Monetary Macroeconomic Modeling

Steve Keenwww.debtdeflation.com/blogsKickstarter: http://t.co/rzFwjEnJ

From the Great Moderation to the Lesser Depression• Sudden decay of economic conditions in 2007-08:

1980 1985 1990 1995 2000 2005 2010 20153210123456789

101112131415

UnemploymentInflation

Unemployment and Inflation

Year; Source BLS, Federal Reserve Flow of Funds

Perc

ent,

Perc

ent c

hang

e p.

a.

0

2008

From the Great Moderation to the Lesser Depression• Crisis not anticipated by DSGE models:

– OECD Economic Outlook June 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.” (Cotis 2007)

• Great Moderation & Depression anticipated by Minsky-oriented model– “From the perspective of economic theory and policy,

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.” (Keen 1995)

From the Great Moderation to the Lesser Depression• Key empirical difference: focus on role of private debt…

1980 1985 1990 1995 2000 2005 2010 201530

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UnemploymentInflationDebt ChangeDebt Ratio

Unemployment, Inflation and Aggregate Private Debt

Year; Source BLS, Federal Reserve Flow of Funds

Perc

ent,

Perc

ent c

hang

e p.

a.

Perc

ent o

f GD

P

0

2008

Growing

debt

ratio

Collapse in debt growth

Minsky approach compared to DGSE approach• Non-equilibrium & instability rather than equilibrium

dynamics– “Stability—or tranquility—in a world with a cyclical

past and capitalist financial institutions is destabilizing” (Minsky 1978)

• Euphoric rather than Rational Expectations– “Once euphoria sets in … Financial institutions …

accept liability structures … that, in a more sober expectational climate, they would have rejected” (Minsky 1972)

• Complexity & Emergent Properties rather than Microfoundations– “every polynomial … is an excess demand function

for a specified commodity in some n commodity economy…” (Sonnenschein 1972)

• Linear production rather than diminishing marginal productivity– “Firms … rarely report the upward-sloping marginal

cost curves that are ubiquitous in economic theory. Indeed, downward-sloping marginal cost curves are more common.” (Blinder 1998)

Minsky approach compared to DGSE approach• Endogenous money rather than money neutrality

– “It is always a question, not of transforming purchasing power which already exists in someone's possession, but of the creation of new purchasing power out of nothing…” (Schumpeter 1934)

– “Debt plays a key role in accommodating year-by-year variation in investment.” (Fama and French 1999)

• Government homeostatic stabilizer rather than “Policy Ineffectiveness”– “Big government prevents the collapse of profits which is

a neces sary condition for a deep and long depression…” (Minsky 1982)

• Non-equilibrium methods needed to model Fisher/Minsky processes– “Theoretically … there must be over-or under-

production, …over- or under-investment … and over or under everything else.

– It is as absurd to assume that, for any long period of time, the variables in the economic organization … will "stay put," in perfect equilibrium, as to assume that the Atlantic Ocean can ever be without a wave.” (Fisher 1933)

The Financial Instability Hypothesis• 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• Rising expectations leads to “The Euphoric

Economy”…

The Financial Instability Hypothesis• 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– 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 Financial Instability Hypothesis• Boom turns to bust• Ponzi financiers first to 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• Turning verbal argument into a model…

Cyclical foundations of Minsky model• Goodwin’s cyclical growth model (1967)

Y K vL Y a

L N

/1 hdw dw t P

Y w L

dK dt I

• As a reduced system of ODEs (in & w = w/a):

1

h

ddt vd Pdt

w

w w

• Generalized for nonlinear investment function & depreciation:

w w

h

Iddt vd Pdt

• As dynamic flowchart

– Capital K determines output Y via accelerator v: – Y determines employment L via labour productivity a:– L determines employment rate given population N:– determines rate of change of the wage rate w:– Output minus the wage bill determines profits :– All profits are invested:

• System has neutral equilibrium– (Dominant eigenvalue has zero

real part)

• Cycles even with linear Phillips curve…

GoodwinLinearWordsMultipleGraphs02.mky

Cyclical foundations of Minsky model• System inherently cyclical—structural nonlinearity that

wage bill = w.L• Nonlinear functions add realism, not cycles themselves

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95

100

105

Linear Phillips CurveNonlinear Phillips CurveNonlinear Phillips & Investment

Goodwin model: closed curves in phase space

Wages share of output %

Empl

oym

ent r

ate

%

• Additional realism to introduce Minsky– Nonlinear investment

function: investment exceeds profits during boom, below profits during slump

• No structural change to model, but more realistic simulated values:

Minsky model: introducing debt• Next element of realism: debt-financed investment:

– “More investment tends to generate more debt, while higher earnings are used to reduce debt.” (Fama and French 1999)

• In equations:– Rate of change of debt equals investment minus profits– Profit net of interest payments on debtdD I

dtY w L r D

• Significant structural change to model• Now 3 dimensions:

– Rate of employment– Wages share of output– Debt to output ratio

Minsky (without government)• As system of ODEs:

1

(1 ) 1 1

h

r d

d I r dd

Iddt

d r I

vd Pdt

r ddt v

w

w

w

w

w w

• Li and Yorke (1975), “Period Three Implies Chaos”– Stability now dependent on initial conditions,

parameters– “Inverse tangent route to chaos” (Pomeau and

Manneville 1980)• Equilibrium convergence for some initial conditions• Divergence for others

– Apparent convergence to stability followed by breakdown

Finance & Economic Breakdown• Stability for some initial conditions & parameter values…

Finance & Economic Breakdown• Apparent stability followed by instability for others

– “Great Moderation” followed by “Great Depression”…

Finance & Economic Breakdown• Model has 2 equilibria:

– “Good equilibrium”:• Positive incomes, positive employment, & finite debt

– “Bad equilibrium”:• Zero wage & profit income, zero employment, &

infinite debt• Size of basin of attraction of good equilibrium a negative

function of debt to output ratio…• Outside this basin, convergence to bad equilibrium likely• Stability of good equilibrium

– Eliminated by “Ponzi” behavior• Debt-financed speculation on asset prices

– Expanded by government counter-cyclical spending• Cash flow to private sector enables debts to be

serviced, repaid• Role of private debt in economy crucial…

Finance & Economic Breakdown• Higher debt ratio gives lower range of stable initial

conditions… Higher debt level reduceseconomic stability

Destabilizing a bad stable equilibrium• Bad equilibrium similar to astronomical Black Hole

– Escape once economy enters its “Event Horizon” impossible unless• Debt is reduced by bankruptcy, debt jubilees

– Like “Hawkins Radiation”: reduce mass of Black Hole

• Reduce real interest rate– Like reducing gravitational constant

• Non-discretionary government spending can destabilize this bad stable equilibrium– Government spending rises when unemployment rises;– Government tax revenues fall when unemployment rises– Spending gives business cash flow to service/repay debt

• Modelled by introducing government net spending as a function of the employment rate: dG g Ydt

Y w L r D G

Destabilizing a bad stable equilibrium• Results in 4-dimensional system:

1

(1 ) 1 1

(1 )

h

r d g

d I r d gd d

Iddt vd Pdt

g g

r I r d gdt vd I r d ggdt v

w

w

w w

w

w

w

• Counter-cyclical government spending– Destabilizes bad equilibrium

• Basin of attraction substantially reduced• Economy can be moved from bad equilibrium with

large stimulus– Makes good equilibrium stable but cyclical…

Destabilizing a bad stable equilibrium• Cyclical stability around good equilibrium

– Stability not absence of cycles but absence of breakdown…

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110Wages ShareEmployment

Minsky model with Government

Years

Per c

ent o

f wor

kfor

ce, G

DP

MinskyGovernmentNonlinearGrouped.mky

A strictly monetary macroeconomic model• Preceding model implicitly monetary

– Debt finances investment in excess of retained earnings• Explicitly monetary model needed to

– Consider impact of inflation, deflation– Properly incorporate banking sector into

macroeconomics• Innovation: using accounting tables to build financial flow

models– Explicitly include bank accounts in macroeconomic

model• Firm Debt, Household Debt, Government Debt, etc.• Deposit accounts of Firms, Households, Government

too• Model endogenous money creation process…

A strictly monetary macroeconomic model• Monetary foundation enables explicit inflation modeling

– Price dynamics derived from lagged demand-supply convergence

1

1P

dP WPdt a s

– Monetary wages with employment, rate of change of employment, and inflation-compensation dynamics

1 ,0 11h

dd

d dW W P w P wt Ptd dt

– Simple model with• Bank lending to Firms only• Deposit and wage income to households• Generates stylized facts of Great

Moderation/Depression– Decline in employment & inflation volatility– Then sudden collapse into deflation & rising

unemployment

A strictly monetary macroeconomic model• Model equations:

( ) ( )

( )( ) ( )

( )( ) ( )

Prices an

Finance

d Wage

Sector

s

V L V

R r L r

L V Lr

L r R r

SD V L Dr L L D D

L r R r W B

D DD D

W

S SL L D D D D

B

B F B

dF B F I Ydt

BdF B F WI Y r F r F W Ldt

dW WW L r W

ddt

dtdB Br F r F r Wdt

dPdt

1

(1 )1 1( )

P

h

WPa s

dW d dW P w Pdt dt P dt

Production

Productivity &

R

RR

R

rRR

L D DLr

R

Y P YKYvYLaLN

IdK Kdt v

F r FK

Populationda adtdN Nd

Y W L

t

rP

Monetary Macroeconomic Model & Economic Data• Uncalibrated model output…• Smoothed actual US data…

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2

0

2

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8

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0

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InflationUnemploymentDebt to GDP

Inflation, Unemployment & Debt Ratio

Perc

ent o

f Wor

kfor

ce, -

Perc

ent p

.a.

Perc

ent o

f GD

P

0

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150160170180190200210220230240250260270280290300

InflationUnemploymentDebt to GDP

Inflation, Unemployment & Debt Ratio

Year; Source BLS

Perc

ent o

f Wor

kfor

ce, -

Perc

ent p

.a.

Perc

ent o

f GD

P

0

Monetary Macroeconomic Model & Economic Data• Income distribution dynamics matter

– Profit share behavior gives no warning of impending crisis

– Rising bank income a sign of danger…

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1

2

3

4

5

6

7

8

9

10ProfitBank Income

Profit and Bank Income Dynamics

Years

Perc

ent o

f GD

P

Extending Monetary Macroeconomic Modelling• Monetary modelling clearly adds to our understanding of

the economy• Preceding model still very simple & incomplete• New research agenda: building a platform for monetary

modelling• Extend existing “system dynamics” technology to handle

money flows• Innovation: accounting double-entry creates stock-flow

consistent monetary dynamics– Bank accounts in columns– Transactions between accounts in rows– Multiple banks—including Central Bank—easily modelled– Double-entry to ensure stock-flow consistency– Complex system of financial flow ODEs built with ease…

Extending Monetary Macroeconomic Modelling• Enter flows in double entry table:

• Define flows visually:

Extending Monetary Macroeconomic Modelling• Simulate numerically:

EndogenousMoney.mky

Extending Monetary Macroeconomic Modelling• Generate stock-flow consistent system of ODEs

automatically:B W

B

W

Firm Lend Int Wages Cons Cons RepayLoans Lend RepaySafe Int ConsWorkers Wages Cons

ddt

ddt

ddt

ddt

• Easily linked to physical production system• Extensible to multiple banks, multiple sectors, input-output

dynamics, international trade and financial flows…

Extending Monetary Macroeconomic Modelling• Multiple banks with Central Bank as clearing house…

Extending Monetary Macroeconomic Modelling• Multiple sectors, input-output dynamics can be modelled…

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0

5

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Capital GoodsConsumer GoodsAgricultureEnergy

The Rate of Profit in a Monetary Multisectoral Model of Production

Years

Prof

it/C

apita

(Per

cent

)

100 prK t( )

100 prC t( )

100 prA t( )

100 prE t( )

t

Conclusion• Economic crisis shows need for macro models to

incorporate financial sector, debt & money dynamics• Minsky’s Hypothesis provides insights missing in DSGE

models• Monetary macro models should be added to toolkit of

Treasuries, Central Banks• Technology to make monetary modelling straightforward

now exists– http://sourceforge.net/p/minsky/home/Home/

• Let’s jointly develop the technology & the models…