A Simple Model of Endogenous Money

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A Simple Model of Endogenous Money

• Steve Keen

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Genesis, Book One

• In the beginning was the ODE

• And the audience looked upon it and said
• Verily, we dont get it
• And there was much wailing and nashing of teeth
• By the presenter
• And lo, the audience said
• Your double-entry bookkeeping must be stuffed!
• And the presenter had an idea
• A double entry bookkeeping approach to systems

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Were All Endogeneists Now

• Endogeneity of money supply a given in
  non-neoclassical economics
• But how to model money creation dynamically?
• Post-Keynesians beset by Accommodationist-Structu
  ralist debate
• Circuitists befuddled over source of profits
• Best work to date within Godleys SAM (Social
  Accounting Matrix) paradigm
• Cross-link stocks flows in a flow matrix
• Ensure all rows columns sum to zero
• every flow comes from somewhere and goes
  somewhere (Godley 1999 394)
• Discrete time modelling
• Derive n-1 model equations (with nth determined)

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Limitations of SAM

• SAM a klunky way to model economic system
• Discrete time distorts system dynamics
• Individual investments are discrete aggregate
  investment is not
• Lags never properly structured
• Everything is xtF(xt-1)
• Stock-flow confusion quite possible
• But appeal is anyone can do difference
  equations
• Better way to do tops down dynamics is the
  differential equation

• But differential equations superficially far
  harder than difference equations
• Simple techniques exist now (like flowchart
  software)
• But still very forbidding to non-specialist

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A simple approach to dynamic systems

• Each column represents a particular stock (system
  state)
• Each row entry represents a flow between stocks
• Specify relations between system states across
  rows

Relations
Equations

• To generate the model, add up each column
• Sum of column is differential equation for stock

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An application Endogenous Money

• Deliberately simplified model
• Entirely linear
• Does not reflect current monetary institutions
• Does answer fundamental questions
• How is money created?
• Is new money continuously needed to sustain
  constant economic activity?
• Can capitalists make a profit on borrowed money?
• Basic model can be easily extended to
• match current institutional arrangements
• Include non-monetary flows (commodity production
  sale, etc.)

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Initial conditions

• Starting position is

• Stage one bank extends loan of L to capitalist

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Stage two obligations initiated by loan

• Loan obliges
• capitalist to pay interest on FL balance
• bank to pay interest on FD balance

• Only sources of funds are Deposit Accounts
• FD for capitalist
• BD for bank

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Stage three flow of interest payments

• Payment of interest keeps
• Loan balance at initial level L
• Transfers money from FD to BD
• Keeps balance in Deposit Accounts at L

• System of coupled ODEs can be read down columns
• Change in FL 0
• Change in FD rD FD - rL FL
• Change in BD rL FL - rD FD

Simulating...
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Simulating stage three

• As a system of equations, this is

• Using L100, rD3, rL5
• Simulating in Mathcad

• All money transferred to BD after 30.5 years
• But model incomplete

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Stage four using the borrowed money

• Money borrowed to finance production
• Workers hired paid w FD

• Workers earn interest on balance in WD

• Stage five workers bankers buy goods from
  capitalists

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Complete model

• Whole model is

• Equations of motion read down the columns e.g.,
  FD

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Complete model

• Complete set of equations

• Simulation shows Circuit works
• Capitalists can borrow money, pay interest on it,
  operate indefinitely
• Activity continues forever with single
  injection of money
• But these are just bank account balances
• What about incomes?

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Income dynamics

• Worker bank income easy
• Wages are the flow w.FD
• Gross interest is the flow rL.FL

• What about profits?
• Derive from w
• w is part of net surplus from production accruing
  to workers
• Surplus constituted by
• Worker-capitalist split ((1-s)ssums to 1)
• Rate of turnover from M to M
• Signified by P
• So we have

conversely

• Profits are

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Income dynamics/debt repayment

• Confirming from simulation program

• Yearly net income of 429.15 exceeds L by factor
  of four
• Reflects turnover of capitalneglected by
  Circuitists
• What if loans repaid?
• Amount RL.FL deducted from FD account
• No seignorage direct by bank into capital
  account
• Re-lent at rate LR
• The outcome repayment of loans creates reserves

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Model with repayment/growth

• Overall system still balanced

• Final extension growth
• Additional reserves/debt at rate FI
• Models Moores Horizontalism

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Model with Growth

• System is now dissipative
• Sum of SAM exceeds zero

Endogenous creation of money

• Walras Law violated in growing economy
• Sum of excess demands gt 0
• Sum of MAMgt0 not all entries are transactions

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Model with Growth

• Full model now is

• System is skeleton for accountingly accurate
  model of Minskys Financial Instability
  Hypothesis

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Conclusion

• Useful framework for making dynamics simple
• Apparent dilemmas in Endogenous money logic
• how can M become M? (Rochon 2004 125)
• As soon as firms repay their debt to the banks,
  the money initially created is destroyed
  (Graziani 1989 5)
• Result from
• Forgetting generation of surplus in production
• Not thinking dynamically when fundamentally

The Economy is dynamic!
Amen!
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Key References

• Fontana, Guiseppe, Realfonzo, R., (eds.),
  (2005), The Monetary Theory of Production,
  Palgrave, New York.
• Godley, Wynne, (1999). Money and credit in a
  Keynesian model of income determination,
  Cambridge Journal of Economics 23, pp. 393-411.
• Graziani, Augusto, (2003). The Monetary Theory of
  Production, Cambridge University Press,
  Cambridge.
• Mathcad www.ptc.com/mathcad
• Moore, Basil, (1983). Unpacking the post
  Keynesian black box bank lending and the money
  supply, Journal of Post Keynesian Economics 5
  pp. 537-556.
• Rochon, Louis-Philippe, (2001), Cambridges
  Contribution to Endogenous Money Robinson and
  Kahn on credit and money, Review of Political
  Economy, 13, pp. 287-307.
• Rochon, Louis-Philippe, (2005), The existence of
  monetary profits within the monetary circuit, in
  Fontana Realfonzo (2005), pp. 125-138.