Managerial Economics

1
Managerial Economics

• Lecture Nine
• Alternative theories of macroeconomic behaviour

2
Recap

• Last week
• Empirical data on economic cycle contradicts
  neoclassical economics
• Prices anti-cyclical
• Wages pro-cyclical
• No diminishing marginal productivity
• Credit leads cycle, money base follows
• Not quantity theory of money but endogenous
  credit money creation
• Complements Blinders survey research
• Supports Schumpeters theory of cycle
• KP conclude with fascinating statement

3
Money, credit and business cycles

• The fact that the transaction component of real
  cash balances (M 1) moves contemporaneously with
  the cycle while the much larger nontransaction
  component (M2) leads the cycle suggests that
  credit arrangements could play a significant role
  in future business cycle theory.
• Introducing money and credit into growth theory
  in a way that accounts for the cyclical behavior
  of monetary as well as real aggregates is an
  important open problem in economics.
• This open problem the focus of Hyman Minskys
  research

4
Like father, like son

• Minsky a student of Schumpeters
• influenced by Keynes and Marx
• Built on foundations of all three (but never
  admitted to inspiration from Marxworked during
  McCarthyist period in USA when reading Marx
  effectively a crime)
• Did first degree in mathematics before economics
  Phd
• During longest period of sustained prosperity in
  Americas history, developed the Financial
  Instability Hypothesis
• Key proposition The most significant economic
  event of the era since World War II is something
  that has not happened there has not been a deep
  and long-lasting depression. (Minsky 1982 xi)
• Why is this significant? Because

5
Financial Instability Hypothesis

• As measured by the record of history, to go more
  than thirtyfive years without a severe and
  protracted depression is a striking success.
• Before World War II, serious depressions occurred
  regularly. The Great Depression of the 1930s was
  just a "bigger and better" example of the hard
  times that occurred so frequently. This postwar
  success indicates that something is right about
  the institutional structure and the policy
  interventions that were largely created by the
  reforms of the 1930s.. (xi)
• So what were these structures interventions?
• Restrained use of debt
• Public spending to ameliorate any downturn
• Both developed in response to Great Depression

6
The Great Depression
WW II
7
The Great Depression
To 25 in 3 years
WW II Brings Sustained Recovery
From effectively zero...
8
Minskian Economic History

• Minskys reading of Depression
• Final in series of financial crises in which
  accumulated debt falling prices overwhelmed
  system
• Deflation (prices fell by up to 10 p.a.) meant
  real rate of interest exceeded 15
• Nominal debt fell but real debt (ratio nominal
  debt to nominal DGP) ballooned
• Irving Fisher claimed debt/GDP ratio was
• 60 in 1929
• 160 by 1933
• Complex price dynamics, mechanics of bankruptcy,
  government public works, etc. partially reduced
  debts
• World War II reduced them to trivial levels

9
USA Interest Rates 1918-2000
Huge deflation caused by post-WWIreturn to the
Gold Standard by UK
Korean War Inflation
Negative real rates during WW II
Even more negative real rate during Post-War
recovery
Massive positive real rates due to deflation in
Great Depression
Post-War stability
and then... chaos!
10
Minskian Economic History

• Post-War success due to
• Reduction of private debt to historically low
  levels
• Culture of prudence after WWII, Great Depression
• versus excess of Roaring Twenties stock market
  boom
• Big government
• Large government spending/taxing role
  counterbalanced private sector tendencies to
  excess during boom, frugality during slump
• Institutions designed to attenuate excessive
  behaviour in borrowing, lending, investing
• Emphasis upon income equality
• Less money for speculation by wealthy
• More for income-financed stable mass consumption

11
Minskian Economic History

• Gradual development of problems since WWII due to
  gradual
• Increase in debt to income levels over many
  business cycles
• Decline in fear of financial collapse as GD
  forgotten
• Relaxation of prudent financial arrangements
• Financial fragility rising from 1950 till early
  1960s
• Financial crises in USA but still high
  growth/employment
• 1973 major financial crisis in period of high
  employment
• Income distribution (high wages) and raw
  materials (high prices) driven inflation
• Stagflation first major post WWII financial
  crisis

12
Financial Instability Hypothesis

• To understand why weve had crises but not a
  Depression, we need
• an economic theory which makes great depressions
  one of the possible states in which our type of
  capitalist economy can find itself.
• We need a theory which will enable us to identify
  which of the many differences between the economy
  of 1980 and that of 1930 are responsible for the
  success of the postwar era. (xi)
• Neoclassical conventional Keynesian models
  cant do this because they are timeless
  equilibrium models
• might explain equilibrium but
• Cant explain location of equilibrium itself
• Omit time processes that are evolutionary and
  non-equilibrium

13
Financial Instability Hypothesis

• Minsky knew suitable model had to
• treat financial crises as normal events in
  unconstrained capitalist economy
• Explain why such events hadnt happened in
  1948-1966
• The first twenty years after World War II were
  characterized by financial tranquility. No
  serious threat of a financial crisis or a
  debtdeflation process took place.
• The decade since 1966 has been characterized by
  financial turmoil. Three threats of financial
  crisis occurred, during which Federal Reserve
  interventions in money and financial markets were
  needed to abort the potential crises. (1982 63)
• Minsky on the historical record 1948-1978

14
Financial Instability Hypothesis

• The first post-World War II threat of a
  financial crisis that required Federal Reserve
  special intervention was the so-called "credit
  crunch" of 1966. This episode centered around a
  "run" on bank-negotiable certificates of deposit.
• The second occurred in 1970, and the immediate
  focus of the difficulties was a "run" on the
  commercial paper market following the failure of
  the PennCentral Railroad.
• The third threat of a crisis in the decade
  occurred in 1974-75 can be best identified as
  centering around the speculative activities of
  the giant banks. In this third episode the
  Franklin National Bank of New York, with assets
  of 5 billion as of December 1973, failed after a
  "run" on its overseas branch. (63)

15
Financial Instability Hypothesis

• The lessons from this history?
• Since this recent financial instability is a
  recurrence of phenomena that regularly
  characterized our economy before World War II, it
  is reasonable to view financial crises as
  systemic, rather than accidental, events.
• From this perspective, the anomaly is the twenty
  years after World War II during which financial
  crises were absent, which can be explained by the
  extremely robust financial structure that
  resulted from a Great War following hard upon a
  deep depression.
• Since the middle sixties the historic
  crisis-prone behavior of an economy with
  capitalist financial institutions has reasserted
  itself (63)

16
Financial Instability Hypothesis

• Minskys view of unbridled capitalism supported
  by record of 19th century trade cycle

• Procyclical prices

• Frequent wage falls

• Financial crisesroughly every20 years

17
Financial Instability Hypothesis

• But post-1973 still differs from pre-WWII periods
  of instability
• The past decade differs from the era before World
  War II in that embryonic financial crises have
  been aborted by a combination of support
  operations by the Federal Reserve and the income,
  employment, and financial effects that flow from
  an immensely larger government sector. This
  success has had a side effect, however
  accelerating inflation has followed each success
  in aborting a financial crisis. (63)
• So how to turn these historical insights into a
  theory?
• Firstly, build on your antecedents

18
Brief HET of Minsky

• Parents met at a Communist Party social function
• No prizes for guessing early formative
  influences!
• Fought in US Army in WWII, decamped post-war to
  do a degree
• Educated during McCarthyist communist witch
  hunt periodno mention ever of Marx in his
  research, for obvious reasons
• PhD supervisor Joseph Schumpeter the archetypal
  theorist of cycles
• Foundation influences thus Marx Schumpeterand
  not Keynes
• With degree in mathematics, attempted to build
  mathematical model of trade cycle (based on
  Hickss difference equation model, extended by
  Kaleckis principle of increasing risk)

19
Brief HET of Minsky

• Kalecki argued investment restrained by
  increasing risk (uncertainty) as capital grows
• Minsky used this at macro level in model of trade
  cycle Model was

• Minsky made b dependent on financial conditions
• b declines as economy grows, thus giving turning
  point to upward explosive movement
• "the accelerator coefficient ... is in part based
  on the productive efficiency of investment, but
  it is also related to the willingness of
  investors to take risks and the terms in which
  investors can finance their endeavours..."
  (Minsky 1965 261)

20
Brief HET of Minsky

• Model went nowhere, but Minsky began to explore
  implications of finance for economic behaviour
• Initially tried from conventional understanding
  of Keynes
• If we make the Keynesian assumption that
  consumption demand is independent of interest
  rates, but assume that investment demand, and
  hence the b coefficient, depends on interest
  rates, then a rising set of interest rates will
  lower the b coefficient. (Minsky 1965, 1982
  262)
• Also went nowhere
• Then, one day, by chance, he read Keyness 1937
  papers
• My interpretations of Keynes is not the
  conventional view which is mainly derived from
  Hicks' "Mr. Keynes and the Classics," an article
  which I believe misses Keynes' point completely
  (Minsky 1982 280)

21
Theres more than one Keynes

• Keynesian economics of IS-LM AS-AD more due to
  Hicks than Keynes
• Different theme in Ch. 12 Ch. 17
• Rather than investment regulated by rate of
  interest
• investment motivated by the desire to produce
  those assets of which the normal supply-price is
  less than the demand price (Keynes 1936 228)
• Demand price determined by prospective yields,
  depreciation and liquidity preference.
• Supply price determined by costs of production
• Two price levels in capitalism
• Normal commodities basically cost plus
• Assets expectations under uncertainty

22
Theres more than one Keynes

• Two price level analysis becomes more dominant
  subsequent to General Theory
• The scale of production of capital assets
  depends, of course, on the relation between
  their costs of production and the prices which
  they are expected to realise in the market.
  (Keynes 1937a 217)
• Marginal Efficiency of Investment (MEI or MEC
  for Capital) analysis akin to view that
  uncertainty can be reduced to the same
  calculable status as that of certainty itself
  via a Benthamite calculus, whereas
• uncertainty in investment is that about which
  there is no scientific basis on which to form
  any calculable probability whatever. We simply do
  not know. (Keynes 1937a 213, 214)

23
Theres more than one Keynes

• Three aspects to expectations formation under
  true uncertainty
• Presumption that the present is a much more
  serviceable guide to the future than a candid
  examination of past experience would show it to
  have been hitherto
• Belief that the existing state of opinion as
  expressed in prices and the character of existing
  output is based on a correct summing up of future
  prospects
• Reliance on mass sentiment we endeavour to fall
  back on the judgment of the rest of the world
  which is perhaps better informed. (Keynes 1936
  214)
• Fragile basis for expectations formation thus
  affects prices of financial assets

24
What is uncertainty?

• Imagine you are very attracted to someone
• This person has accepted invitations from 1 in 5
  of the people who have asked him/her out
• Does this mean you have a 20 chance of success?
• Of course not
• Each experience of attraction is unique
• What someone has done in the past with other
  people is no guide to what he/she will do with
  you in the future
• His/her response is not risky it is uncertain.
• Ditto to individual investments
• success/failure of past instances give no guide
  to present odds

25
How to cope with relationship uncertainty?

• We try to find out beforehand
• ask friendseliminate the uncertainty
• We do nothing
• paralysed into inaction
• We ask regardless
• compel ourselves into action
• We follow conventions
• follow the herd of the social conventions of
  our society
• play the game hope for the best
• So what about investors?

26
Theres more than one Keynes

• In the midst of incalculable uncertainty,
  investors form fragile expectations about the
  future
• These are crystallised in the prices they place
  upon capital asset
• These prices are therefore subject to sudden and
  violent change
• with equally sudden and violent consequences for
  the propensity to invest
• The marginal efficiency of capital/investment
  is simply ratio of yield from asset to its
  current demand price, and therefore there is a
  different marginal efficiency of capital for
  every different level of asset prices (Keynes
  1937a 222)

27
Theres more than one Keynes

• In 1969, Minsky states that his own ideas about
  uncertainty "seem to be consistent with those of
  Keynes" (1969a, 1982 191, footnote 6), citing
  Keynes 1937
• Eventually concludes
• capitalism is inherently flawed, being prone to
  booms, crises and depressions. This instability,
  in my view, is due to characteristics the
  financial system must possess if it is to be
  consistent with full-blown capitalism. Such a
  financial system will be capable of both
  generating signals that induce an accelerating
  desire to invest and of financing that
  accelerating investment. (Minsky 1969b 224)
• Combines elements of Marx, Keynes Schumpeter
• Christens his model the Financial Instability
  Hypothesis

28
Financial Instability Hypothesis

• The natural starting place for analyzing the
  relation between debt and income is to take an
  economy with a cyclical past that is now doing
  well.
• The inherited debt reflects the history of the
  economy, which includes a period in the not too
  distant past in which the economy did not do
  well.
• Acceptable liability structures are based upon
  some margin of safety so that expected cash
  flows, even in periods when the economy is not
  doing well, will cover contractual debt payments.
• As the period over which the economy does well
  lengthens, two things become evident in board
  rooms. Existing debts are easily validated and
  units that were heavily in debt prospered it
  paid to lever. (65)

29
Financial Instability Hypothesis

• After the event it becomes apparent that the
  margins of safety built into debt structures were
  too great.
• As a result, over a period in which the economy
  does well, views about acceptable debt structure
  change. In the dealmaking that goes on between
  banks, investment bankers, and businessmen, the
  acceptable amount of debt to use in financing
  various types of activity and positions
  increases.
• This increase in the weight of debt financing
  raises the market price of capital assets and
  increases investment. As this continues the
  economy is transformed into a boom economy (65)
• This transforms a period of tranquil growth into
  a period of speculative excess

30
Financial Instability Hypothesis

• Stable growth is inconsistent with the manner in
  which investment is determined in an economy in
  which debt-financed ownership of capital assets
  exists, and the extent to which such debt
  financing can be carried is market determined.
• It follows that the fundamental instability of a
  capitalist economy is upward. The tendency to
  transform doing well into a speculative
  investment boom is the basic instability in a
  capitalist economy. (65)
• This characteristic of capitalism necessarily
  missed by IS-LM/AS-AD analysis because process
  fundamentally non-equilibrium in nature

31
Financial Instability Hypothesis

• Whether neoclassical or Keynesian, IS-LM/AS-AD
  analysis omits time and debt
• Difference between Keynesian (1950-1973) and
  Neoclassical (1973) economic management
  outcomes may reflect deterioration of economy
• but neither theory could have seen it coming
• Minsky notes Hicks also rejects IS-LM
• John R. Hicks, "Some Questions of Time in
  Economics," in Evolution, Welfare and Time in
  Economics Essays in Honor of Nicholas
  GeorgescuRoegen (Lexington, Mass. Lexington
  Books, 1976), pp. 135-151. In this essay Hicks
  finally repudiates the potted equilibrium version
  of Keynes embodied in the IS-LM curves he now
  views IS-LM as missing the point of Keynes and as
  bad economics for an economy in time. (Minsky
  1982 70)

32
Financial Instability Hypothesis

• But both equilibrium theories missed causal
  factors behind deterioration
• Evolution of riskier behavior financial
  arrangements as long period of tranquility
  changed expectations
• Stabilityor tranquilityin a world with a
  cyclical past and capitalist financial
  institutions is destabilizing.
• Resulting cyclical/secular increase in debt
  levels made economy more fragile, more
  susceptible to financial crises
• Spelling Minskys model out step by step

33
Financial Instability Hypothesis

• Economy in historical time
• Debt-induced recession in recent past
• Firms and banks conservative re debt/equity
  ratios, asset valuation
• Only conservative projects are funded
• Recovery means conservative projects succeed
• Firms and banks revise risk premiums
• Accepted debt/equity ratio rises
• Assets revalued upwards

34
The Euphoric Economy

• Self-fulfilling expectations
• Decline in risk aversion causes increase in
  investment
• Investment expansion causes economy to grow
  faster
• Asset prices rise, making speculation on assets
  profitable
• Increased willingness to lend increases money
  supply (endogenous money)
• Riskier investments enabled, asset speculation
  rises
• The emergence of Ponzi (Bondy?) financiers
• Cash flow from investments always less than
  debt servicing costs
• Profits made by selling assets on a rising market
• Interest-rate insensitive demand for finance

35
The Assets Boom and Bust

• Initial profitability of asset speculation
• reduces debt and interest rate sensitivity
• drives up supply of and demand for finance
• market interest rates rise
• But eventually
• rising interest rates make many once conservative
  projects speculative
• forces non-Ponzi investors to attempt to sell
  assets to service debts
• entry of new sellers floods asset markets
• rising trend of asset prices falters or reverses

36
Crisis and Aftermath

• Ponzi financiers go bankrupt
• can no longer sell assets for a profit
• debt servicing on assets far exceeds cash flows
• Asset prices collapse, drastically increasing
  debt/equity ratios
• Endogenous expansion of money supply reverses
• Investment evaporates economic growth slows or
  reverses
• Economy enters a debt-induced recession ...
• High Inflation?
• Debts repaid by rising price level
• Economic growth remains low Stagflation
• Renewal of cycle once debt levels reduced

37
Crisis and Aftermath

• Low Inflation?
• Debts cannot be repaid
• Chain of bankruptcy affects even non-speculative
  businesses
• Economic activity remains suppressed a
  Depression
• Big Government?
• Anti-cyclical spending and taxation of government
  enables debts to be repaid
• Renewal of cycle once debt levels reduce

38
Minskian Economic History

• Since WWII
• Debt has risen in ratchet-like manner
• Rise during boom
• Peak then fall during slump
• Cycle renews with higher initial debt level
• Government spending rescued system in each slump
• Massive inflation in asset prices as by-product
• Monetarist/Neoclassical policy has
• reduced counter-vailing impact of government
  spending
• driven down inflation rate to near-deflation
  levels
• Debt levels now highest in history, inflation
  near zero

39
Minskian Economic History of Australia

• Data from recent (2004) PhD thesis
• Luke Reedman, "As assessment of the Development
  of Financial Fragility in the Australian economy
• Rise in debt to GDP from 50 to 135 1960-2000

40
Minskian Economic History of Australia

• Interest payments peaked in 1989/90
• Corporate indebtedness decreased since 1990

• BUT Household debt levels rising

41
Minskian Economic History of Australia

• BUT Corporate indebtedness decreased since 1990

• BUT overall fragility higher given debt
  repayments

42
Minskian Economic History of Australia

• AND situation of Sydney households worst in
  history

• Debt financial fragility has risen as Minsky
  predicted

43
Minskian Economic History of Australia

• Household corporate sector now more susceptible
  to financial crisis than ever before

Note key acceleration point of mid-1970's
44
Minskian Economic History of Australia

• Cyclical ratcheting up of gap between
  expenditure and debt over last 40 years
• Household corporate sector now net borrowers
• A positive gap means that capital expenditures
  exceed available internal funds. (153)

45
Modelling Financial Instability

• Minskys verbal model appears confirmed by data
• But (for better or worse!) only mathematical
  models cut it with economists
• Vigorous methodological debates about role of
  mathematics in economics
• Considered in History of Economic Thought
• Whatever outcome of debate, reality is that
  mathematical models are key part of rhetoric of
  economics
• If you cant say it with maths, economists
  wont listen
• Can this be modelled mathematically?
• Yes but not with equilibrium tools
• Need something like what Minsky tried
  mathematical models that incorporate time

46
Modelling Financial Instability

• Mathematical models that incorporate time are
• Differential equations
• Difference equations
• Not taught at undergraduate level in most
  universities (including UWS)
• Sometimes taught at advanced (Masters/PhD) level
• But frequently at inadequate level
• Modern sciences (biology, physics, maths itself)
  show differential equations only able to model
  real-world processes when they are
• Nonlinear
• Involve three or more variables (third order)
• Most economics courses dont go beyond linear
  second order equations

47
Modelling Financial Instability

• Several attempts to model Minsky in literature
• See references in final slide
• My model based on Goodwins trade cycle model
  (next slide)
• Key component of dynamic model is rate of change
  of x with respect to time
• Mathematically shown as dx/dt

• Similar to calculus you have done in Maths 1.3
  etc. BUT
• One key difference calculus considers equations
  of form

• Rate of change of dependent variable a function
  of value of independent variable

• Differential equations rate of change of
  dependent variable a function of its own value

48
Modelling Financial Instability

• Maths gets quite complicated (overview only
  here!) but
• Dividing by dependent variable puts equation in
  percentage change form

• Rate of change

• Percentage rate of change

• rate of change thinking therefore essentially
  dynamic
• Often complicated models easily expressed in
  percentage rate of change terms
• Applying this to model a cyclical economy
• The natural starting place for analyzing the
  relation between debt and income is to take an
  economy with a cyclical past that is now doing
  well (Minsky 1982 65)

49
Modelling Financial Instability

• First stage Goodwins model (of Marxs cyclical
  growth theory)
• Causal chain
• Capital (K) determines Output (Y)
• Output determines employment (L)
• Employment determines wages (w)
• Wages (w?L) determine profit (P)
• Profit determines investment (I)
• Investment I determines capital K
• chain is closed

accelerator
Chain is closed
productivity
Rate of change terms vital
Phillips curve
Investment function
Depreciation
50
Modelling Financial Instability

• Goodwins model reduces to two rate of change
  expressions

• rate of change of employment rate equals
  rate of economic growth minus rate of
  population growth and technical change

• Employment will rise if the rate of economic
  growth exceeds the sum of population growth
  technical change

• rate of change of wages share of GDP equals
  increase in wages (Phillips curve) minus rate
  of technical change

• Workers share of output will rise if the
  increase in wages exceeds the rate of technical
  change

51
Modelling Financial Instability

• Click on graph to run it dynamically

• Adding debt relatively easy

52
Modelling Financial Instability

• Debt finances investment
• Debt will grow if desired investment exceeds
  retained earnings
• Interest is paid on outstanding debt

where

• Adds 3rd rate of change expression

• The debt to output ratio will grow if the rate
  of interest exceeds the rate of growth and
  investment exceeds EBIT

53
Modelling Financial Instability

• Generates system which can be stable if starts
  near equilibrium

• But which can suffer debt-induced breakdown if
  far from equilibrium

54
Modelling Financial Instability

• Exactly the same model
• Different initial conditions

• Cyclical pattern of debt to output very similar
  to data on US and Australian economies

55
Modelling Financial Instability

• Click on graph to run it dynamically

• Model replicates Minskys verbal description of
  free market (no government) capitalist economy
• What about mixed economy?

56
Modelling Financial Instability

• Add in government sector with spending a function
  of unemployment rate

• rate of change of government spending is a
  function of the rate of employment

• Results in 4th rate of change expression

• The government spending to output ratio will
  grow if the rate of growth of government spending
  exceeds the rate of economic growth

57
Modelling Financial Instability

• Results in model which is cyclical but not
  unstable

58
Modelling Financial Instability

• How does model compare to reality?
• Real world a mixture of free market mixed
  economy models
• Model government holds the line on unemployment
• Real-world ones progressively reduced commitment
  to employment since WWII
• Models investment (etc.) parameters fixed
• Real world (and Minskys) behaviours evolve over
  time
• more speculation as memory of crisis recedes
• No price dynamics in model
• Real-world inflation can reduce debt burden
• But deflation increases it
• Price dynamics can be added to model

59
Modelling Financial Instability

• Minsky prognosis for world/Australian economies
• Debt levels now at historic highs
• Inflation now close to zero (except for oil,
  China impact on raw material pricessteel etc.)
• Government anti-cyclical spending weakened by 30
  years of neoclassical economic policy
• Recessions inevitable (economy fundamentally
  cyclical)
• Next one could be extended by impact of
• Substantial debt levels
• Low or falling prices
• Precursor Japans economic crisis 1990-2005
• Next week A managerial look at finance
• Finale to run Minsky models dynamically, install
  Vissim viewer (on WebCT) and run Vissim models

60
References

• Minsky Models
• Deleplace, G. Nell, E.J. (eds.), 1996, Money in
  Motion The Post Keynesian and Circulation
  Approaches, Macmillan, London.
• Deleplace, G. Nell, E.J., 1996b Monetary
  Circulation and Effective Demand, in Deleplace,
  G. Nell, E.J. (1996a).
• Desai, M., 1973, Growth Cycles and Inflation in
  a Model of the Class Struggle, Journal of
  Economic Theory, Vol. 6, 527-545.
• Desai, M., 1995, An Endogenous Growth-Cycle with
  Vintage Capital Economics of Planning, Vol 28,
  Iss 2-3, 87-91.
• Jarsulic, M., 1989, Endogenous credit snd
  endogenous business cycles, Journal of Post
  Keynesian Economics, Vol. 12, 35-48.
• Keen, S., 1995. Finance and economic breakdown
  modelling Minskys Financial Instability
  Hypothesis, Journal of Post Keynesian Economics,
  Vol. 17, No. 4, 607-635.
• Keen, S., 1996. The chaos of finance, Economies
  et Societes, Vol. 30, special issue Monnaie et
  Production No. 10, 55-82.
• Keen, S., 1997. From stochastics to complexity
  in models of economic instability, Nonlinear
  Dynamics, Psychology and Life Sciences, Vol. 1,
  No. 2, 151-172.
• Keen, S., 1999. The nonlinear dynamics of debt
  deflation, Complexity International, Volume 6
  http//journal-ci.csse.monash.edu.au/ci/vol06/keen
  /keen.html.
• Keen, S., 2000. The nonlinear economics of debt
  deflation, in Barnett, W., Chiarella, C., Keen,
  S., Marks, R., Schnabl, H., (eds.), Commerce,
  Complexity and Evolution, Cambridge University
  Press, 83-110.
• Skott, P., 1989, Effective Demand, Class
  Struggle and Cyclical Growth, International
  Economic Review, Vol. 30 No. 1, 231-247.
• Goodwin, R.M., 1950, A non-linear theory of the
  cycle, Review of Economics and Statistics, Vol.
  32, 316-320.
• Goodwin, R.M., 1967, A Growth Cycle, in
  Feinstein, C.H. (ed.), Socialism, Capitalism and
  Economic Growth, Cambridge University Press,
  Cambridge, 54-58. Reprinted in Goodwin, R.M.,
  1982, Essays in Dynamic Economics, MacMillan,
  London.