers
3. Workers
4. Banks
5. The state
This is like the Kaleckian model except that firms are more
clearly distinguished from rentiers and banks are added to
the model.
If we assume that none of the agents need be in financial balance
and that all transactions are performed in terms of accounts
held with the banking sector, then money, in the form of
bank balances, will not in general be conserved.
We need to assume that the rentiers have net credit
balances with the banks such that a rentier can live
on the interest on that balance. We assume all their
capital is in the form of bank balances. We further
assume that firms only raise new capital by
bank borrowing.
We have the following aggregate accounting relationships
Workers income = wages + welfare benefits - workers tax
Workers expenditure = workers income - net workers savings
Rentiers income = r *(net capital) - rentiers tax
Rentiers expenditure = rentiers income - delta(net rentiers capital)
State income = rentiers tax + workers tax
State expenditure = state purchases + welfare benefits
delta( state money) = state expenditure - state income
Firms net income = workers expenditure + rentiers expenditure + state purchases
Firms net expenditure = wages + r'*(net debt)
delta( firms net debt )= firms expenditure - firms income
Banking Sector
-------------
This enforces aggregate balances
Change in bank liabilities =
net workers savings +
delta(net rentier capital)
Change bank assets =
delta( state money)+
delta(firms net debt)
What constitutes money in this system? If we assume that
state money consists entirely of credit balances with the
state bank, which are only held by other banks, then the
effective purchasing money is in the form of credit balances
with the banking sector by firms, rentiers and workers.
Even at this level of abstraction where we are aggregating
over whole sectors, it is clear that the change in bank
liabilities, and thus the change in the money stock,
is unlikely to be zero.
If we disaggregate the sectors, and in particular disaggregate
the firm sector, we see that some firms may have net
debit and some net credit balances with the banking sector.
The equations for the banking sector then become:
Change in bank liabilities =
net workers savings +
delta(net rentier capital) +
delta(internal firmsector debt)
Change bank assets =
delta( state money)+
delta(firms net debt) +
delta(internal firmsector debt)
Where the delta(internal firm sector debt) is the growth of all
firms overdrafts minus the growth of the net debt of the
firm sector to other sectors.
This last term, will depend on the statistical distribution
of firms in the phase plane whose y axis is the relative
change in a firms gearing ratio, and whose x axis is its
current gearing ratio. We cannot assume that this
distribution is degenerate. A theoretical study,
( without any simulations to back it up ) that I
did some time ago indicated that not only is this
distribution non- degenerate, but that it has
dynamic instabilities.
Briefly, as the rate of interest rises, it tends
to push firms that are already in debt to go further
into debt, whilst firms that have net credit balances
tend to go further into credit.
This increases the mass of money in the form of bank
deposits, and thus raises the interest rate (unless
there is a coresponding rise in the quantity of state
money), which further exacerbates the situation.
The net effect is that the entropy of the firm sector
will rise.
However, it is not only money that is non-conserved,
firms are not conserved either - once their indebtedness goes
beyond a certain point they go bankrupt. This enforces
a reduction in the assets of the banking sector, violating
the accounting identities assumed for that sector.
The conclusion I draw from this is that although stochastic
and statistical models have to be the way to go, one must
be very cautious about imposing conservation principles
on them if they are to be:
a) internally consistent
b) plausible as models
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