The Economics E-Journal
The Economics E-Journal is a relatively new journal that implements several new approaches to academic publishing:
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It is open access and free. Most academic journals are restricted to subscribers or those with access to academic libraries that subscribe, which excludes the general public from access to intellectual endeavour.
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Anyone paper submitted to the journal is permanently available. Normally only papers that have been refereed and accepted for publication can be accessed.
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Anyone can comment on a paper, and comments and the number of downloads goes some way to influencing whether a paper is published in the journal proper.
Papers are still refereed as in a standard journal, and those that are accepted by the referees are published in the journal section of the webpage.
The paper below was submitted to the journal at the invitation of the editors for a special edition on “Managing Financial Instability in Capitalist Economies“. It took some time to get through the refereeing process, but the paper is finally available online (I was critical of some of the feedback I received—there are in my opinion some teething problems still to be surmounted in balancing the range of people that can comment on papers in this journal against the need to have critically informed readers making the ultimate decision. However the final paper was also much improved by the interactions with referees and the editors).
Click here for a PDF version of this paper ; you can also read it as a webpage below. I’ve changed the theme for my blog recently to get around formatting hassles, since the previous theme inserted a page break every time I used italic font!. There were still some formatting hassles–I had to substitute for some Greek characters with the English spelling of the Greek letter for example–but it is better than with the old theme.
This post below deserves the moniker “wonkish”, but I hope that it is still generally readable.
Preliminaries
Bruun and Heyn-Johnsen (2009) state the paradox that economics has failed to provide a satisfactory explanation of how monetary profits are generated, even though the generation of a physical surplus in production is an essential component of non-neoclassical economics. They emphasise that our ability to explain phenomena like the “Great Recession” will be limited while ever we are unable to explain this fundamental aspect of capitalism.
In fact this paradox can be solved very simply, using insights from Circuit Theory Graziani (1990). Graziani’s brilliant initial proposition was that a credit economy must be using a non-commodity as money, since the alternative of “an economy using as money a commodity coming out of a regular process of production, cannot be distinguished from a barter economy” Graziani (1995: 518). From the fact that an intrinsically valueless token is nonetheless accepted as full payment in the exchange of goods, Graziani derived the conclusion that:
any monetary payment must therefore be a triangular transaction, involving at least three agents, the payer, the payee, and the bank… Since in a monetary economy money payments go necessarily through a third agent, the third agent being one that specialises in the activity of producing means of payment (in modern times a bank), banks and firms must be considered as two distinct kinds of agents (Graziani 1995: 518–519).
Unfortunately, attempts by Graziani and subsequent Circuitist authors to develop a viable mathematical model of the creation of monetary profits in a pure credit economy have to date been a failure—a situation well expressed in Rochon’s lament “How does M become M+?” (Rochon 2005: 125). This failure was not due to any weakness in the underlying vision of a pure credit economy, but to confusions of stocks with flows emanating largely from inappropriate mathematical approaches use by these authors. A simple dynamic monetary model that uses the bank account as its fundamental unit explains how capitalists can and do make a profit. In brief, “M becomes M+” via the price mechanism, which converts the sale of the physical surplus generated in production into money.
The topic has become clouded by many other issues—from the basis for the value of money itself to the impact of debt repayment on the money stock. So that I can focus solely on this issue of how monetary profits are generated, I deliberately abstract from these important but—in this context—tangential issues, as outlined below.
There are disputes in Post Keynesian monetary theory over the logical basis for the existence and value of money—notably between Chartalists who assert that taxation is the basis of money’s value, and some Circuitists—including Graziani (1989)—who assert that its acceptance in completing obligations between buyer and seller in an exchange is sufficient. The mathematical conundrum about whether capitalists can make a monetary profit when the source of their initial capital is borrowed money exists independently of this philosophical debate. The consensus to date has been that it is mathematically impossible for capitalists in the aggregate to make profits (see for example Bellofiore et al. 2000). I abstract from these philosophical and ex origo debates in order to focus simply on the mathematical issue, to show that this consensus is false.
This dispute, and the current consensus conclusion, also exist within the confines of models of a pure credit economy—that is, models that treat money as a non-commodity issued by a private banking system, and abstract from the existence of both the State itself, and State or fiat money. The mathematical issue is therefore best treated in a model of a pure credit economy, even if a complete model of the existing monetary system must include both fiat and credit money.
Finally, there is a difference between modern Post Keynesian theorists and Keynes over what happens to money that is used to repay debt. The convention in Circuit literature is that money used to repay debt is destroyed:
To the extent that bank debts are repaid, an equal amount of money is destroyed (Graziani 2003: 29–30).
Money is created as banks lend-mainly to business-and money is destroyed as borrowers fulfill their payment commitments to banks. Money is created in response to businessmen’s and bankers’ views about prospective profits, and money is destroyed as profits are realized Minsky (1982: xxi).
Keynes, on the other hand, spoke of a “revolving fund of credit” which was continuously replenished by the repayment of debt, which implies that money used to repay debt may be temporarily taken out of circulation, but is not destroyed:
If investment is proceeding at a steady rate, the finance (or the commitments to finance) required can be supplied from a revolving fund of a more or less constant amount, one entrepreneur having his finance replenished for the purpose of a projected investment as another exhausts his on paying for his completed investment (Keynes 1937: 247).
I side with Keynes on this issue, but to avoid complications resulting from this difference of interpretation, I first consider the historically relevant example of a private bank using paper notes that it itself creates—see Figure 1 for an example of such a note issued during the “Free Banking” period in the USA (Dwyer 1996).
A paper note model is also consistent with Graziani’s original paper on the monetary circuit, where he observed that “A true monetary economy must therefore be using a token money, which is nowadays a paper currency” (Graziani 1989: 3). These banks did not destroy their notes when debts were repaid, but treated their specie as a “revolving fund”, with notes stored until they could be recirculated in new loans:
Free banks were rarely able to keep all of their allowable note issues in circulation at all times. Ratios of idle notes to total legal circulation in New York ranged from a low of 4 percent in 1852 to a high of 21.6 percent during the panic of 1857. The proportion of idle notes dipped below 10 percent in only three years and hovered around 15 percent throughout the 1850s (Bodenhorn and Haupert 1996: 688).
Though the historical stability of this period is disputed,
a private banking system of this type is not intrinsically unstable, and as I show below, capitalists can make a profit in such a system, even if their ventures are 100% debt-financed.
Figure 1: Bank of Florence (Nebraska) Dollar Note (Smithsonian Institution 2010)
The Basic Model: A Set Quantity of Notes
Consider a private bank which, having fulfilled the legal requirements for Free Banking (see Bodenhorn 2008: 183–184), creates a stock N of dollar notes like those in Figure 1. These notes are initially held by the new bank in its vault. The bank then issues loans to firms, which enables the firm to hire workers, who then produce output which is sold to workers, capitalists and bankers.
A minimum of 5 classes of accounts are needed to model this system:
- The bank vault (BV), into which the newly-minted notes are first placed
- Firm deposit accounts (FD), into which actual transfers of loaned dollars are made
- Workers deposit accounts (WD), into which wages are paid by firms
- A bank transactions account (BT), into and out of which interest payments are made
- Firm loan accounts (FL), where ledger entries that record the quantity of notes that have been lent to firms
The first four of these are physical repositories of notes. The fifth is not a repository for notes, but a ledger recording the legal claim that the bank has upon those to whom it has lent. Operations on it therefore do not involve monetary transfers, but record the impact of those transfers on the indebtedness of borrowers.
The basic transactions that occur in this model are detailed in Table 1. Seven of these steps involve the physical transfer of money:
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Lending of money from the bank vault to the firms’ deposit accounts (row 1)
- Payment of interest by firms to the bank’s transactions account (row 4)
- Payment of interest by the bank to firms’ deposit accounts (row 6)
- Payment of wages (row 7)
- Payment of interest on workers’ account balances (row
- Payment for consumption of the output of firms by bank and workers (row 9)
- Repayment of loans by firms (row 10)
Four steps are ledger entries only, involving the recording of a money transfer related to the level of debt:
- Recording the loans to firms (row 2)
- Compounding the debt at the rate of interest on loans (row 3)
- Recording the payment of interest on loans (row 5)
- Recording the repayment of loans (row 11)
Table 1: Basic Financial Transactions in a Free Banking Economy
| Row | Transaction | Type | Bank vault (BV) | Bank transaction (BT) | Firm loan (FL) | Firm deposit (FD) | Worker deposit (WD) |
| 1 | Lend money | Money transfer |
–a |
a |
|||
| 2 | Record loan | Ledger entry |
a |
||||
| 3 | Compound debt | Ledger entry |
b |
||||
| 4 | Pay interest | Money transfer |
c |
–c |
|||
| 5 | Record payment | Ledger entry |
–c |
||||
| 6 | Deposit interest | Money transfer |
–d |
d |
|||
| 7 | Wages | Money transfer |
–e |
e |
|||
| 8 | Deposit interest | Money transfer |
–f |
f |
|||
| 9 | Consumption | Money transfer |
–g |
g+h |
–h |
||
| 10 | Repay loan | Money transfer |
i |
–i |
|||
| 11 | Record repayment | Ledger entry |
–i |
||||
| Sum of flows |
i–a |
c–d–f–g |
a+b–c–i |
a–c+d–e+g+h–i |
e+f–h |
The financial flows in each column of Table 1 can be summed to describe the dynamics of the bank accounts in this model:
To model this system, we need to provide values for the operations a to i. Table 2 specifies these, with each operation being related to the current level of the relevant account—lending from the vault, for example, is assumed to occur at a constant rate ”beta”V related to the current amount of money in the vault at time t, BV(t).
Table 2: Financial Operations
| Flow | Description | |
| a | Loans to firms at the rate bV times the balance in the vault at time t BV(t) | bv.BV(t) |
| b | The rate of interest on loans rL times the level of loans at time t FL(t) | rL.FL(t) |
| c | Payment of interest on loans | rL.FL(t) |
| d | Payment of interest on firm deposits FD(t) at the rate rD | rD.FD(t) |
| e | Payment of wages by firms at the rate fD times firm deposits at time t FD(t) | fD.FD(t) |
| f | Payment of interest on deposits at the rate rD | rD.WD(t) |
| g | Payment for goods by banks at the rate bT times the level of the bank transaction account at time t BT(t) | bT.BT(t) |
| h | Payment for goods by workers at the rate wD times the level of the bank transaction account at time t WD(t) | wD.WD(t) |
| i | Repayment of loans at the rate “phi”L times the outstanding loan balance at time t FL(t) |
fL.FL(t) |
The full dynamic system is given by Equation :
As is easily shown, with realistic parameter values (see Table 3; the values are explained later in the text prior to Table 5, and Table 5 itself) this describes a self-sustaining system in which all accounts settle down to equilibrium values, and in which capitalists earn a monetary profit.
Table 3: Parameter Values
| Parameter | Value | Description |
| bV | ¾ p.a. | Rate of outflow of notes from the vault BV |
| rL | 5% p.a. | Rate of interest on loans |
| rD | 2% p.a. | Rate of interest on deposits |
| fD | 2 p.a. | Rate of outflow of notes from FD to pay wages |
| bT | 1 p.a. | Rate of outflow of notes from BT to pay for bankers consumption |
| wD | 26 p.a. | Rate of outflow of notes from WD to pay for workers consumption |
| fL | 1/7 p.a. | Rate of repayment of loans |
Figure 2: Bank Account Balances over Time
Figure 2 shows the dynamics of this system with an initial stock of N=100 million dollar notes.
The equilibrium values of the accounts can be solved for symbolically in this constant money stock model:
From Account Balances to Incomes
The equilibrium yearly wages of workers (and gross interest earnings by bankers) can be calculated from Equation , and they in part explain why, in contrast to the conventional belief amongst Circuitist writers, capitalists can borrow money, pay interest, and still make a profit. Though only $100 million worth of notes were created, the circulation of those notes generates workers’ wages of $151 million per annum (given the parameter values used in this simulation), 1.5 times the size of the value of the notes in the economy (see Figure 3):
This indicates the source of the Circuitist conundrums: the stock of money has been confused with the flow of economic activity that money can finance over time. A stock—the initial amount of notes created in this model—has been confused
Figure 3: Wages and Gross Interest
with a flow—the economic turnover in notes per year. In fact, for a wide range of values for the parameter ?D, the flows initiated by the money borrowed by the firms over a year exceed the size of the loan itself.
This is possible because the stock of money can circulate several times in one year—something that Marx accurately enunciated over a century ago in Volume II of Capital (though his numerical example is extremely large):
“Let the period of turnover be 5 weeks, the working period 4 weeks… In a year of 50 weeks … Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ times 2,000 makes £25,000″ (Marx and Engels 1885, Chapter 16: The Turnover of Variable Capital).
Aggregate wages and aggregate profits therefore depend in part upon the turnover period between the outlay of money to finance production and the sale of that production. This turnover period can be substantially shorter than a year, in which case fD will be substantially larger than 1, as I explain below.
The Making of Monetary Profits
A second fundamental insight from Marx lets us explain what fD is, and simultaneously derive an expression for profits: the annual wages bill reflects both the turnover period, and the way in which the surplus value generated in production is apportioned between capitalists and workers. The value of fD therefore reflects two factors: the share of surplus (in Sraffa’s sense) that accrues to workers; and the turnover period measured in years—the time between M and M+. Labelling the share going to capitalists as s and the share to workers as (1–s), and labelling the turnover period as tS and expressing it as a fraction of a year, I can perform the substitution shown in below:
Money wages are therefore:
Since national income resolves itself into wages and profits (interest income is a transfer between classes, and sums to zero across all classes), we have also identified gross profit:
Using a value of s= 40%—which corresponds to historical norm of 60% of pre-interest income going to workers (see Figure 4)—this implies a value for tS of 0.3.
This means that the turnover period in Marx’s terminology is roughly 16 weeks. This is much longer than in Marx’s numerical illustration above, but still sufficient to give capitalists profits that are substantially greater than the servicing costs of debt. Figure 5 shows the annual incomes for each class in society over time; all are positive and the equilibrium levels (once account levels stabilise) are $151 million, $98 million and $2.5 million for workers, capitalists and bankers respectively out of a national income of $252 million (see Equation ).
Figure 4: Wages Percentage of US GDP
Figure 5: Class Incomes after Interest Payments
The value of tauS also determines the velocity of money: the ratio of nominal GDP to the proportion of the money stock in circulation (the equivalent of M3–M0 in monetary statistics, since in this pure credit model there is no fiat money), which is 3 given the parameters used in this simulation. This is within the highly volatile range suggested by historical data (see Figure 6).
Table 4 summarises the equilibrium values for account balances, gross and net incomes in this hypothetical pure credit economy.
Figure 6: US GDP to Money Supply Ratios
Table 4: Equilibrium Account Balances, Gross and Net Incomes
| Account balances | Class incomes | Net incomes | |
| Bank vault | 16 | N/A | N/A |
| Firm loans | 84 | N/A | N/A |
| Firms | 75.6081 | 100.811 (profits) | 98.123 |
| Workers | 5.8205 | 151.216 (wages) | 151.333 |
| Bankers | 2.5714 | 4.2 (debt servicing) | 2.571 |
| Totals | 84 (in Deposits) | 252.027+4.2 | 252.027 |
We can also derive a symbolic expression for the equilibrium level of profits
pe:
This allows us to specify the general conditions under which equilibrium monetary profits will exceed zero, given the existence of a physical surplus from production. They are far from onerous: the rate at which the bank transaction account turns over each year has to exceed the rate of interest on loans 
and the rate at which the workers’ deposit account turns over has to exceed the rate of interest on deposits 
. Reasonable values for these parameters easily meet these conditions, as detailed below.
Other Parameters and Time Lags
The parameters rL and rD are nominal interest rates, and their values are roughly in line with historical norms at times of low-inflation; that leaves the parameters bV, fL, fD and bT to account for.
The values for “phi”V and fL respectively specify how rapidly the balance in the vault is turned over, and how rapidly loans are repaid, and were chosen so that the equilibrium value of BV would be roughly the value noted by Bodenhorn and Haupert (1996: 688) of 15% of available notes:
The parameters “omega”D and “beta”T signify how rapidly workers and bankers respectively spend their bank balances on the output produced by firms: workers are assumed to turnover their accounts 26 times a year—which corresponds to workers living from fortnightly paycheque to paycheque, with only modest savings. Bankers are assumed to turnover their account just once a year, reflecting their much higher per capita incomes.
In the remainder of the paper, all parameters are expressed using the systems engineering concept of a time constant, which gives the fundamental frequency of a process. In every case, the time constant is the inverse of the parameter used thus far; for instance, the value of 26 for wD corresponds to workers’ consumption having a fundamental frequency of 1/26th of a year, or two weeks.
Table 5: Time Constants in the Model
| Parameter and value | Time constant and value | Meaning |
| bV = ¾ | tV = 4/3 years | Banks lend their reserve holdings of notes every 15 months |
| fL= 1/7 | tL= 7 years | Firms repay their loans every 7 years |
| wD = 26 | tW= 1/26 years | Workers spend their savings every 2 weeks |
| bT = 1 | tB= 1 year | Bankers spend their savings every 1 year |
| tP= 1 year | Time constant in price setting (introduced in Equation ) | |
| t M= 15 years | Banks double the money supply every 15 years (introduced in Table 7 on page 24) |
Production, Prices and Monetary Profits
Consider a simple production system in which output is proportional to the labour input L with constant labour productivity a:
Labour employed in turn equals the monetary flow of wages divided by the nominal wage rate W:
Prices then link this physical output subsystem to the financial model above. In equilibrium, it must be the case that the physical flow of goods produced equals the monetary demand for them divided by the price level. We can therefore derive that in equilibrium, the price level will be a markup on the monetary wage, where the markup reflects the rate of surplus as defined in this paper.
To answer Rochon’s vital question, M becomes M+ (that is, monetary profits are realised) via a price-system markup on the physical surplus produced in the factory system. This markup can be derived simply by considering demand and supply factors in equilibrium. The flow of demand is the sum of wages and profits (since interest payments are a transfer and do not contribute to the value of output—despite Wall Street’s bleatings to the contrary). The monetary value of demand is thus:
The physical units demanded equals this monetary demand divided by the price level:
In equilibrium this physical demand will equal the physical output of the economy:
Solving for the equilibrium price Pe yields:
The markup is thus the inverse of workers’ share of the surplus generated in production. Circuit theory therefore provides a monetary expression of Marx’s theory of surplus value, as it was always intended to do.
With these physical and price variables added to the system, we are now able to confirm that profit as derived from the financial flows table corresponds to profit as the difference between the monetary value of output and the wage bill (in this simple single-sectoral model).
Table 6: Parameters and Variables for Physical Production Subsystem
| Variable, parameter or initial condition | Definition | Value |
| a | Labour productivity a = Q/L | 2 |
| W | Nominal wage | 1 |
| Pe | Equilibrium price  |
0.833 |
| P0 | Initial price | 1 |
| Le | Equilibrium employment  |
151.216 |
| Qe | Equilibrium output  |
302.432 |
Using the values given in Table 6, it is easily confirmed that the equilibrium level of profits derived from the financial flows corresponds to the level derived from the physical production system:
The price relation given above applies also only in equilibrium. Out of equilibrium, it is reasonable to postulate a first-order convergence to this level, where the time constant ?P reflects the time it takes firms to revise prices. This implies the following dynamic pricing equation:
A simulation also confirms that the monetary flows (demand) and the monetary value of physical flows (supply) converge over time (Figure 7).
This solves the “paradox” of monetary profits: it was not a paradox at all, but a confusion of stocks with flows in previous attempts to understand the monetary circuit of production.
Figure 7: Supply, Demand and Price Convergence
Analysing the “Great Recession”
We can now use this framework to consider one aspect of the current financial crisis: if a “credit crunch” occurs, what is the best way for government to address it?—by giving fiat money to the banks to lend, or by giving it to the debtors to spend?
Our current crisis is, of course, more than merely a “credit crunch”—a temporary breakdown in the process of circulation of credit. It is also arguably a secular turning point in debt akin to that of the Great Depression (Keen 2009), as Figure 8 illustrates. While the model developed here cannot assess this claim, it can assess the differential impact of a sudden injection of fiat money to rescue an economy that has experienced a sudden drop in the rate of circulation and creation of private credit. This is an important point, since although the scale of government response to the crisis was enormous across all affected nations, the nature of that response did vary: notably, the USA focused its attention on boosting bank reserves in the belief—as expressed by President Obama—that the money multiplier made refinancing the banks far more effective than rescuing the borrowers:
And although there are a lot of Americans who understandably think that government money would be better spent going directly to families and businesses instead of banks – “where’s our bailout?,” they ask – the truth is that a dollar of capital in a bank can actually result in eight or ten dollars of loans to families and businesses, a multiplier effect that can ultimately lead to a faster pace of economic growth (Obama 2009: 3. Emphasis added).
Figure 8: Private Debt to GDP Ratios, USA & Australia
The Australian policy response to the crisis, on the other hand, was pithily summed up in the advice given by its Treasury: “go early, go hard, go households” (Gruen 2008). Though many other factors differentiate these two countries—notably Australia’s position as a commodity producing supplier to China—the outcomes on unemployment imply that the Australian measures more successful than the American “money multiplier” approach (see Figure 9).
The next section applies this endogenous money model to consider a differential response to a credit crunch in a growing economy: an injection of funds is made into either the Banks’ Vault accounts—simulating the USA’s policy response—or into the Workers’ Deposit accounts—simulating the Australian response.
Figure 9: Unemployment Rates USA and Australia
Endogenous Money Creation and Economic Growth
To model a credit crunch in a growing economy, while otherwise maintaining the structure of the Free Banking/pure credit money model above, I move beyond the limitations of a pure paper money system to allow for endogenous money creation as described in Moore (1979):
“In the real world banks extend credit, creating deposits in the process, and look for the reserves later” (Holmes 1969, Moore 1979: 53); see also more recently Disyatat (2010: 7 “loans drive deposits rather than the other way around”).
In the model, new credit to sustain a growing economy is created by a simultaneous increase in the loan and deposit accounts for the borrower. The financial flows in this system are given in Table 7. The two changes to Free Banking model are the addition of row 12 (and its ledger recording in row 13), with the qualitatively new operation of Money Creation being added to the previous operation of Money Transfer, and a “Deus Ex Machina” injection of fiat money into either Bank Vault or Worker Deposit accounts one year after a credit crunch.
Again, simply to illustrate that the system is viable, a constant growth parameter “tau” M has the banks doubling the stock of loans every 15 years (see Table 3):
A credit crunch is simulated by varying the three crucial financial flow parameters tauV, tauL, and tauM at an arbitrary time in the following simulation (at t=25 years): tauV and tauM are doubled and tauL is halved, representing banks halving their rates of circulation and creation of new money and firms trying to repay their loans twice as quickly (see Table 8). The government fiat-money rescue is modelled as a one-year long injection of a total of $100 million one year after the credit crunch.
Several extensions to the physical side of the model are required to model economic growth. In the absence of Ponzi speculation (which is the topic of a later
Table 7: Endogenous Money Creation
| Row | Transaction | Type | Bank vault (BV) | Bank trans-action (BT) | Firm loan (FL) | Firm deposit (FD) | Worker deposit (WD) |
| 1 | Lend money | Money transfer |
–a |
a |
|||
| 2 | Record loan | Ledger entry |
a |
||||
| 3 | Compound debt | Ledger entry |
b |
||||
| 4 | Pay interest | Money transfer |
c |
–c |
|||
| 5 | Record payment | Ledger entry |
–c |
||||
| 6 | Deposit interest | Money transfer |
–d |
d |
|||
| 7 | Wages | Money transfer |
–e |
e |
|||
| 8 | Deposit interest | Money transfer |
–f |
f |
|||
| 9 | Consumption | Money transfer |
–g |
g+h |
–h |
||
| 10 | Repay loan | Money transfer |
i |
–i |
|||
| 11 | Record repayment | Ledger entry |
–i |
||||
| 12 | New money | Money creation |
j |
||||
| 13 | Record loan | Ledger entry |
j |
||||
| 14 | Government policy | Exogenous injection into either BE or WD |
k |
||||
|
k |
|||||||
| Sum of flows |
i–a+k |
c–d–f–g |
a+b–c–i+j |
a–c+d–e+g+h–i+j |
e+f–h+k |
ey supply is only warranted if economic growth is occurring, which in turn requires a growing population and/ or labour productivity. These variables introduce the issue of the employment rate, and this in turn raises the possibility of variable money wages in response to the rate of unemployment—a Phillips curve. These additional variables are specified in Equation :
Table 8: Financial Flow Parameters before and after a Credit Crunch
| Pre-credit crunch | Post-credit crunch | Impact of credit crunch |
| tV = 4/3 years | tV = 8/3 years | Banks lend their reserve holdings of notes every 15 months |
| tL= 7 years | tL= 3.5 years | Firms repay their loans every 3.5 years |
| t M= 15 years | t M= 30 years | Banks double the money supply every 30 years |
| k=$100 million | Injected either into bank vault BE or worker deposit WD at year 26, one year after the credit crunch |
The parameter values and functional form for this physical growth extension are shown in Table 9.
Figure 10 shows the impact of the credit crunch upon bank accounts: loans and deposits fall while the proportion of the money supply that is lying idle in bank reserves rises dramatically.
The US empirical data to date has displayed a similar pattern, though with a much sharper increase in bank reserves as shown in Figure 11.
A very similar pattern to the empirical data is evident in the model when the US policy of increasing bank reserves is simulated (Figure 12).
The simulation of Australian household-oriented policies generates a very different dynamic: reserves still rise dramatically during the credit crunch, but their increase is not further augmented by the policy intervention. Instead, firm and worker deposits rise substantially (see Figure 13), whereas they fall in the bank-oriented rescue.
This higher level of money in circulation in the household-oriented policy intervention is the cause of the dramatic difference in the outcomes of the two policy interventions: the household-oriented approach has a far more immediate and substantial impact upon employment (Figure 14). Contrary to the expectations of President Obama and his mainstream economic advisers, there is far more “bang for your buck” out of a household rescue than out of a bank rescue.
Table 9: Parameters and Function for Growth Model
| Variable or parameter | Description | Value |
| alpha | Rate of growth of labor productivity | 1% p.a. |
| beta | Rate of growth of population | 2% p.a. |
| Pop | Population | Initial value = 160 |
| lambda | Employment rate | Initial value = 94.5% |
|
|
Phillips curve:
|
|
Figure 10: Bank Accounts before and after a Credit Crunch
Figure 11: Drop in Business Loans and Dramatic Rise in Bank Reserves during Great Recession
Figure 12: Simulating US Bank-oriented Policy towards a Credit Crunch
Figure 13: Simulating Australian Household-oriented Policy towards a Credit Crunch
Figure 14: Comparing Bank-oriented and Household-oriented Policies
Conclusion
The paradox of monetary profits is solved simply by avoiding the problem so wittily expressed by Kalecki, that economics is “the science of confusing stocks with flows” cited in Godley and Lavoie (2007). With that confusion removed by working in a framework that explicitly records the flows between bank accounts and the production and consumption they drive, it is obvious that Circuit Theory achieves what it set out to do: to provide a strictly monetary foundation for the Marx–Schumpeter–Keynes–Minsky tradition in economics. As an explicitly monetary model, it also provides an excellent foundation for explaining the processes that led to the “Great Recession”, and for testing possible policy responses to it.
Acknowledgements
This work results from a collaborative research effort between the United Nations Environment Program (UNEP) and CSIRO Sustainable Ecosystems to establish a regional report on Resource Efficiency: Economics and Outlook for Asia?Pacific. I thank 4 anonymous referees, an editor and Trond Andresen (Norwegian University of Technology) for comments that greatly improved the final paper.
References
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Brilliant? It’s just plain wrong. One can distinguish and economy using a commodity (of any kind suitable which includes ones produced by regular processes of production) money from barter. In a barter economy no commodity is suitable for use as money, or no such commodity (or set of commodities) has been settle on by the market. Commodities suitable for use as money have certain properties that have been outlined by the Austrians, so I will not repeat here.
BTW, you can have a credit economy with a commodity money, and even without fractional reserve banking. You just need contract law and people willing to borrow and lend on the basis of interest.
There is no such thing as intrinsic value. Value is subjective. Supposedly “valueless tokens” can have value in trade. Credit based money has value in paying off the creditor. For example, early American schemes at credit money had value because the government accepted them in payment of taxes. The same is true of all fiat currencies in existence today.
This whole line of thinking smells of foundationalist thinking. There are no foundations to prices. One cannot follow the stream back to the source. Mises’ brilliant conclusion is that it prices are subjective and relative, and that goods have no “intrinsic value”. As Rothbard pointed out prices evolve from prior states of affair via past and current subjective valuations of the participants, and as revealed by trade.
This is wrong too. A non-barter economy based on a commodity money like gold has no bankers, and no need for a third party.
Humans specialize in production. In a barter economy someone who produces eggs and wants beef has to find either: Someone who produces beef who wants eggs, or some other producer that produces something which a beef producer wants, or the same three levels deep, or four, ….
It’s not likely that the beef producer will want the eggs in a proportionate quantity to the amount of beef desired, nor with the same timing. Commodity money solves these problems by being a common unit of exchange and a store of value. The store of value property of money (the fact that it doesn’t rot, and doesn’t grow on trees) allows a bridging of the issues related to the timing of transactions. Other properties of money such as divisibility, malleability, ease of assay, etc. allow it to be used as a unit of exchange, which solves the problem of the mismatch in quantities in the trades.
When the market has settled on a commodity money the person who wants eggs can sell them for money, and then go buy the beef with that money. No banker involved.
Graziani is lost before he even starts.
Steve,
“We can now use this framework to consider one aspect of the current financial crisis: if a “credit crunch” occurs, what is the best way for government to address it?—by giving fiat money to the banks to lend, or by giving it to the debtors to spend?”
No you can’t use your framework for deciding because it is not a proper simulation of the real world. There is no capital (real goods) in your model and no prices for example. Your last sentence is a false dichotomy. Another option is to do nothing which you exclude from consideration as “best”. Your model has no means of capturing how price corrections will solve the issue. It is empircally at odds with the 1920 depression and recovery where the solution was to do neither of your two options.
Your final graph on employment levels works in the simulation but you have to remember what you are simulating, a system without real capital or prices, one where it is assumed that all companies make a profit, that is static where prices do NOT serve the purpose of communicating information. Your model could just as well describe the operation of a command economy run by Stalin where he decides which firms can borrow.
In short it your conclusion about “what is best” is a non sequitur. The math is useless without proper reasoning.
In your model economy, exactly where do the capitalists get the real funds to pay their workers until their projects have completed? Printing credit currency does not generate the real savings (the food, supplies, etc) required for converting into real capital (eg. industrial machinery) needed to generate profits. The workers need to feed and cloth themselves while they are building that loom, or cultivator.
Could it be that the Australian economy is behaving differently because injecting new money with the banks is not a good way to keep inflating the bubble compared to handing it out to the borrowers? I also think there are other major differences between the US and Australia that that explain the differences in behavior like being a commodities exporter to a developing country that is itself still in the boom phase of a bubble (including housing bubble), and also one that is still benefiting from restructuring of the world economy due to the opening of freer trade.
I see printing up money to hand to people who bet badly on the housing market as nearly as bad as printing it up to hand to the people who lent them the money.
You are subsidizing a bad transaction, and as Hazlett wisely taught you need to pay attention not just to the near term but the long term. Over the long term the extra money increases price levels (yes it does as is empirically proven by countries on fiat vs. non-fiat currencies which is the proper way to compare), which ends up hurting the poor, those on fixed incomes, and savers.
It has to harm someone because you are printing up warrants against goods without increasing the quantity of goods. It’s only a matter of figuring out who is harmed. That is simple because it is the people who are currently holding fiat notes (the warrants).
When I have the direct simple proof to the solution of the mutilated chessboard then why should I believe an opposing solution that involves complicated math based on improper assumptions about the scope of the problem?
Also, even if you feel the borrowers are blameless, you cannot control the subsidization of the transaction to the point where none of the benefit goes to the bankers. Giving the money to the borrowers to pay the lenders means that the lenders make out on a bad loan when the market should have punished them too.
If you do feel the borrowers are blameless and incompetent then from a moral standpoint, if you are consistent, you must also believe that no borrower ever deserves the profits they gain from a rise in value of that which they borrowed against. Thus to truly correct the system in a fair fashion you’d need to undo all the transactions. Which is ridiculous.
Why should only those who were the very most irresponsible (as proven by the fact that they failing to meet payments, or lent to deadbeats) be the ones to be bailed out? Perhaps we should do the opposite. We should hand out free money in directly opposite proportion to how much your payments on loans are. Seems more fair to say, we need to inject X billion into the system in order to bring fiat currency levels into line with bank leverage, divide by the population and a) hand out the same amount of free cash to everyone including those who never borrowed a cent. or b) hand out the money in inverse proportion to how much total debt people are in.
I’m not suggesting that because that would still harm savers, and the poor in the long run, but it makes more sense.
Our economies are based on a temporal pyramid scheme called fractional reserve banking. Some of us, the non-fools, recognized that fact and arranged our lives so we would not get stuck with the bag. Now that you other fools finally catch on (not really you just are noticing the bag is empty but have no idea why) you now want to throw all the rules out the window and print money to bail out your preferred charity cases at the expense of the wise.
The pyramid scheme is crashing. The problem is that the fantasy profits and retirements were never a reality. There are real losses that the government lowering of interest rates caused, and the issue now is who to stick holding the bag. For some reason everyone who was in on the pyramid scheme thinks the losses should fall on those who never participated. They certainly aren’t trying to shift the losses between themselves. The banks know they can’t shift it onto the bankrupt borrowers, and the bankrupt borrowers can’t shift it onto the banks (who live off their payments). Therefore they dig into the pockets of those who were responsible (or at least more so).
I see the Keynesians and the Monetarists acting as rationalizers to screw the responsible to the major benefit of bankers (and lesser so the irresponsible borrowers), whereas I see you Steve as rationalizing the screwing of the responsible to bail out the irresponsible borrowers.
Yep, I have a mortgage, and a house, and sure my net worth will go down on paper if we do not bail one way or the other, but I won’t fool myself into thinking it is right to screw some foreigner (or net saver) to maintain my net worth. Printing more money will do just that. It will screw the foreigners holding the cash.
I borrowed specifically because I knew where the political pressure would be. Had I been even more frugal I would have been even more screwed by my responsible behavior. I won’t however pretend that there is an economic need to make my bets on the idiocy of the rest of the country pay off.
The world has lived through many a fractional reserve contraction where no bailouts were done, no spending projects, and things corrected via price changes, and much faster than things are going now. The economy needs to readjust and bailouts to either bankers or borrowers just delays that process. The delaying is what hurts because people consume their savings waiting for things to turn round.
I can see I’m way late for this discussion; is anybody still interested?
TITINT, were you happy with those explanations? I confess I have the same problem: where is the profit? Most definitions of “profit” would have the firm’s deposit account increasing over time. Profit as a flow, with no increase in net worth? It’s not very intuitive. (Incidentally, which flow?)
Of course it’s a no-brainer that in a closed system with constant money, no player can accumulate money indefinitely – once he has all the money, it’s the end of the game, i.e. no steady state.
So I think it hinges on the definition of “profit” – does anybody have one which is understandable and is compatible with Steve’s conclusions?
Hi Harry,
The basic model I built was of an economy with no growth and a constant money stock–just to show that it was nonetheless sustainable and generated positive incomes for all classes over time. The world we live in is one of growth with expanding money stock. In that situation, everyone is “saving”–it is the first derivative of the relevant bank account and in fact is modeled directly in my tabular financial system.
Hi Steve,
Thanks for the response. I realize that the model is basic, and not really intended to represent the real world.
But I have been wondering about “money supply” – hence an earlier question about when money is destroyed. In the absence of large bank failures which might wipe out deposit accounts, and in the presence anyway of widespread deposit insurance, I wonder whether money is not ever being destroyed, and money stock is only ever increasing. And if so what the end result is likely to be, especially as debt levels are gradually reduced.
I wonder that myself Harry, and it will take a bit of delving into actual bank procedures in the case of bankruptcy to work it out. The key issues include how banks apportion for losses when those losses have to be financed out of their own equity (ie prior to the bank itself going bankrupt when state guarantees of deposits take over and effectively convert bank deposits from credit-backed money to fiat money).
Hi Steve,
I appreciate your paper a lot, and see it as the completion of your earlier draft article, Keyne’s revolving fund of finance and transactions in the circuit.
I wonder what you have to say about the implications of your model and bank credit money regarding geography?
It seems to me that your findings corroborate the viability of regional credit currencies — currencies used to support, say, some portion but not all of a region’s transaction and investment needs. The credit-currency could be bank created as in your model, or business created, as in using trade credit as a means for financing. Furthermore, such regional, credit-currencies may in effect use a single national currency as its “base” or “backing.”
The Swiss Wir domestic currency is a case in point. It uses trade credit among businesses (denominated in Swiss Francs) as the basis for transactionable currency.
Your use of “free banking notes” at the beginning of the article points to this possibility, it seems to me (or is this only a coincidence?).
-Torrey
Hi Torrey,
It’s a coincidence, but a meaningful one. A regional currency would be viable if not abused in the manner that many 19th century free banking currencies were–fraud, Ponzi Schemes, and seignorage, as well as (in some instances) not expanding fast enough to support growing commerce.
Steve,
As regards avoiding the abuses of the banks in the free banking era, might a different internal organizational form help? A credit union has democratic oversight of the “bank” by the people with accounts. It seems to me that the rank-and-file would militate against the abuses you outline that would result in pain to them. (assuming a one person, one vote credit union with fairly short election cycles as compared to political election cycles).
Reading the above comments, I find it absolutely fascinating that grown-up, very learned men, having studied this subject to death, still can’t quite have a straight simple agreement about the in/outs of our financial system(s).
As an engineer, I’m very tempted to conclude that the problem/questions are not phrased properly (by the economic community, not just Steve), and/or the financial rules not clear/mutually exclusive, hence the never-ending variety of possible/plausible view points.
Perhaps everyone (in economics) should take a few steps back for a better view?
Indeed Virgule! That’s why I wrote Debunking Economics. The whole discipline has gone utterly awry and we need to start again–and engineering would be a far better starting point than economic theory.
Hi Virgule, great point. I think the issue is that the whole discipline of actually modelling the economy is very immature. Friedman’s “F-Twist” has been used to excuse all kinds of unrealistic assumptions, so it’s refreshing that Steve actually puts the effort in to justify the assumptions here.
That said, this is obviously a toy model. Having just read it for the first time, I’m surprised that no-one has pointed out the key internal contradiction: the assumption of different, yet constant values for w_D and b_T. The difference is justified by the differences in income and savings between workers and bankers. However, by the same logic, a richer banker should have a lower b_T than a poorer banker, i.e. b_T should decrease as a function of B_T.
If this were incorporated into the model, B_T would likely grow to consume the entire system; you would lose the convergence that this paper says resolves the “paradox” of monetary profits.
No you wouldn’t Tom. Of course it’s a toy model, but it’s robust to a wide range of parameter values. Allowing for dispersion as you suggest would make it more realistic, but wouldn’t alter the overall outcomes.
I agree that’s it’s robust to a wide range of parameter values. I’ve played with QED and tried different constant values. However, that’s not what I’m talking about; I’m talking about changing b_T from a constant to a function of B_T.
For example, say the banker is Warren Buffett. Despite a constantly growing fortune, his consumption remains steady at g = $X (that is, b_T = X/B_T). Solving the equation for equilibrium of B_T (i.e. 0 = dB_T/dt = c-d-f-X), we get X = c-d-f. This is the ONLY equilibrium point. If X is greater than c-d-f, Buffett will have to plunder the vault or curtail his spending. If X is less than c-d-f, B_T will grow to consume the system.
Now that’s an extreme example, but it’s much more realistic than constant b_T. In fact you’ve admitted as much by having different w_D and b_T.
If g=$x, which is a constant, not a variable relative to time, then dx/dt = 0.
Thus dB_T(t)/dt = c-d-f
Your assumption makes the model simpler but does not change the outcome.
Yes, but I wouldn’t make b_T a function of B_Y alone but B_T divided by output.
Your idea makes b_T->infinity as time->infinity, which of course produces the outcome you note. But it also means that Warren Buffett (or being more accurate, whoever runs Goldman Sacks) being satisfied with a mere $1 billion dollars income forever, even if GDP rises.
Kys, the unstable equilibrium I referred to is at dB_T/dt = 0. Yes, dX/dt = 0, but it’s not relevant and not in any equations.
I’m not claiming to know the precise nature of b_T. I’m just showing that it’s definitely not a constant and that a choice of function based on reality can affect the end result quite dramatically.
I’m also not talking about constant income – I’m talking about constant consumption. The whole point of the situation I identified is that past a tipping point, the banker’s income keeps growing even as his consumption remains relatively constant.
I don’t understand your point about GDP. Real or nominal?
Hi Virgule, Steve and Tom,
Taking an “engineering approach” to economics is precisely the WRONG thing to do. This is how economics has gotten itself into such a mess (for example, the Arrow Debreu approach, the concept of “equilibrium” — totally engineering). Economics is not a positive science, it is an interpretive science. See Georgescu-Roegen, Herman Daly, or such philosophers as Jurgen Habermas, John Searle and of course Marx. The phenomena of economics, such as “money,” is overdetermined, dialectical. Is a credit card money, a source of credit? Is money a medium of exchange or a store of value? Is that asset’s price its exchange value or use value? Economics is a social science and as such its methodology is hermeneutic and interpretive, not positive/objective.
Hi Torrey, I actually agree with you. Real progress in economics will be mostly through empirical observation and interpretation – otherwise it’s just people arguing about the precise details of fantasy worlds.
Steve’s work is useful because he stands for something: that if models are built bottom-up, they should have realistic assumptions. That’s a key paradigm shift, and it opens the models up to criticism. The next step may well be: reality is too complex to include all of the relevant assumptions, so we should abandon bottom-up model building.
So yes, I believe the top-down approach is more likely to succeed: learning the history of economic reality rather than the history of economic thought.
Hi Tom,
Don’t get me wrong: (quantitative) models have a place in economics. (And, I like Steve’s model of endogenous money alot! And I do a lot of modeling myself as an applied economist.) But from a wider perspective, the phenomena of economics — e.g. money, property, and markets, among others — are constructed by social consensus, collective intentionality and are “observer relative” (to use Searle’s terms). They are epistemologically objective but ontologically subjective. They are real, but they only exist in peoples’ minds. They do not exist independently of the attitudes of people. They are not naturally occurring objects of nature. Without this recognition, particularly macroeconomics will be doomed to continuous ideological battles.
Steve, sorry I should have addressed my earlier comment to you (August 4, 2011 at 12:33 am – except for the first paragraph).
Torrey, I don’t subscribe to the distinctions you’re making regarding objective v subjective, absolute v relative, real v all in the mind, natural v artificial. It all depends on the level of abstraction that you’re working at. I think Steve taps into a much better framework when he talks about the fallacy of strong reductionism (slides 17-18 at that link).
I also recommend Leonard Susskind’s thoughts on what is “fundamental” (from 1:11:10, but especially from 1:19:10).
Tom Shaw,
Sorry for my late repsponse.
By definition,
1. w_D is the rate of outflow of notes from Worker Deposit W_D to pay for workers’ consumption.
2. b_T is the rate of outflow of notes from Bank Transaction B_T to pay for bankers’ consumption.
For simulation purposes, 26 p.a. & 1 p.a. are assigned to w_D & b_T respectively, both of which are realistic. I therefore do not see any “internal contradiction” like you do.
In equilibrium, g = b_T * B_T = bankers’ consumption = bankers’ net income = Bank Transaction Account, which means Steve’s reply is accurate.
As to your assumption that g = $x,
1. The assumption does not hold when x > c-d-f because bankers can not plunder the vault.
2. When x < c-d-f, bankers save money. Where do they put the money? do you need a new entry "Banker Deposit" that gives bankers interests? do bankers seek to lend out their savings to firms at higher interest rates? Do they simply consume more when savings reach certain levels? Do these considerations help in solving the paradox of monetary profits?
I look forward to a meaningful discussion.