Modelling Minskys Financial Instability Hypothesis: From Implicit to Explicit Money

Steve KeenUniversity of Western Sydney

Debunking Economicswww.debtdeflation.com/blogs

www.debunkingeconomics.comwww.cfesi.org

0 1 2 3 4 5 6 7 8 9 10 11 12 1325

20

15

10

5

0

5

10

15

20

25

Great Depressionincluding GovernmentGreat Recessionincluding Government

Debt-financed demand percent of aggregate demand

Years since peak rate of growth of debt (mid-1928 & Dec. 2007 resp.)

Per

cent

0

Typical neoclassical forecast in 2007

– OECD Chief Economist Jean-Philippe Cotis 2007– “the current economic situation is in many

ways better than what we have experienced in years…

– Our central forecast remains indeed quite benign:• a soft landing in the United States,• a strong and sustained recovery in Europe,…• In line with recent trends, sustained growth

in OECD economies would be underpinned by strong job creation and falling unemployment.” (p. 9)

• Based on OECD “small macroeconomic model”

0 10 20 30 40 50 60 70 80 90 100 1105

0

5

10

15

InflationUnemployment

Great Moderation to Great Recession

Year

Per

cen

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.a.

0

70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 1102

0

2

4

6

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10

12

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InflationUnemploymentU-6 Measure

US Inflation and Unemployment since 1970

Year

Per

cent

70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 1102

0

2

4

6

8

10

12

14

16

InflationUnemploymentU-6 Measure

US Inflation and Unemployment since 1970

Year

Per

cent

And all’s well… until 2008• “the past two decades has seen not only significant

improvements in economic growth and productivity but also a marked reduction in economic volatility… dubbed "the Great Moderation.” (Bernanke 2004)

• Whoa!• Did anybody

get the number of that Black Swan?…

• Nope:

Inflation & Unemploment Falling

Inflation & Unemploment Falling Unem

plo

yment

Unem

plo

yment

Deflation

Deflation

• “Nobody could have seen it coming…”

Debt to GDP

“Nobody could have seen it coming…”• “The Queen asked me: ‘If these

things were so large, how come everyone missed them? Why did nobody notice it?’.”

• When Garicano explained that at “every stage, someone was relying on somebody else and everyone thought they were doing the right thing”, she commented: “Awful.”

• As obvious as the nose on a swan’s face to some of us…• A debt-driven boom and collapse

InflationUnemployment

Why WE did see “It” coming!• At least 12 anticipated & warned of Great Recession

(Bezemer 2009, 2010, 2011)

AnalystDean BakerWynne GodleyFred HarrisonMichael HudsonEric Janszen

Stephen KeenJakob Brøchner Madsen

Kurt RichebächerNouriel RoubiniPeter Schiff Robert Shiller

• “Distinction between financial wealth and real assets…

• Concern with debt as the counterpart of financial wealth…

• Growth in financial wealth and the attendant growth in debt can become a determinant (instead of an outcome) of economic growth …

• Recessionary impact of the bursting of asset bubbles…

• Emphasis on the role of credit cycles in the business cycle…”

• Common themes Bezemer 2009

Credit in a Boom/Depression Pair• Expanding debt in Boom, deleveraging in Depression

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 20200

20

40

60

80

100

120

140

160

180

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220

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260

280

300

320

Private DebtGovernment Debt

US Debt to GDP Ratios

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 20121 10

71.05 10

71.1 10

71.15 10

71.2 10

71.25 10

71.3 10

71.35 10

71.4 10

71.45 10

71.5 10

71.55 10

71.6 10

71.65 10

71.7 10

71.75 10

71.8 10

71.85 10

71.9 10

71.95 10

72 10

7GDPGDP plus Change in Debtincluding Government Debt

Aggregate Demand in the USA, 1986-2011

US $

bil

lion

Change in private debt now• $4 trillion boost (+28%) 2008; $2.5 trillion cut (-18%) 2010

1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 194040000

50000

60000

70000

80000

90000

100000

110000

GDP alone+ Change in Private Debt+ Change in Public Debt

US Aggregate Demand GDP 1920-1940

Year

$ m

illio

nChange in private debt “Then”

• $8.5 billion boost (+9%) 1928; $9.2 billion cut (-18%) 1933

Change in private debt now• Slowdown in debt growth explains the inexplicable now…

1975 1980 1985 1990 1995 2000 2005 2010 20155

2.5

0

2.5

5

7.5

10

12.5

15

InflationUnemployment

Great Moderation to Great Recession

0

2008

ChangeInDebt

GDP ChangeInDebt

• Define debt-financed aggregate demand as

1975 1980 1985 1990 1995 2000 2005 2010 2015

0

11

10

9

8

7

6

5

4

3

2

1

0

30252015105

0

5

10

15

20

25

30

U-3 UnemploymentDebt % Agg. Demand

Great Moderation to Great Recession

Une

mpl

oym

ent R

ate

(inv

erte

d)

Deb

t-fi

nanc

ed P

erce

nt D

eman

d

0

0

2008

• Unemployment falls when debt rises…

Change in private debt “Then”• Same

process applied in Roaring Twenties and Great Depression… 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940

10

5

0

5

10

15

20

25

30

InflationUnemployment

Roaring Twenties to Great Depression

0

1930

1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940

0

28262422201816141210

86420

30262218141062

26101418222630

UnemploymentDebt % Agg. Demand

Roaring Twenties to Great Depression

Deb

t to

GD

P

Deb

t-fi

nanc

ed P

erce

nt D

eman

d

0

0

1930

The Credit Accelerator• Since AD = GDP + Debt• Then AD = GDP + Debt

– “Credit Impulse” (Biggs et al. 2010)

DebtCreditAccelerator

GDP

• Change in GDP dominant factor in change in employment

• But Credit Impulse made this recession “Great”

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 201530

25

20

15

10

5

0

5

10

Acceleration of private debtChange in Private Employment

Acceleration of private debt & change in employment, USA

Year

Per

cent

p.a

.

0

The Credit Impulse• Negative impulse this time worse than Great Depression

20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115300

250

200

150

100

50

0

50

100

30

25

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0

5

10

UnemploymentUnemploymentCredit ImpulseCredir Impulse

Annual Change in Unemployment & Debt Acceleration

Year

Cha

nge

in U

nem

ploy

men

t

Acc

eler

atio

n/D

ecel

erat

ion

of D

ebt

00

-15%-15%

-25%-25%

• That’s why the US is in a crisis• Driving asset prices as well

as GDP…

Mortgage debt dynamics in the USA

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 20128

6

4

2

0

2

4

20

10

0

10

20

Mortgage AccelerationHouse Price Change

Mortgage Acceleration & Real House Price Change

www.debtdeflation.com/blogs

Mo

rtg

age

Acc

eler

atio

n (

per

cent

of

GD

P)

p.a

.

CP

I-ad

just

ed H

ouse

Pri

ce C

han

ge

per

cen

t p.a

.

0

VB End

Why Neoclassical economists didn’t see It coming• DSGE the dominant modelling framework today• Like IS-LM before it, non-monetary model• Seen as superior to IS-LM because it is based on micro:

– “Dynamic Stochastic General Equilibrium” model…• “simple, analytically convenient, and has largely

replaced the IS-LM model as the basic model of fluctuations in graduate courses…

• Unlike the IS-LM model, it is formally, rather than informally, derived from optimization by firms and consumers.” (Blanchard 2009)

• This is not an advantage: it is instead a fallacy– Robert Solow on DSGE modelling…

Solow rejects DSGE• “The prototypical real-business-cycle model goes like

this. There is a single, immortal household—a representative consumer—that earns wages from supplying labor. It also owns the single price-taking firm…

• This is nothing but the neoclassical growth model…• [When I built it] … It was clear … what I thought it did

not apply to, namely short-run fluctuations ... the business cycle...

• Now ... an article today [on the] 'business cycle' … will be ... a slightly dressed up version of the neoclassical growth model.

• The question I want to circle around is: how did that happen?”

Solow: SMD conditions invalidate DSGE

• “Suppose you wanted to defend the use of the Ramsey model as the basis for a descriptive macroeconomics. What could you say? ...

• You could claim that … there is no other tractable way to meet the claims of economic theory.

• I think this claim is a delusion.• We know from the Sonnenschein-Mantel-Debreu

theorems that…” (Solow 2008)• Sonnenschein-Mantel-Debreu: demand curve for a

single market can have any (polynomial) shape at all– Even study of a single market can’t be

reduced to study of a single utility-maximizing agent

– Yet DSGE macro models the whole economy as a single utility-maximizing agent

SMD: “Anything goes” for market demand curves

• SMD Conditions (Sonnenschein 1973):– Market demand curves do not obey the „Law of Demand“– Even if summing „well behaved“ individual demand

curves

• Proof by contradiction:– Assume market demand curves do obey Law of

Demand– Derive conditions under which this is true– Contradict initial assumption• Therefore they don‘t obey the „Law“ of

Demand

q

P

q

P

Q

P

Neoclassical reaction• A very few reacted rationally:

– Alan Kirman 1989• “If we are to progress further we may well be

forced to theories in terms of groups who have collectively coherent behavior.

• Thus demand and expenditure functions if they are to be set against reality must be defined at some reasonably high level of aggregation.

•The idea that we should start at the level of the isolated individual is one which we may well have to abandon.”

• But most didn’t know about these conditions at all…

Mark Thoma in 2010

• Mark Thoma said... “One thing I learned from it is that I need to read the old papers by Sonnenschein (1972), Mantel (1974), and Debreu (1974) since these papers appear to undermine representative agent models…

• I need to learn the full extent to which this work undermines the whole microfoundations approach

• I didn't understand that extent to which representative agent models are an analytical convenience to work around this problem (the DSGE theorists who understood this kept quiet about it).”

• Some that did—even those that discovered them—reacted irrationally…

Representative agent madness instead

• Gorman 1953– “we will show that there is just one community

indifference locus through each point if, and only if, the Engel curves for different individuals at the same prices are parallel straight lines…

– The necessary and sufficient condition quoted above is intuitively reasonable.• It says, in effect, that an extra unit of

purchasing power should be spent in the same way no matter to whom it is given.”

• Intuitively reasonable?– No, it’s intuitively false!

• Real consequence: even behavior of a single market an emergent phenomenon…

Macro an “emergent property”

• Real meaning of SMD conditions– Macroeconomic behavior an “emergent property” of

interaction of agents in a complex system• Cannot deduce behavior of macroeconomy from

behavior of utility-maximizing individuals• Cannot reduce macroeconomics to “applied

microeconomics”• But that is what DSGE models do!• Fallacy of “Strong Reductionism”

– Believe “macroeconomics is applied microeconomics”

– But SMD conditions prove otherwise• “macroeconomics cannot be applied

microeconomics”

Fallacy of Strong Reductionism

• Can’t deduce even market behavior from model of individual behavior– Let alone deduce macro behavior from individual

• Common knowledge in real sciences: Anderson, “More is Different”, Science (1972)– The behavior of large and complex aggregates of

elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles.

– Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.”

Fallacy of Strong Reductionism• “one may array the sciences … “The elementary

entities of science X obey the laws of science Y”X Y

Solid state or many-body physics

Elementary particle physics

Chemistry Many-body physicsMolecular biology ChemistryCell biology Molecular biology… …Psychology PhysiologySocial sciences Psychology• But this hierarchy does not imply that science X is “just applied Y”. At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology, nor is biology applied chemistry.” (Anderson 1972)

• And “macroeconomics is not applied microeconomics”

Macro model must be able to generate Depression• Minsky 1982

– “Can “It”—a Great Depression—happen again…? – To answer these questions it is necessary to have an

economic theory which makes great depressions one of the possible states in which our type of capitalist economy can find itself…

– The abstract model of the neoclassical synthesis cannot generate instability.

– When the neoclassical synthesis is constructed, capital assets, financing arrangements that center around banks and money creation, constraints imposed by liabilities, and the problems associated with knowledge about uncertain futures are all assumed away.

– For economists and policy-makers to do better we have to abandon the neoclassical synthesis.”

A tentative, but not-bankrupt, alternative

• A Minskian macroeconomics must:– Treat the economy as inherently monetary;– Model it dynamically;– Consider social classes rather than isolated

agents;– Consider rational but not prophetic behavior;– Have endogenous creation of money by banking

sector; – Give credit and debt have pivotal roles; and– Be able to generate a Great Depression as a

feasible state of the core model• First, Minsky’s verbal model…

Minsky’s FIH: dynamic-disequilibrium-debt model• Economy in historical time• Debt-induced recession in recent past• Firms and banks conservative re debt/equity, assets• Only conservative projects are funded

– Recovery means most projects succeed• Firms and banks revise risk premiums

– Accepted debt/equity ratio rises– Assets revalued upwards…

• “Stability is destabilising”– Period of tranquility causes expectations to rise…

• Self-fulfilling expectations– Decline in risk aversion causes increase in

investment– Investment expansion causes economy to grow

faster

The Euphoric Economy• Asset prices rise: speculation on assets profitable• Increased willingness to lend increases money supply

– Money supply endogenous, not controlled by CB• Riskier investments enabled, asset speculation

rises• The emergence of “Ponzi” financiers

– Cash flow less than debt servicing costs– Profit by selling assets on rising market– Interest-rate insensitive demand for finance

• Rising debt levels & interest rates lead to crisis– Ponzi “investments” inherently loss-making– Rising rates make conservative projects speculative– Non-Ponzi investors sell assets to service debts– Entry of new sellers floods asset markets– Rising trend of asset prices falters or reverses

The Assets Boom and Bust

• Ponzi financiers go bankrupt:– Can no longer sell assets for a profit– Debt servicing on assets far exceeds cash flows

• Asset prices collapse, increasing debt/equity ratios• Endogenous expansion of money supply reverses• Investment evaporates; economic growth slows• Economy enters a debt-induced recession

– Back where we started...• Process repeats once debt levels fall

– But starts from higher debt to GDP level• Final crisis where debt burden overwhelms economy• My work: converting this from verbal description to

mathematical model…

Theoretical dynamics of debt: Minsky + Circuit

• Monetary model of capitalism built from combination of:– Goodwin’s growth cycle– Minsky’s Financial Instability Hypothesis– Circuit theory of endogenous money creation

• Product: “Monetary Circuit Theory”—MCT• Physical side: Goodwin put into mathematical form

Marx’s “growth cycle” model in Capital I, Ch. 25:– “The mechanism of the process of capitalist

production removes the very obstacles that it temporarily creates. The price of labor falls again to a level corresponding with the needs of the self-expansion of capital, whether the level be below, the same as, or above the one which was normal before the rise of wages took place…”

Keen 1995 Model Foundations: Nonlinear dynamics• Inherently cyclical growth (Goodwin 1967, Blatt 1983)

Y/

lr1

Labour Productivitya

L

dw/dt 1/SIntegrator

w++

1Initial Wage

*L

W

WY +

-Pi I dK/dt

• Closes the loop:

1Initial Capital +

+1/SIntegrator

dK/dt

K 1/3Accelerator

Y

L/

lr100

PopulationN

l

PhillipsCurve dw/dt+- *

10WageResponse

.96"NAIRU"

• Capital K determines output Y via the accelerator:

• Y determines employment L via productivity a:

• L determines employment rate l via population N:

• l determines rate of change of wages w via Phillips Curve

• Integral of w determines W (given initial value)

• Y-W determines profits P and thus Investment I…

K 1/3Accelerator

Y

/lr1

Labour Productivitya

L

/lr

1Population

Nl

PhillipsCurve dw/dt

1/SIntegrator

w++

1Initial Wage *

LW

Y +-

Pi I dK/dt

3Initial Capital +

+1/SIntegrator

+- *10

WageResponse

.96"NAIRU"

Goodwin's cyclical growth model

Time (Years)0 2 4 6 8 10

.50

.75

1.00

1.25

1.50Employment

Wages

Goodwin's cyclical growth model

Employment.9 .95 1 1.05

Wa

ge

s.7

.8

.9

1.0

1.1

1.2

1.3

Modelling Minsky with Implicit Money…

• Debt essential to introduce Minsky– “Debt seems to be the residual variable in

financing decisions. Investment increases debt, and higher earnings tend to reduce debt.” (Fama & French 1997)

– “The source of financing most correlated with investment is long-term debt… These correlations confirm the impression that debt plays a key role in accommodating year-by-year variation in investment.” (Fama & French 1998)

• Nonlinear investment function of rate of profit:– Low—invest nothing;– Medium—invest as much as earn;– High—invest more than earn

Modelling Minsky with Implicit Money…

• Important (normal) feature of dynamic modelling: increasing generality of model makes it more realistic– No need for absurd assumptions to maintain

fiction of equilibrium, coherent micro/macro behaviour, etc.

• Exponential form:– Investment=Profit at profit rate of 3%– Investment>Profit at profit rate > 3%– Investment<Profit at profit rate < 3%– Slope of change at 3%=2– Minimum investment –1% output (depreciation)

Modelling Minsky with Implicit Money…

• Investment increases debt; profit decreases it• Debt rises if investment exceeds profits• Debt also increases due to interest on outstanding debt…

DebtProfi t

I nvestment +

-1/ S

+

+

0

I nitial Debtr0.03

*

Output/

l

r

• Profit net of both wages and interest payments:

Profi tOutput Wages+

+ I nterest

• And the whole model is:

Modelling Minsky with Implicit Money…

• Notice debt becomes negative

• Capitalists accumulate

• Equilibrium is stable in Fisher’s sense…

/l

rEmployment

/l

rPopulationProductivity

Capital Output

Profi tOutput

Employment Rate

Wages

Graphs

DebtProfi t

I nvestment +

-1/ S

+

+

0

I nitial Debtr0.03

*

+

+

Debt

Time (Years)

0 200 400

-50000000000

-25000000000

0

Debt/ Output

Time (Years)

0 100 200 300 400-2

-1

0

1

Output/

l

r

I nterest

basic_minsky_private_stable.vsm

Modelling Minsky with Implicit Money…

• “we may tentatively assume that, ordinarily and within wide limits, all, or almost all, economic variables tend, in a general way, towards a stable equilibrium” (Fisher 1933)

• But this stability is…– “so delicately poised that, after departure from it

beyond certain limits, instability ensues” (Fisher 1933: 339).

• Start further from equilibrium, system is unstable:

Modelling Minsky with Implicit Money…• Higher initial

level of unemployment leads to disaster…

/l

rEmployment

/l

rPopulationProductivity

Capital Output

Profi tOutput

Employment Rate

Wages

Graphs

r0.03*

+

+

Debt

Time (Years)

0 50 100 150

0

250000

500000

750000Debt/ Output

T ime (Years)

0 50 100 150

0

2.5

5.0

7.5

Output/

l

r

I nterest

134

I nitial_ Population

Debt

I nvestment

Profi t• Inverse tangent route to chaos

• Existence of equilibrium depends on initial conditions

• Higher initial level, apparent stability then collapse…

MinskyDebtChaos.vsm

Modelling Minsky with Implicit Money…

• Nonlinear model can be– Locally stable around equilibrium

• “linear” component of system dominates) but– Globally unstable

• past a certain range, nonlinear overwhelm linear

• Below one, a^3 is less than a^2 is less than a…

• Above 1, a^3 is bigger than a^2 is bigger than a…

– Start too far from equilibrium, a debt-induced collapse

• Inspired a “rhetorical flourish” in 1995 paper

O u t[4 4 9 ]=

0 5 1 0 1 5 2 0 2 5 3 01 00

2 00

3 00

4 00

5 00

Yea r

Out

put

A G rea t Mo dera tio n?

2 50 2 60 2 70 2 80 2 90 3 00

2 1 0 8

4 1 0 8

6 1 0 8

8 1 0 8

1 1 0 9

Yea r

Out

put

Followed by a brea kdown

0 5 0 1 00 1 50 2 00 2 50 3 000 .6

0 .7

0 .8

0 .9

1 .0

Yea r

Em

ploy

men

tR

ate

Em plo ym ent Cy cle with Debt

0 5 0 1 00 1 50 2 00 2 50 3 00

0 .6

0 .7

0 .8

0 .9

Yea r

Wag

esSh

are

ofO

utpu

t

W a ge Sha re Cy cle with Debt

Modelling Minsky with Implicit Money…

• Keen, 1995:• “This vision of a capitalist economy with finance

requires us to go beyond that habit of mind which Keynes described so well,

• the excessive reliance on the (stable) recent past as a guide to the future.

• The chaotic dynamics explored in this paper should warn us against accepting a period of relative tranquility in a capitalist economy

• as anything other than a lull before the storm.”

Modelling Minsky with Implicit Money…• Finally, government:

– Minsky: government spending works by• Giving firms a cash flow during slump, thus

letting them pay off their debts;• Restraining cash flow during boom, thus

attenuating euphoric expectations– Model: government pays subsidy (can be

negative) to firms, where change in subsidy is a function of the rate of employment…

– Constant parameters means model government “resolute” against unemployment•Actual governments have clearly shifted

on this…dG L

Y gdt N

Modelling Minsky with Implicit Money…

• Government Subsidy:– Constant if Unemployment = 5%– Increasing if Unemployment > 5%– Reducing if Unemployment < 5%

E_ rate

0 +

+

* 1/ S

Output

Exponential:

x,

y,

slope at (x,y),

min.

0.95

0

-0.5

• Profit now net of wages, interest, & government subsidy…

Profi tOutput Wages

+

+

-

I nterest

G

Modelling Minsky with Implicit Money…• Cyclical instability

– depending on slope of government reaction functionEmployment rate

Time (Years)

0 100 200 300 4000

.5

1.0

1.5

2.0Wage Share

Time (Years)

0 100 200 300 400.6

.7

.8

.9

1.0

1.1Limit Cycle

.6 .725 .85 .975 1.1.80

.85

.90

.95

1.00

1.05

Debt/ Output

Time (Years)

0 100 200 300 400-2

0

2

4Government spending to output

Time (years)

0 100 200 300 400-.20

.05

.30

.55

.80

basic_minsky_government.vsm

Modelling Minsky with Endogenous Money…

• Monetary Foundation Graziani “Circuit Theory” (1989)– “The starting point of the theory of the circuit, is that

a true monetary economy is inconsistent with the presence of a commodity money.

– A commodity money is by definition a kind of money that any producer can produce for himself. But an economy using as money a commodity coming out of a regular process of production, cannot be distinguished from a barter economy.

– A true monetary economy must therefore be using a token money, which is nowadays a paper currency”

• Endogeneity of money supply well established– But ignored by neoclassical modellers

Skip Neoclassical attitude to banksSkip Neoclassical attitude to banks

Neoclassical Theory wrong from first principles• Neoclassical vision of money & debt:

– “Patient agent” lends to “Impatient agent”– Bank as intermediary– No change in aggregate demand– E.g., Krugman trying to explain why distribution of

debt matters—while assuming aggregate level doesn’t:• “we begin by setting out a flexible-price

endowment model in which “impatient” agents borrow from “patient” agents, but are subject to a debt limit.”

– A crisis?• “If this debt limit is, for some reason, suddenly

reduced, the impatient agents are forced to cut spending” (2010, p. 3)

Neoclassical Theory wrong from first principles• Patient lends to Impatient

• Patient’s spending power goes down• Impatient’s spending power goes up• No change in aggregate demand• Banks mere intermediaries (ignored in analysis)• Versus reality: new spending power endogenously

created

Monetary Circuit Theory• Basic process of endogenous money creation• Entrepreneur approaches bank for loan

• Bank grants loan & creates deposit simultaneously

• Alan Holmes, Senior Vice-President New York Fed, 1969:

• “In the real world, banks extend credit, creating deposits in the process, and look for the reserves later.” (1969, p. 73)

• New loan puts additional spending power into circulation

• Modeling this using strictly monetary framework:

Explicitly Monetary Minsky Model• Input financial relations in Table:

Assets Liabilities Equity

Reserve Loan Firm Deposit

Worker Deposit

Bank Equity

Lend -A A

Record Loan

A

Interest B

Pay Interest -B B

Record -B

Wages -C C

Consumption

D+E -D -E

Repay Loan F -F

Record -F

New Money G

Record G• System of dynamic equations derived automatically:

dReserves A F

dtd

Loan A F Gdtd

FirmDeposit A B C D E F GdtdWorkerDeposit C D

dtd

BankEquity B Edt

• Placeholders replaced by behavioural functions:

VLV

L r V r

TT L L D D D

B

V LL r

V r L r

V L T DD D D L L r

V r L r B H

DD D D

H

BFdB

dt

BdB r F r F H

dt

B FdF Y Inv

dt

B F B HdF r F r F W L Y Inv

dt

HdH r H W L

dt

Explicitly Monetary Minsky Model

• Coupled with physical output model via– Price equation (derivation in Keen 2010)

1 1

1P

d WP P

dt a

• Monetary “Phillips curve” including all 3 factors in

Phillips– Unemployment– Rate of change of unemployment– Cost of living adjustment

1 1h

d d dW W P P

dt dt P dt

Explicitly Monetary Minsky Model

• Full system of 14 coupled differential equationsFinancial Sector

tBV t( )d

d

FL t( )

RL r t( ) BV t( )

LC r t( ) BV 0( ) BV0

tBT t( )d

drL FL t( ) rD FD t( ) rD HD t( )

BT t( )

B BT 0( ) BT0

tFL t( )d

d

BV t( )

LC r t( ) FL t( )

RL r t( ) P t( ) Yr t( ) Inv r t( ) FL 0( ) FL0

tFD t( )d

drD FD t( ) rL FL t( )

BV t( )

LC r t( ) FL t( )

RL r t( ) BT t( )

B

HD t( )

W P t( ) Yr t( ) Inv r t( )

W t( ) Yr t( )

a t( ) FD 0( ) FD0

tHD t( )d

drD HD t( )

HD t( )

W

W t( ) Yr t( )

a t( ) HD 0( ) HD0

Physical output, labour and price systems

Level of output Yr 0( ) Yr0Yr t( )Kr t( )

v

Employment L t( )Yr t( )

a t( )L 0( ) L0

Rate of Profit r t( )P t( ) Yr t( ) W t( ) L t( ) rL FL t( ) rD FD t( )

v P t( ) Yr t( ) r 0( ) r0

Rate of employmentt t( )d

d t( ) g t( ) ( )[ ] 0( ) 0

Rate of real economic growth g t( )Inv r t( )

v g 0( ) g0

tW t( )d

dW t( )( ) Ph t( )( ) g t( ) ( )[ ][ ]

1Pc

1W t( )

a t( ) 1 s( ) P t( )

Rate of change of wages W 0( ) W0

Rate of change of prices P 0( ) P0

tP t( )d

d

1Pc

P t( )W t( )

a t( ) 1 s( )

Rate of change of capital stocktKr t( )d

dKr t( ) g t( ) Kr 0( ) Kr0

Rates of growth of population and productivityta t( )d

d a t( )

tN t( )d

d N t( ) N 0( ) N0 a 0( ) a0

Explicitly Monetary Minsky Model• Generates both “Great Moderation” & “Great Depression”

0 10 20 30 40 50 6025

20

15

10

5

0

5

10

15

20

25

0

100

200

300

400

500

InflationUnemploymentDebt to GDP

Inflation, Unemployment and Debt

Infl

atio

n &

Une

mpl

oym

ent P

erce

nt

Deb

t to

GD

P R

atio

Per

cent

0

Explicitly Monetary Minsky Model• Fits stylized facts of crisis

1980 1985 1990 1995 2000 2005 2010 20155

2.5

0

2.5

5

7.5

10

12.5

15

1

1.5

2

2.5

3

UnemploymentInflationDebt to GDP

Unemployment, Inflation & Debt (smoothed)

Year

Per

cent

Rat

io to

GD

P

0

Explicitly Monetary Minsky Model• Approach extensible to multiple commodity modelFinancialSystem

tBR t( )d

d

FLA1 t( )

RL prA t( ) 2 BR t( )

RR prC t( ) 2 BR t( )

RR prE t( ) 2 BR t( )

RR prK t( ) 2 BR t( )

RR prA t( ) FLA2 t( )

RL prA t( ) FLC1t( )

RL prC t( ) FLC2 t( )

RL prC t( ) FLE1t( )

RL prE t( ) FLE2t( )

RL prE t( ) FLK1 t( )

RL prK t( ) FLK2 t( )

RL prK t( )

tFLK1 t( )d

d

BR t( )

RR prK t( ) FLK1 t( )

RL prK t( ) FLK1 t( )

NM prK t( )

tFLK2 t( )d

d

BR t( )

RR prK t( ) FLK2 t( )

RL prK t( ) FLK2 t( )

NM prK t( )

tFLC1 t( )d

d

BR t( )

RR prC t( ) FLC1 t( )

RL prC t( ) FLC1 t( )

NM prC t( )

tFLC2 t( )d

d

BR t( )

RR prC t( ) FLC2 t( )

RL prC t( ) FLC2 t( )

NM prC t( )

tFLA1 t( )d

d

BR t( )

RR prA t( ) FLA1 t( )

RL prA t( ) FLA1 t( )

NM prA t( )

tFLA2 t( )d

d

BR t( )

RR prA t( ) FLA2 t( )

RL prA t( ) FLA2 t( )

NM prA t( )

tFLE1t( )d

d

BR t( )

RR prE t( ) FLE1t( )

RL prE t( ) FLE1t( )

NM prE t( )

tFLE2t( )d

d

BR t( )

RR prE t( ) FLE2t( )

RL prE t( ) FLE2t( )

NM prE t( )

tFDK1 t( )d

d

BR t( )

RR prK t( ) rL FLK1 t( ) LK1 t( ) WM t( )FDA1 t( )

pr prA t( ) FDC1 t( )

pr prC t( ) FDE1 t( )

pr prE t( ) FDK1 t( )

pr prK t( ) FDK2 t( )

pr prK t( ) FLK1 t( )

RL prK t( ) FLK1 t( )

NM prK t( ) BI t( )

2 KBC

FDA1 t( )

KAC

FDC1 t( )

KCC

FDE1 t( )

KEC

FDK1 t( )

CKA

FDK1 t( )

CKC

FDK1 t( )

CKE

FDK1 t( )

KKC

FDK2 t( )

KKC

HD t( )

2 KWC FDK1 t( ) rD FDK1 t( ) KA LK1 t( ) WM t( ) KC LK1 t( ) WM t( ) KE LK1 t( ) WM t( )

tFDK2 t( )d

d

BR t( )

RR prK t( ) rL FLK2 t( ) LK2 t( ) WM t( )FDA2 t( )

pr prA t( ) FDC2 t( )

pr prC t( ) FDE2 t( )

pr prE t( ) FDK1 t( )

pr prK t( ) FDK2 t( )

pr prK t( ) FLK2 t( )

RL prK t( ) FLK2 t( )

NM prK t( ) BI t( )

2 KBC

FDA2 t( )

KAC

FDC2 t( )

KCC

FDE2 t( )

KEC

FDK2 t( )

CKA

FDK2 t( )

CKC

FDK2 t( )

CKE

FDK1 t( )

KKC

FDK2 t( )

KKC

HD t( )

2 KWC FDK2 t( ) rD FDK2 t( ) KA LK2 t( ) WM t( ) KC LK2 t( ) WM t( ) KE LK2 t( ) WM t( )

tFDC1 t( )d

d

BR t( )

RR prC t( ) rL FLC1 t( ) LC1 t( ) WM t( )FDC1 t( )

pr prC t( ) FLC1 t( )

RL prC t( ) FLC1 t( )

NM prC t( ) BI t( )

2 CBC

FDA1 t( )

CAC

FDC1 t( )

CCA

FDC1 t( )

CCC

FDC2 t( )

CCC

FDC1 t( )

CCE

FDE1 t( )

CEC

FDC1 t( )

KCC

FDK1 t( )

CKC

HD t( )

2 CWC FDC1 t( ) rD FDC1 t( ) AC LA1 t( ) WM t( ) CA LC1 t( ) WM t( ) CC LC1 t( ) WM t( ) CC LC2 t( ) WM t( ) CE LC1 t( ) WM t( ) ECLE1 t( ) WM t( ) KC LK1 t( ) WM t( )

tFDC2 t( )d

d

BR t( )

RR prC t( ) rL FLC2 t( ) LC2 t( ) WM t( )FDC2 t( )

pr prC t( ) FLC2 t( )

RL prC t( ) FLC2 t( )

NM prC t( ) BI t( )

2 CBC

FDA2 t( )

CAC

FDC2 t( )

CCA

FDC1 t( )

CCC

FDC2 t( )

CCC

FDC2 t( )

CCE

FDE2 t( )

CEC

FDC2 t( )

KCC

FDK2 t( )

CKC

HD t( )

2 CWC FDC2 t( ) rD FDC2 t( ) AC LA2 t( ) WM t( ) CA LC2 t( ) WM t( ) CC LC1 t( ) WM t( ) CC LC2 t( ) WM t( ) CE LC2 t( ) WM t( ) ECLE2 t( ) WM t( ) KC LK2 t( ) WM t( )

tFDA1 t( )d

d

BR t( )

RR prA t( ) rL FLA1 t( ) LA1 t( ) WM t( )FDA1 t( )

pr prA t( ) FLA1 t( )

RL prA t( ) FLA1 t( )

NM prA t( ) BI t( )

2 CBA

FDA1 t( )

CAA

FDA2 t( )

CAA

FDA1 t( )

CAC

FDC1 t( )

CCA

FDA1 t( )

CAE

FDE1 t( )

CEA

FDA1 t( )

KAC

FDK1 t( )

CKA

HD t( )

2 CWA FDA1 t( ) rD FDA1 t( ) AA LA1 t( ) WM t( ) AA LA2 t( ) WM t( ) AC LA1 t( ) WM t( ) CA LC1 t( ) WM t( ) AE LA1 t( ) WM t( ) EA LE1 t( ) WM t( ) KA LK1 t( ) WM t( )

tFDA2 t( )d

d

BR t( )

RR prA t( ) rL FLA2 t( ) LA2 t( ) WM t( )FDA2 t( )

pr prA t( ) FLA2 t( )

RL prA t( ) FLA2 t( )

NM prA t( ) BI t( )

2 CBA

FDA1 t( )

CAA

FDA2 t( )

CAA

FDA2 t( )

CAC

FDC2 t( )

CCA

FDA2 t( )

CAE

FDE2 t( )

CEA

FDA2 t( )

KAC

FDK2 t( )

CKA

HD t( )

2 CWA FDA2 t( ) rD FDA2 t( ) AA LA1 t( ) WM t( ) AA LA2 t( ) WM t( ) AC LA2 t( ) WM t( ) CA LC2 t( ) WM t( ) AE LA2 t( ) WM t( ) EA LE2 t( ) WM t( ) KA LK2 t( ) WM t( )

tFDE1 t( )d

d

BR t( )

RR prE t( ) rL FLE1t( ) LE1 t( ) WM t( )FDE1 t( )

pr prE t( ) FLE1t( )

RL prE t( ) FLE1t( )

NM prE t( ) BI t( )

2 CBE

FDA1 t( )

CAE

FDE1 t( )

CEA

FDC1 t( )

CCE

FDE1 t( )

CEC

FDE1 t( )

CEE

FDE2 t( )

CEE

FDE1 t( )

KEC

FDK1 t( )

CKE

HD t( )

2 CWE FDE1 t( ) rD FDE1 t( ) AE LA1 t( ) WM t( ) EA LE1 t( ) WM t( ) CE LC1 t( ) WM t( ) ECLE1 t( ) WM t( ) EELE1 t( ) WM t( ) EELE2 t( ) WM t( ) KE LK1 t( ) WM t( )

tFDE2 t( )d

d

BR t( )

RR prE t( ) rL FLE2t( ) LE2 t( ) WM t( )FDE2 t( )

pr prE t( ) FLE2t( )

RL prE t( ) FLE2t( )

NM prE t( ) BI t( )

2 CBE

FDA2 t( )

CAE

FDE2 t( )

CEA

FDC2 t( )

CCE

FDE2 t( )

CEC

FDE1 t( )

CEE

FDE2 t( )

CEE

FDE2 t( )

KEC

FDK2 t( )

CKE

HD t( )

2 CWE FDE2 t( ) rD FDE2 t( ) AE LA2 t( ) WM t( ) EA LE2 t( ) WM t( ) CE LC2 t( ) WM t( ) ECLE2 t( ) WM t( ) EELE1 t( ) WM t( ) EELE2 t( ) WM t( ) KE LK2 t( ) WM t( )

tHD t( )d

dLA1 t( ) WM t( ) LA2 t( ) WM t( ) LC1 t( ) WM t( ) LC2 t( ) WM t( ) LE1 t( ) WM t( ) LE2 t( ) WM t( ) LK1 t( ) WM t( ) LK2 t( ) WM t( )

HD t( )

CWA

HD t( )

CWC

HD t( )

CWE

HD t( )

KWC HD t( ) rD HD t( )

tBI t( )d

drL FLA1 t( ) rL FLA2 t( ) rL FLC1 t( ) rL FLC2t( ) rL FLE1t( ) rL FLE2t( ) rL FLK1 t( ) rL FLK2 t( )

BI t( )

CBA

BI t( )

CBC

BI t( )

CBE

BI t( )

KBC FDA1 t( ) rD FDA1 t( ) FDA2 t( ) rD FDA2 t( ) FDC1 t( ) rD FDC1 t( ) FDC2 t( ) rD FDC2 t( ) FDE1 t( ) rD FDE1 t( ) FDE2 t( ) rD FDE2 t( ) FDK1 t( ) rD FDK1 t( ) FDK2 t( ) rD FDK2 t( ) HD t( ) rD HD t( )

Production system

Capital 1 Capital 2

KK1 0( ) KK10 KK2 0( ) KK20

Capital StocktKK1 t( )d

d

FDK1 t( )

pr prK t( ) PK t( ) KK1 t( )

tKK2 t( )d

d

FDK2 t( )

pr prK t( ) PK t( ) KK2 t( )

Output QK1 0( ) QK10 QK2 0( ) QK20

tQK1 t( )d

d

1

QKQK1 t( )

1

vKKK1 t( )

tQK2 t( )d

d

1

QKQK2 t( )

1

vKKK2 t( )

Employment LK1 0( ) LK10 LK2 0( ) LK20

tLK1 t( )d

d

1

LKLK1 t( )

QK1 t( )

aK t( )

tLK2 t( )d

d

1

LKLK2 t( )

QK2 t( )

aK t( )

Prices PK 0( ) PK0

tPK t( )d

d

1

PKPK t( )

WM t( )

aK t( ) 1 sK

Consumption 1 Consumption 2

KC1 0( ) KC10 KC2 0( ) KC20

tKC1 t( )d

d

FDC1 t( )

pr prC t( ) PK t( ) KC1 t( )

tKC2 t( )d

d

FDC2 t( )

pr prC t( ) PK t( ) KC2 t( )

QC1 0( ) QC10 QC2 0( ) QC20

tQC1 t( )d

d

1

QCQC1 t( )

1

vCKC1 t( )

tQC2 t( )d

d

1

QCQC2 t( )

1

vCKC2 t( )

LC1 0( ) LC10 LC2 0( ) LC20

tLC1 t( )d

d

1

LCLC1 t( )

QC1 t( )

aC t( )

tLC2 t( )d

d

1

LCLC2 t( )

QC2 t( )

aC t( )

PC 0( ) PC0

tPC t( )d

d

1

PCPC t( )

WM t( )

aC t( ) 1 sC

Agriculture 1 Agriculture 2

KA1 0( ) KA10 KA2 0( ) KA20

tKA1 t( )d

d

FDA1 t( )

pr prA t( ) PK t( ) KA1 t( )

tKA2 t( )d

d

FDA2 t( )

pr prA t( ) PK t( ) KA2 t( )

QA1 0( ) QA10 QA2 0( ) QA20

tQA1 t( )d

d

1

QAQA1 t( )

1

vAKA1 t( )

tQA2 t( )d

d

1

QAQA2 t( )

1

vAKA2 t( )

LA1 0( ) LA10 LA2 0( ) LA20

tLA1 t( )d

d

1

LALA1 t( )

QA1 t( )

aA t( )

tLA2 t( )d

d

1

LALA2 t( )

QA2 t( )

aA t( )

PA 0( ) PA0

tPA t( )d

d

1

PAPA t( )

WM t( )

aA t( ) 1 sA

Energy 1 Energy 2

KE1 0( ) KE10 KE2 0( ) KE20

tKE1 t( )d

d

FDE1 t( )

pr prE t( ) PK t( ) KE1 t( )

tKE2 t( )d

d

FDE2 t( )

pr prE t( ) PK t( ) KE2 t( )

QE1 0( ) QE10 QE2 0( ) QE20

tQE1 t( )d

d

1

QEQE1 t( )

1

vEKE1 t( )

tQE2 t( )d

d

1

QEQE2 t( )

1

vEKE2 t( )

LE1 0( ) LE10 LE2 0( ) LE20

tLE1 t( )d

d

1

LELE1 t( )

QE1 t( )

aE t( )

tLE2 t( )d

d

1

LELE2 t( )

QE2 t( )

aE t( )

PE 0( ) PE0

tPE t( )d

d

1

PEPE t( )

WM t( )

aE t( ) 1 sE

Wages WM 0( ) WM0 tWM t( )d

dPh t( )( ) WM t( )

Employment Rate 0( ) 0 t( )LK1 t( ) LK2 t( ) LC1 t( ) LC2 t( ) LA1 t( ) LA2 t( ) LE1 t( ) LE2 t( )

Pop t( )

Technical ChangetaK t( )d

d aK t( ) aK 0( ) aK0

taC t( )d

d aC t( ) aC 0( ) aC0

taA t( )d

d aA t( ) aA 0( ) aA0

taE t( )d

d aE t( ) aE 0( ) aE0

Population GrowthtPop t( )d

d Pop t( ) Pop 0( ) Pop0

Aggregate Sectoral Capital Stock

Capital Consumer Agriculture Energy

KK 0( ) KK10 KK20 KC 0( ) KC10 KC20KA 0( ) KA10 KA20 KE 0( ) KE10 KE20

KK t( ) KK1 t( ) KK2 t( ) KC t( ) KC1 t( ) KC2 t( )KA t( ) KA1 t( ) KA2 t( ) KE t( ) KE1 t( ) KE2 t( )

Rates of profit

prK t( )rL FLK1 t( ) FLK2 t( ) rD FDK1 t( ) FDK2 t( ) FDK1 t( ) FDK2 t( ) WM t( ) LK1 t( ) LK2 t( ) PK t( ) QK1 t( ) QK2 t( ) KA WM t( ) LA1 t( ) LA2 t( ) KC WM t( ) LC1 t( ) LC2 t( ) KE WM t( ) LE1 t( ) LE2 t( )

PK t( ) KK1 t( ) KK2 t( )

prK 0( ) prK0

prC t( )rL FLC1 t( ) FLC2 t( ) rD FDC1 t( ) FDC2 t( ) FDC1 t( ) FDC2 t( ) WM t( ) LC1 t( ) LC2 t( ) PC t( ) QC1 t( ) QC2 t( ) CA WM t( ) LA1 t( ) LA2 t( ) CC WM t( ) LC1 t( ) LC2 t( ) CE WM t( ) LE1 t( ) LE2 t( )

PK t( ) KC1 t( ) KC2 t( )

prC 0( ) prC0

prA t( )rL FLA1 t( ) FLA2 t( ) rD FDA1 t( ) FDA2 t( ) FDA1 t( ) FDA2 t( ) WM t( ) LA1 t( ) LA2 t( ) PA t( ) QA1 t( ) QA2 t( ) AA WM t( ) LA1 t( ) LA2 t( ) AC WM t( ) LC1 t( ) LC2 t( ) AE WM t( ) LE1 t( ) LE2 t( )

PK t( ) KA1 t( ) KA2 t( )

prA 0( ) prA0

prE t( )rL FLE1t( ) FLE2t( ) rD FDE1 t( ) FDE2 t( ) FDE1 t( ) FDE2 t( ) WM t( ) LE1 t( ) LE2 t( ) PE t( ) QE1 t( ) QE2 t( ) EA WM t( ) LA1 t( ) LA2 t( ) ECWM t( ) LC1 t( ) LC2 t( ) EEWM t( ) LE1 t( ) LE2 t( )

PK t( ) KE1 t( ) KE2 t( )

prE 0( ) prE0

Explicitly Monetary Minsky Model• Basic system generates multisectoral limit cycle

0 20 40 60 80 1005

0

5

10

15

Capital GoodsConsumer GoodsAgricultureEnergy

The Rate of Profit in a Monetary Multisectoral Model of Production

Years

Pro

fit/C

apita

(P

erce

nt)

100 prK t( )

100 prC t( )

100 prA t( )

100 prE t( )

t

20 25 30 35 402

0

2

4

6

Real Rate of Economic Growth

Per

cent

p.a

.

100 GDPRealChange t( )

t

20 25 30 35 4010

20

30

40

50

0

10

20

30

40

GDPDebt

Change in Nominal Credit and Nominal GDP

Per

cent

cha

nge

p.a.

Explicitly Monetary Minsky Model

• Monetary and income distribution dynamics

94 96 98 100 102 10455

60

65

70

75

80

85

90

95

100

15

10

5

0

5

10

15

20

25

30

WagesProfitInterest

Income Distribution Limit Cycles

Employment Rate

Wag

es S

hare

of

Out

put

Cap

italis

t & B

anke

r S

hare

s

20 25 30 351 10

5

1 106

1 107

1 108

10000

1 105

1 106

1 107

LoansDepositsBank Reserves (RHS)

Bank Assets & Liabilities

• Minsky modelling approach clearly “works”– How to make it more accessible?

• INET funding to develop GUI program “Minsky”

Making Monetary Dynamics Accessible

• Prototype “QED” already available– http://www.debtdeflation.com/blogs/qed/

Minskian Prognosis• Deleveraging till Ponzi debt overhang eliminated

– (USA, 50-100% of GDP from 300% peak)• Continued shortfall of aggregate demand• Government deficits attenuate decline• But less effective given private sector deleveraging

– However austerity will make it worse• Private debt abolition a better policy (Hudson,

Graeber)– Long term decline from honouring debts that were

dishonourably created• We are in a Great Depression• And bad economic thinking helped us get here…

Minskian Prognosis• “To conclude, evidence-based macro research needs

to replace faith-based models.• Theory needs to be applied in a less heavy handed

and exclusionary manner, and data should be used to discriminate between theories.” (Muellbauer 2010, p. 27)• Amen!

References• Anderson, P. W. (1972). "More Is Different." Science 177(4047): 393-396.• Bezemer, D. J. (2009). ““No One Saw This Coming”: Understanding Financial Crisis Through

Accounting Models.” Groningen, The Netherlands, Faculty of Economics University of Groningen.

• Blatt, J. M. (1983). Dynamic economic systems : a post-Keynesian approach. Armonk, N.Y, M.E. Sharpe.

• Bezemer, D. J. (2010). "Understanding financial crisis through accounting models." Accounting, Organizations and Society 35(7): 676-688.

• Clark, J. B. (1898). "The Future of Economic Theory." The Quarterly Journal of Economics 13(1): 1-14.

• Fama, E. F. and K. R. French (1999). "The Corporate Cost of Capital and the Return on Corporate Investment." Journal of Finance 54(6): 1939-1967.

• Fama, E. F. and K. R. French (2002). "Testing Trade-Off and Pecking Order Predictions about Dividends and Debt." Review of Financial Studies 15(1): 1-33.

• Friedman, M. (1969). The Optimum Quantity of Money. The Optimum Quantity of Money and Other Essays. Chicago, MacMillan: 1-50.

• Goodwin, R. (1967). A growth cycle. Socialism, Capitalism and Economic Growth. C. H. Feinstein. Cambridge, Cambridge University Press: 54-58.

• Keen, S. (1995). "Finance and Economic Breakdown: Modeling Minsky's 'Financial Instability Hypothesis.'." Journal of Post Keynesian Economics 17(4): 607-635.

• Keen, S. (2010). "Solving the Paradox of Monetary Profits." Economics: The Open-Access, Open Assessment E-Journal, 4 (2010-31)

• Keen, S. (2011). "A monetary Minsky model of the Great Moderation and the Great Recession." Journal of Economic Behavior & Organization In Press, Corrected Proof.

• Kirman, A. (1989). "The Intrinsic Limits of Modern Economic Theory: The Emperor Has No Clothes." Economic Journal 99(395): 126-139.

References

• Lucas, R. E., Jr. (1972). Econometric Testing of the Natural Rate Hypothesis. The Econometrics of Price Determination Conference, October 30-31 1970. O. Eckstein. Washington, D.C., Board of Governors of the Federal Reserve System and Social Science Research Council: 50-59.

• Lucas, R. E., Jr. (2004). "Keynote Address to the 2003 HOPE Conference: My Keynesian Education." History of Political Economy 36: 12-24.

• Kydland, F. E. and E. C. Prescott (1990). "Business Cycles: Real Facts and a Monetary Myth." Federal Reserve Bank of Minneapolis Quarterly Review 14(2): 3-18.

• Marx, K. and F. Engels (1885). Capital II. Moscow, Progress Publishers.• Muellbauer, J., (2010) “Household decisions, credit markets and the macroeconomy:

implications for the design of central bank models”, BIS Working Papers No 306• Minsky, H. P. (1982). Can "it" happen again? : essays on instability and finance. Armonk, N.Y.,

M.E. Sharpe.• Samuelson, P. A. and W. D. Nordhaus (2010). Microeconomics. New York, McGraw- Hill Irwin.• Schumpeter, J. A. (1934). The theory of economic development : an inquiry into profits,

capital, credit, interest and the business cycle. Cambridge, Massachusetts, Harvard University Press.

• Shafer, W. and H. Sonnenschein (1993). “Market demand and excess demand functions”. Handbook of Mathematical Economics. K. J. Arrow and M. D. Intriligator, Elsevier. 2: 671-693.

• Sonnenschein, H. (1973). "Do Walras' Identity and Continuity Characterize the Class of Community Excess Demand Functions?" Journal of Economic Theory 6(4): 345-354.

• Varian, H. R. (1984, 1992). Microeconomic analysis. New York, W.W. Norton.