Ponzi Maths–Part 2

flattr this!

In the previous post, I outlined my basic model of a pure credit economy, in which a single initial loan allowed a continous flow of economic activity (at a constant level) over time. The basic flowtable of that system was:

 

Type 1 -1 -1 -1
Account Firm Loan (FL) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A      
Interest on Deposit   +B -B  
Pay Interest on Loan -C -C +C  
Pay Wages   -D   +D
Interest on Deposit     -E +E
Consume   +F+G -F -G

The next stage of the model allows for repayment of loans, and re-circulation of these repayments. For this, another account is needed: a capital account that records the inactive reserves of the banking system--those reserves the banking system has available for lending. The two additional steps that are considered now are:

  1. The firm pays money to the bank that is to be taken off its outstanding debt. This is a transfer of H from the firm's deposit account to the bank's capital account, and in recognition of receiving it, the bank is olbiged to reduce the recorded amount of outstanding debt by the same amount; and
  2. The bank can now re-lend existing inactive reserves to firms. This is a transfer of money I from the bank's capital account to the firm's deposit account, and in recognition of having given it to the firm, the bank records that the firm's debt has risen by the same amount.

Adding these new flows to the table generates the following system:

Type 1 0 -1 -1 -1
Account Firm Loan (FL) Bank Reserves (BR) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A        
Interest on Deposit     +B -B  
Pay Interest on Loan -C   -C +C  
Pay Wages     -D   +D
Interest on Deposit       -E +E
Consume     +F+G -F -G
Repay Loan -H +H -H    
Relend Reserves +I -I +I    

This is still an equilibrium system--though it operates at a lower level than the previous one where a single injection of credit money circulated indefinitely, because there is less money in active circulation. The next step--and the one that explains how money can expand endogenously--is to introduce the creation of new credit money. The mechanism is extremely simple. As Basil Moore, the pioneer of "endogenous money" theory, argued decades ago, major firms have "lines of credit" that enable them to increase their spending at will, in return for accepting a matching increase in their debt levels. In a growing economy, these "lines of credit" (and their domestic equivalent, the gap between aggregate credit card balances and aggregate limits) are growing all the time.

In this simple model, this simultaneous expansion of both debt and money is captured by the sum J being added to the firm's deposit account, in return for the bank adding the same sum to the outstanding debt of the firm.

 

Type 1 0 -1 -1 -1
Account Firm Loan (FL) Bank Reserves (BR) Firm Deposit (FD) Bank Deposit (BD) Worker Deposit (WD)
Interest on Loan +A        
Interest on Deposit     +B -B  
Pay Interest on Loan -C   -C +C  
Pay Wages     -D   +D
Interest on Deposit       -E +E
Consume     +F+G -F -G
Repay Loan -H +H -H    
Relend Reserves +I -I +I    
Extend Credit +J   +J    

 

With this extension, we move out of the realm of equilibrium--so long as J is positive, the money supply and the economy will be expanding (we also comprehensively invalidate "Walras' 'Law'", a cornerstone of neoclassical economics--but that's a topic for a later post). Starting from the equilibrium values of the previous system, the bank balances and incomes in the system grow as indicated by the next two graphs.

All the mod­els so far describe “well behaved” finan­cial sys­tems: the banks make their money out of the spread between loan and deposit rates of inter­est (other exten­sions cover non-bank lend­ing, which is part of the expla­na­tion of why debt exceeds money; but that’s another topic in itself). Next we intro­duce a badly behaved finan­cial inter­me­di­ary: one that pre­tends to make more money than the oth­ers, but in real­ity makes none at all–a Ponzi Scheme.

This is enough for one post; to be con­tin­ued in Ponzi Maths–Part 3.

About Steve Keen

I am a professional economist and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous debts accumulated in Australia, and our very low rate of inflation.
Bookmark the permalink.

4 Responses to Ponzi Maths–Part 2

  1. marcf999 says:

    Steve,
    1/ Can you expand on the dif­fer­ence you make between Bank Deposit and Bank Reserves? I am not sure I under­stand the dis­tinc­tion clearly.

    2/ Regard­ing the sen­tence: “The next step–and the one that explains how money can expand endogenously–is to intro­duce the cre­ation of new credit money.“
    a/ You seem to pos­tu­late J, the “new credit-money” rather than derive it. In this sys­tem credit money growth is a hypoth­e­sis not a con­se­quence? Min­sky clearly talks of credit money expan­sion as a con­se­quence of ponzi demand
    b/ fur­ther­more J is defined as nMxFD in the next post, mean­ing a sort of money mul­ti­plier on the deposits of firms alone? Can you expand on this hypothesis?

  2. Steve Keen says:

    Hi Marc,

    Here I’m prob­a­bly tak­ing a famil­iar­ity with some of the endoge­nous money lit­er­a­ture for granted.

    1. On the first point, the dif­fer­ence relates to Graziani’s argu­ments that, for a credit money sys­tem to work, it must be the case that seignor­age is not pos­si­ble. If a bank could spend or con­sume on the basis of what was in its reserves–if it could in effect spend what was paid to it as repay­ment for loans–then seignor­age would be occurring.

    The divi­sion of the banks finances into a Deposit account–really a Profit and Loss account–and a reserve account mim­ics this. Actual bank finances these days would be far more com­pli­cated; this sim­ply imple­ments the basic con­cept in a hypo­thet­i­cal pure credit economy.

    2a. On the sec­ond, there is a sub­stan­tial lit­er­a­ture devel­oped by Basil Moore around how money is endoge­nously cre­ated via the exis­tence of “lines of credit” for major cor­po­ra­tions. The same thing applies to over­drafts for small firms, and credit cards for indi­vid­u­als. These are always being extended to new enti­ties, or expanded for exist­ing ones in a grow­ing econ­omy. My model sim­ply for­malises that.

    2b. It’s not a mul­ti­plier but a flow function–an expo­nen­tial growth term, the mir­ror image of the func­tions used for debt repay­ment where expo­nen­tial decay applies. As a dif­fer­en­tial equa­tion, it sim­ply says that (if nM is 0.1 or 10%) that “the money sup­ply grows at 10% per annum”.

    In a more com­plex exten­sion to the model, this growth rate would depend on firms’ will­ing­ness to take on debt–so it would be dri­ven from the bor­rower side rather than the lender. For now I sim­ply use a set con­stant so that my model pro­vides a skele­ton of how a finan­cial sys­tem works.

    I think you might ben­e­fit from read­ing some of the ref­er­ences I’ve given in the asso­ci­ated paper that I’ve sent you by Moore, Graziani and Min­sky, to see where some of these ideas come from.

  3. marcf999 says:

    Steve,

    thanks for the clar­i­fi­ca­tion on seignor­age (the word seems to throw off you spell checker).

    Yes I under­stand you are pos­tu­lat­ing new money cre­ation now. I have read most papers you have sent (not browsed ref­er­ences yet) and was par­tic­u­larly keen on the “not keen on bailouts”. The nar­ra­tive in there is really good and points at mon­e­tary lev­els that can­not be con­trolled.
    I looked at the ponzi math in the 3 chap­ter here I think you are very close to a uni­fied endoge­nous model of new money cre­ation. My per­sonal graal would be link­ing mon­e­tary lev­els to prices in dynam­ics. I am mak­ing good progress in my under­stand­ing of what your model cap­tures, your nar­ra­tive is richer than the mod­els and pro­vides a lot of food for thought.

    It is funny I was think­ing this morn­ing in the car that a way to cap­ture endoge­nous cre­ation of credit money would be to model demand for credit money. Ponzi demand as opposed to pos­tu­lat­ing money cre­ation would intro­duce a dynamic growth of credit. Demand for credit has got to be a func­tion of price deriv­a­tive which in your dP=p(D-Q) means that a pos­i­tive dP means more demand than Q and that in turns increases D by cre­at­ing money for ponzi. In other words demand for credit increases asset prices which increases demand for credit. Do you have a for­mula on that? I think that pos­tu­late would close the loop.

    I am still search­ing for a endoge­nous min­sky moment. The endoge­nous shock… how do we get at it from the dynam­ics? Will prob­a­bly fol­low by email.

  4. marcf999 says:

    regard­ing seignor­age… if I under­stand your expla­na­tion cor­rectly, it means that banks can­not spend the loans that are repaid because it was all credit money that came out of noth­ing. Bad debt essen­tially vio­lates the no-seignorage rule. The money is in cir­cu­la­tion, WAS SPENT and will not be recov­ered. Futher­more this money is senior in cap­i­tal struc­tures to equity cap­i­tal. So fake money will devour equity cap­i­tal in bad debt explo­sions, wit­ness the banks and their equity as we speak. We are float­ing bal­ance sheets that were com­posed of credit money that was fake in the first place but needs to be mate­ri­al­ized with equity cap­i­tal as it turns bad. This fur­ther depresses the demand and could be a sig­nif­i­cant fac­tor in the Min­sky nar­ra­tive, we are clearly see­ing this at the moment imho.

Leave a Reply