M 1 - Public Research Institute
Download
Report
Transcript M 1 - Public Research Institute
Modeling Cyclical Growth
Steve Keen
School of Economics & Finance
University of Western Sydney
The Project
• UNEP specification of non-equilibrium economic model
– Linked to CSIRO bio-physical model
• My brief:
– Take single sectoral model of cycles (Keen 1995 etc.)
– Single sectoral model of credit (Keen 2009 etc.)
– Combine into multi-sectoral cyclical model of credit
and production
• Never previously done
– Previous attempts at dynamic “IO” input-output
(multi-sectoral) models generally failed
• Fatal instabilities—negative prices etc.
– No previous attempts to model multisectoral
monetary dynamics
Trends in economic data
• Growth the norm in market economies...
7
Trends in Economic Data
Various: $, Index, Number
110
6
110
100000
10000
1000
100
10
1960
GDP
Employment
Prices
Debt
1970
1980
1990
Year
2000
2010
Cycles in economic data
• As are cycles...
– Previous data, de-trended:
Cycles in Economic Data
10
Detrended Percent change p.a.
GDP
Employment
5
Prices
Debt
0
5
10
1960
1970
1980
1990
Year
2000
2010
Conventional economic models
• “Neoclassical” General Equilibrium models
– Focus on trend
– Ignore cycles
– Ignore money
– Presume system is
• In equilibrium unless “shocked”
• Will return to equilibrium after “exogenous shock”
– Yet models have “dual instability” dilemma
• Prices or quantities or both must be unstable
• Effectively a barter system
– Money only affects relative prices & inflation
• Cycles assumed to be caused by noneconomic factors
– Agriculture/weather/sunspots... (meteors?)
Conventional economic models
• “The capitalistic economy is stable, and absent some
change in technology or the rules of the economic game,
the economy converges to a constant growth path with
the standard of living doubling every 40 years.”
– Edward C. Prescott (Nobel Prize 2004 for Real
Business Cycle Theory), 1999
• “As ... discussed in ... “The Dynamic General Equilibrium
Model,” the model features a representative household
[i.e., one only!] that chooses paths of consumption,
leisure, and investment to maximize utility. The paths of
TFP and population are exogenously given, and the agent
has perfect foresight over their values. We start the
model at date T0 = 1980 and let time run out to infinity...”
Conesa 2007
Conventional economic models
• “The model could be described as broadly new Keynesian
in its dynamic structure but with an equilibrating long
run.
• Activity is demand determined in the short run but supply
determined in the long run…
• The model will eventually return to a supply
determined equilibrium growth path in the absence of
demand or other shocks.”
– Australian Treasury TRYM Model (2001)
• Cycles treated as exogenous to model of economy...
Conventional economic models
• E.g. unemployment in Australian Treasury TYRM model
History
12.0
History taken as given
Convergence to
equilibrium assumed
11.0
10.0
% of Labour Force
Projection
Unemployment Rate
Dynamic Path
9.0
Steady State Path
8.0
Equilibrium long run
growth rate assumed
7.0
6.0
5.0
4.0
Mar-80
Mar-83
Mar-86
Mar-89
Mar-92
Mar-95
Mar-98
Mar-01
Mar-04
Mar-07
Mar-10
Conventional economic models
• Treatment of money and debt
– In general, money ignored
• “One thing which has not changed over the past five
years is the philosophy underpinning the model.
• It remains small, highly aggregated, empirically
based, and non-monetary in nature.” Australia’s
RBA (2005)
• Money “neutrality” assumed
– Affects price level but not real output
– Universally, private debt ignored
• Versus empirical data...
Endogenous Money
• “The fact that the transaction component of real cash
balances (M1) 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.”
– Kydland and Prescott (1990, p. 15. Emphasis added)
• 1990 analysis confirmed by more recent data
– E.g., leads and lags for Australia 1954-2009:
Endogenous Money
• Credit leads cycle with significant correlation
• All other variables lag or have low correlations:
Leading and Lagging Correlations
with business cycle
0.80
Correlation Coefficient
0.60
-15
0.40
Money Base
M1
0.20
M3
0.00
-10
-5
Credit
0
5
-0.20
-0.40
Lead or Lag in Months
10
15
Key role of private debt
• “Our tests produce a clear story about short-term
financing decisions in response to earnings and
investment...
– The leverage and debt regressions then confirm that,
for dividend payers, debt is indeed the residual
variable in financing decisions.
– Like dividend payers, non-payers primarily use debt to
absorb short-term variation in earnings and
investment.” (Fama & French 2000; emphases added)
Objectives for our economic model
• Non-equilibrium
– Economy itself inherently & endogenously cyclical
– Model had to represent this
• Multi-sectoral
– Many non-neoclassical endogenous cycle models
– But none to date were multi-sectoral
• Explicitly monetary
– Key role of money & debt shown in data
– Incorporate interplay of debt, money and cycles
• 3 key foundations
– Goodwin “Growth Cycle” model (1967)
– Minsky “Financial Instability Hypothesis”
– Graziani “Circuit Theory” model of credit creation
Foundations (1) Cycles: Goodwin’s “Growth Cycle”
• Capital K determines output Y via the accelerator:
K
1/3
Accelerator
Y
• Y determines employment L via productivity a:
Y
l
r
1
a
Labour Productivity
/
L
• L determines employment rate l via population N:
L
l
r
100
N
Population
/
l
• l determines rate of change of wages w via P.C.
+
.96
"NAIRU" 10
WageResponse
*
PhillipsCurve
dw/dt
• Integral
of w determines W (given initial value)
1
Initial Wage
dw/dt
+
1/S
+
Integrator
w
L
*
W
• Y-W determines profits P and thus Investment I…
Y
W
+
-
Pi
I
dK/dt
• Closes the loop:
1
Initial Capital
dK /dt
+
1/S
+
Integrator
Foundations (1) Cycles: Goodwin’s “Growth Cycle”
• Goodwin’s“Lokta-Volterra” model generates cycles:
K
1/3
Accelerator
l
r
1
a
Labour Productivity
1
Population
.96
"NAIRU"
+
10
WageResponse
Goodwin's cyclical growth model
1.50
/
L
/
Employment
Wages
1.25
l
1.00
.75
PhillipsCurve
*
dw/dt
.50
1
Initial Wage
Y
l
r
N
Y
w
L
+
1/S
+
Integrator
+
-
*
0
2
4
6
Time (Years)
8
10
W
Goodwin's cyclical growth model
1.3
Pi
I
1.2
dK/dt
3
Initial Capital
+
1/S
+
Integrator
Wages
1.1
1.0
.9
.8
.7
.9
.95
1
Employment
1.05
• Cycles
caused by
essential
nonlinearity:
• Wage rate
times
employment
• Behavioural
nonlinearities
not needed for
cycles;
• Instead,
restrain values
to realistic
levels
Foundations (2) Debt: Minsky’s “FIH”
• Only theory that predicts this financial crises:
– “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.”
(Can "It” Happen Again? A Reprise)
• Time-&-debt-aware 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…
Foundations (2) Debt: Minsky’s “FIH”
• Period of tranquility causes expectations to rise…
– “Stability—or tranquility—in a world with a cyclical past and
capitalist financial institutions is destabilizing.” (The
Financial Instability Hypothesis: A Restatement)
• Self-fulfilling expectations
– Decline in risk aversion causes increase in investment
• Investment expansion causes economy to grow faster
– Asset prices rise
• speculation on assets profitable
– Increased willingness to lend increases money supply
• Money supply endogenous money, not under Fed control
– 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
Foundations (2) Debt: Minsky’s “FIH”
• Eventually:
– 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
• 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...
Foundations (3): Endogenous money
• Fundamental Endogenous Money insight
– “Loans create Deposits”
• Reverse of “Money Multiplier” model
• Suggested directly modeling bank credit creation via
account dynamics
– Simple model of “Wicksellian” pure credit economy
• No government sector or fiat money (yet)
• Explicitly monetary model
• “Double-entry book-keeping” meets symbolic math
Foundations (3): Endogenous money
• New methodology for dynamic modelling
– Table where each column represents a stock
– Each row represents relations between system states…
Dynamic System
“System States”
Flows
Stock A
Stock B
…
Stock Z
Accounting
+ Flow 1
- Flow 1
…
…
Sum(=0)
…
…
+ Flow 2
- Flow 2
Sum
d
dt
A t
d
dt
B t
d
dt
Z t
• To generate the model, symbolically add up each column
– Sum of column is differential equation for stock
• Continuous time, not “discrete” time
• Strictly monetary model of pure credit multicommodity production economy developed…
Foundations (3): Endogenous money
• Input system as table:
"Type"
0
1
1
1
0
"Account"
"Bank Reserves" "Firm Loan" "Firm Deposit" "Worker Deposit" "Bank Income"
"Account"
BR( t)
FL( t)
FD( t )
W D( t )
BI( t)
0
A
0
0
0
"Compound Interest"
"Pay Interest on Loan"
0
B
B
0
B
Interest
flows:
bank<―>firm
"Interest on Deposit"
0
0
C
0
C
S2
"Wages"
0
0 firm―>workers
D
D
0
Wage
flows:
"Interest on Deposit"
0
0
0
E
E
Interest
flows:
bank―>workers
"Consumption"
0
G
F
G
Consumption
flows:0 bank &F workers―>firms
"Repay Loan"
H
H
H
0
0
Debt
repayment
flows:
firms
―>bank
"Lend Reserves"
I
I
I
0
0
Reserve
relending
flows:
bank―>firms
"New Money"
0
J
J
0
0
New Money/Debt flows: bank<―>firms
• Symbolic substitutions for placeholders above:
• E.g., A is “loan interest rate times outstanding debt”
A rL FL t
• Time lags used for behavioural variables
Foundations (3): Endogenous money
• Simple code develops
mode automatically:
SystemODEs ( x)
Functions submatrix( x2 2 1 cols ( x) 1)
Equations submatrix( x3 rows ( x) 1 1 cols ( x) 1)
for i 0 cols ( Functions ) 1
E
i
d
Functions
i
dt
Equations i
return E
d
SystemODEs S2 FD( t)
d t
R
L
FL( t)
FD( t)
BR( t)
d
FL( t)
L
M
R
dt
FD( t) ( s 1)
W D( t )
FL( t)
FD( t)
BR( t)
BI( t)
rD FD( t) rL FL( t)
S
W
L
M
R
B
FD( t) ( s 1)
W D( t )
d
W D( t) rD W D( t)
S
W
dt
BI( t)
d
BI( t ) rL FL( t ) rD FD( t) rD W D( t)
B
dt
d
BR( t)
dt
FL( t)
BR( t)
Modelling a Credit Crunch
• Simple production model linked to financial flows
Q a L
– Output is Labour times productivity
1 s FD
– Labour is Money Wages flow divided by
L
S W
Money Wage rate
– Wage set by Phillips curve unemployment- 1 d
L
W Ph
W dt
money wage change function
N
– Price (necessary link between $ accounts and
physical output) lagged convergence to markup
d
1
W
over monetary cost of production
P P
dt
P
a 1 s
• Single sectoral model generates stable dynamics
• Can be used to consider some policy questions
• But no cycles as yet
• Policy example—stimulus to overcome credit crunch
Modelling a Credit Crunch
• What’s better? Stimulus to lenders or debtors?
Bank Assets
5000
$ billion injection into economy
Government stimulus as 1 year duration pulse
100
Bank Liabilities (Deposits)
Loans
Unlent Reserves
10000
4000
8000
3000
6000
2000
4000
1000
2000
50
0
0
10
20
30
Time (Years)
40
50
0
60
URate
Firms
Households
Banks
0
10
InfRate
20
B_D
H_D
Unemployment
25
0
20
22
24
26
28
30
Time (Credit Crunch at t=25)
• Injected into either
BR (Bank Reserves)
or FD (Firm Deposits)
in simulation
• Stimulus far more
effective if given to
debtors
40
50
60
40
50
60
F_D
Inflation
No Stimulus
Bank Injection
Borrowers Injection
20
30
Time (Years)
10.0
7.5
No Stimulus
Bank Injection
Borrowers Injection
5.0
2.5
15
0
10
-2.5
-5.0
5
-7.5
0
0
10
20
30
Time (Years)
40
50
Parameters &
Initial Conditions
Financial
System
60
StimBank
0
0
10
20
3
25
30
Time (Years)
Debt to Output Ratio
25
NoStimulus
Production
System
-10.0
No Stimulus
Bank Injection
Borrowers Injection
20
C_size
tCC
15
StimFirm
StimFirm
F_L
Y
l
r
10
1.
5
/
100
60.
0
0
10
20
30
40
Time (Years)
50
60
Producing a multi-sectoral nonequilibrium model
• Minsky model
– Goodwin cycles
– Debt “ratchets up” of in series of cycles
• With “Ponzi lending”, tends towards Depression
– But implicit money only (debt to GDP ratio)
• Graziani model
– Explicit money
– Monetary determination of equilibrium output
– But no cycles
• Blending two models necessitates multi-sectoral model
– Capital sector for purchases of investment goods
– Easily built using “Table to Dynamic Model” technology
A Multi-sectoral monetary model
• More complicated table (2 sector version shown here):
"Type"
0
1
1
1
1
1
1
"Name"
"BR"
"K1 L" "K2 L" "C1 L" "C2 L"
"K1 D"
"K2 D"
"Symbol"
BR( t)
FLK1( t) FLK2( t) FLC1( t ) FLC2( t)
FDK1( t)
FDK2( t)
0
A
B
C
D
0
0
"Compounding Debt"
"Deposit Interest"
0
0
0
0
0
E
F
"Investment"
0
0
0
0
0
I ( J K ) J ( I L)
"Wages"
0
0
0
0
0
M
N
S1 "Intersectoral Demand"
0
0
0
0
0
Q
R
"Interest Workers"
0
0
0
0
0
0
0
"Pay Interest"
0
V
W
X
Y
V
W
0
0
0
0
0
Z
AA
AB
"Consumption"
AF AG AH AI
AF
AG
AH
AI
AF
AG
"Repay Loans"
"Recycle Reserves" ( AJ AK AL AM) AJ
AK
AL
AM
AJ
AK
0
AN
AO
AP
AQ
AN
AO
"New Money"
FDC1( t)
FDC2( t)
W D( t)
BI( t)
0
0
0
0
G
H
0
( E F G H)
K
L
0
0
O
P
M N O P
0
S ( Q T)
T ( R S)
0
0
0
0
U
U
X
Y
0
V W X Y
Z AC AD AE AC AA AB AD AE
AD
AE
2
2
AH
AI
0
0
AL
AM
0
0
AP
AQ
0
0
1
1
1
0
"C1 D"
"C2 D"
"W D"
"B I"
• Capital and Consumer Goods Sectors
• All sectors in 2 halves to force recording of intra FDK1( t)
sectoral monetary purchases
pr prK ( t )
• Investment & inter-sectoral demand I
pr prK ( t) FDK2( t)
• Time lags are time-varying
functions of rate of profit rather
than constant parameters
pr prK ( t )
pr prK ( t )
J
F
K Deposits pr prC( t) FDC1( t)
L
pr ( t) pr prC( t)
pr C
FDC2( t)
pr ( t)
pr C
A Multi-sectoral monetary model
• More complex financial model results
– Constrained by nonlinear behavioural relations
Money relending as function of rate of profit
Time lag relending existing inactive money stock
50
0
50
80
90
100
0
110
Employment Rate (percent normal participation rate)
5
10
Rate of profit in percent
Lag in new money creation as function of rate of profit
Investment time lag as function of rate of profit
14
Time lag in years for doubling of money
10
Time lag for doubling of capital stock
50
Loan repayment time lag as function of rate of profit
Time lag for loan repayment in years
Rate of change of Money Wages percent
Wage Change Function
8
6
4
2
0
0
5
Rate of profit in percent
12
10
8
10
6
0
5
Rate of profit in percent
40
30
20
10
0
0
5
Rate of profit in percent
10
• (Nonlinear functions
not essential for
dynamics but
constrain simulation
values to more
realistic ranges)
10
A Multi-sectoral monetary model
• Allied to lagged Goodwin growth cycle production model
– Investment minus Depreciation determines Capital
d
KK1( t)
dt
– Output function of capital stock
– Employment function of output
FDK1( t)
pr prK ( t) PK1( t)
KK1( t)
QK
vK
QK1( t)
1
d
LK1( t)
LK1( t)
LK
aK ( t )
dt
d
QK1( t)
dt
1
QK1( t)
KK1( t)
• Model of financially driven cyclical economy
• Simulations shown here lead to sustained cycles
• (No speculative debt in model as yet)
• Overall system very complex
• But easily simulated in modern software
• Scales indefinitely (more sectors easily added)
1
A Multi-sectoral monetary model
• Model requires minimum of
– 4n+3 financial ODEs
– 2n Loan & 2n Deposit
– Bank Income
– Bank Reserves
– Household Deposit
• 5n sectoral equations
– capital, output, labour,
prices, productivity
• 1 population equation
• 40 ODEs in this 4 sector
model
Given
d
BR( t )
dt
FLA1( t)
RL prA ( t)
BR( t)
d
FLK1( t)
dt
RR prK( t)
d
FLK2( t)
dt
RR prK( t)
BR( t)
RR prC( t)
BR( t)
d
FLC2( t)
dt
RR prC( t)
RR prA ( t)
BR( t)
d
FLA2( t)
dt
RR prA ( t)
d
FLE1( t)
dt
RR prE( t)
BR( t)
BR( t)
d
FLE2( t)
dt
RR prE( t)
d
FDK2( t)
dt
RR prK( t)
BR( t)
FLC2( t)
RL prC( t)
RL prA ( t)
FLA2( t)
RL prA ( t)
FLE1( t)
RL prE( t )
FLE2( t)
RL prE( t )
NM prK( t)
FLK2( t)
NM prK( t)
FLC1( t )
NM prC( t)
FLC2( t )
FLA1( t)
FLK1( t)
NM prE( t)
FLA2( t)
RL prA ( t )
FLC1( t)
RL prC( t )
FLC2( t)
RL prC( t )
FLE1( t)
RL prE( t)
FLE2( t)
RL prE( t)
FLK1( t)
RL prK( t)
FLK2( t)
RL prK( t)
rL FLK1( t) LK1( t) W M ( t)
rL FLK2( t) LK2( t) W M ( t)
FDA1( t )
pr prA ( t)
FDA2( t )
pr prA ( t)
FDC1( t)
pr prC( t )
FDC2( t)
pr prC( t )
FDE1( t)
pr prE( t)
FDE2( t)
pr prE( t)
FDK1( t)
pr prK( t)
FDK1( t)
pr prK( t)
FDK2( t)
pr prK( t)
FDK2( t)
pr prK( t)
FLK1( t)
RL prK( t)
FLK2( t)
RL prK( t)
FLK1( t)
NM prK( t)
FLK2( t)
NM prK( t)
FDK1( t)
CKA
FDK2( t)
CKA
FDK1( t)
CKC
FDK2( t)
CKC
FDK1( t)
FDK1( t) rD FDK1( t) KA LK1( t) W M ( t) KC LK1( t) W M ( t) KE LK1( t) W M ( t)
CKE
FDK2( t)
RR prA ( t)
d
FDA2( t)
dt
RR prA ( t)
d
FDE1( t)
dt
RR prE( t)
d
FDE2( t)
dt
RR prE( t)
BR( t)
BR( t)
BR( t)
BR( t)
FDC2( t)
rL FLC2( t ) LC2( t) W M ( t)
pr prC( t)
FDA1( t)
rL FLA1( t) LA1( t) W M ( t)
pr prA ( t)
FLC2( t)
RL prC( t)
FLA1( t )
RL prA ( t)
NM prC( t )
BI( t)
FLA1( t)
FLC2( t)
NM prA ( t)
2 CBC
BI( t)
2 CBA
FDA2( t)
FDC2( t)
CAC
FDA1( t)
CAA
FDC1( t)
CCA
CCC
FDA2( t)
CCC
FDA1( t)
CAA
FDC2( t)
CCE
FDC1( t )
CAC
FDC2( t)
CCA
FDE2( t)
CEC
FDA1( t)
CAE
FDK2( t )
FDE1( t)
2 CWC
FDK1( t)
CEA
W D( t)
CKC
CKA
FDE1( t)
rL FLE1( t ) LE1( t) W M ( t)
pr prE( t)
FLE1( t)
RL prE( t)
W D( t )
2 CWA
FLE1( t)
NM prE( t)
BI( t)
2 CBE
FDA1( t)
CAE
FDE1( t)
FDC1( t)
CEA
CCE
FDE1( t)
CEC
FDE1( t)
CEE
FDE2( t)
CEE
FDK1( t)
CKE
W D( t)
LK1( 0)
PK1( 0)
FDK1( t)
QK2( 0)
1
QK
QK1( t)
1
vK
KK1( t)
Population Growth
d
Pop ( t)
dt
Consumption 2
KC1( 0)
KC2( 0)
PK10
1
PK
PK2( 0)
PK1( t)
aK( t) 1 s K
W M( t)
1
d
W M( t)
dt
( t)
aK( t)
FDA10
FDA2( 0)
FDA20
FDE1( 0)
FDE10
BI( 0)
FDE20
W D0
BI0
QK2( t)
1
vK
KK2( t)
LC1( 0)
QK2( t)
LK2( t)
LK
aK( t)
PK
aK( t) 1 s K
W M( t)
QC2( 0)
1
QC
QC1( t)
1
vC
KC1( t)
PC
PC1( t)
aC( t) 1 s C
W M( t)
KC2( t)
QC2( t)
1
vC
QA1( 0)
KC2( t)
LA10
1
PC
PC2( t)
1
PA1( 0)
aC( t) 1 s C
W M( t)
LA
LA1( t)
QA1( t)
aA ( t )
Capital
KK( 0)
KK10 KK20
KK1( t ) KK2( t)
Pop ( 0)
d
aC( t)
dt
aC( t)
aC( 0)
d
aA ( t )
dt
aC0
aA ( t)
Agriculture
Energy
KA10 KA20
KA ( 0)
KA ( t)
KA1( t) KA2( t)
KE( 0)
KE( t )
KE10 KE20
KE1( t) KE2( t)
Sectoral Rates of Profit
prC( t)
prC( 0)
100 rL FLK1( t) FLK2( t) rD FDK1( t) FDK1( t) FDK2( t) W M ( t) LK1( t) LK2( t) PK1( t) QK1( t) QK2( t) KA W M ( t) LA1( t) LA2( t) KC W M ( t) LC1( t) LC2( t) KE W M ( t) LE1( t) LE2( t)
prK( 0)
KK1( t) PK1( t) KK2( t) PK2( t)
100 rL FLK10 FLK20 rD FDK10 FDK10 FDK20 W M0 LK10 LK20 PK10 QK10 QK20 KA W M0 LA10 LA20 KC W M0 LC10 LC20 KE W M0 LE10 LE20
KK10 PK10 KK20 PK20
100 rL FLC1( t) FLC2( t) rD FDC1( t) FDC1( t) FDC2( t) W M ( t) LC1( t) LC2( t) PC1( t) QC1( t) QC2( t) CA W M ( t) LA1( t) LA2( t) CC W M ( t) LC1( t) LC2( t) CE W M ( t) LE1( t ) LE2( t)
KC1( t ) PK1( t) KC2( t) PK2( t)
100 rL FLC10 FLC20 rD FDC10 FDC10 FDC20 W M0 LC10 LC20 PC10 QC10 QC20 CA W M0 LA10 LA20 CC W M0 LC10 LC20 CE W M0 LE10 LE20
KC10 PK10 KC20 PK20
100 rL FLA1( t) FLA2( t) rD FDA1( t) FDA1( t ) FDA2( t) W M ( t) LA1( t) LA2( t) PA1( t) QA1( t) QA2( t) AA W M ( t) LA1( t) LA2( t) AC W M ( t) LC1( t) LC2( t) AE W M ( t) LE1( t) LE2( t )
prA ( t)
prA ( 0)
KA1( t) PK1( t) KA2( t) PK2( t)
100 rL FLA10 FLA20 rD FDA10 FDA10 FDA20 W M0 LA10 LA20 PA10 QA10 QA20 AA W M0 LA10 LA20 AC W M0 LC10 LC20 AE W M0 LE10 LE20
KA10 PK10 KA20 PK20
100 rL FLE1( t) FLE2( t) rD FDE1( t) FDE1( t) FDE2( t) W M ( t) LE1( t) LE2( t) PE1( t) QE1( t) QE2( t) EA W M ( t) LA1( t) LA2( t) EC W M ( t) LC1( t) LC2( t) EE W M ( t) LE1( t) LE2( t)
prE( t)
prE( 0)
KE1( t ) PK1( t) KE2( t) PK2( t)
d
PA2( t)
dt
aA ( 0)
Pop 0
KC1( t) KC2( t)
prK( t)
Energy 1
KA20
KE1( 0)
FDA2( t)
pr prA ( t) PK2( t)
KA2( t)
QA20
QE1( 0)
1
Q ( t)
KA2( t)
QA A2
vA
1
LA20
1
LA
1
d
QE1( t)
dt
LE1( 0)
LA2( t)
QA2( t)
aA ( t )
d
LE1( t)
dt
PA20
PA
d
KE1( t)
dt
W M( t)
aA ( t ) 1 s A
PA2( t)
PE1( 0)
d
PE1( t)
dt
Energy 2
KE10
KE2( 0)
FDE1( t)
pr prE( t) PK1( t)
KE1( t)
QE10
QE2( 0)
1
QE
QE1( t)
1
vE
KE1( t)
LE10
QE1( t)
LE1( t)
LE
aE( t)
d
LE2( t)
dt
PE10
1
d
QE2( t)
dt
LE2( 0)
1
PE
d
KE2( t)
dt
PE2( 0)
W M( t)
aE( t) 1 s E
PE1( t)
d
PE2( t)
dt
KE20
100 rL FLE10 FLE20 rD FDE10 FDE10 FDE20 W M0 LE10 LE20 PE10 QE10 QE20 EA W M0 LA10 LA20 EC W M0 LC10 LC20 EE W M0 LE10 LE20
KE10 PK10 KE20 PK20
aA0
d
aE( t)
dt
aE( t)
aE( 0)
FDE2( t)
pr prE( t ) PK2( t)
KE2( t)
QE20
1
QE
QE2( t)
1
vE
KE2( t)
LE20
QE2( t)
LE2( t)
LE
aE( t)
1
PE20
1
PE
Pop ( t)
aK0
KC10 KC20
KC( 0)
Ph ( ( t) ) W M ( t )
Consumer
KC( t)
d
LA2( t)
dt
PA2( 0)
W M( t)
1
P ( t)
PA A1
aA ( t ) 1 s A
Aggregate Sectoral Capital Stock
KK( t)
d
QA2( t)
dt
LA2( 0)
PA10
d
PA1( t)
dt
d
KA2( t)
dt
QA2( 0)
1
Q ( t)
KA1( t)
QA A1
vA
d
LA1( t)
dt
PC20
KA1( t)
1
1
d
PC2( t)
dt
QA10
LA1( 0)
QC2( t)
LC2( t)
LC
aC( t)
KA2( 0)
FDA1( t)
pr prA ( t) PK1( t)
d
QA1( t)
dt
Agriculture 2
KA10
d
KA1( t)
dt
LC20
PC2( 0)
1
1
QC
d
LC2( t)
dt
PC10
QC20
LC2( 0)
QC1( t)
LC1( t)
LC
aC( t)
1
KA1( 0)
FDC2( t)
pr prC( t ) PK2( t)
d
QC2( t)
dt
LC10
d
PC1( t)
dt
KC20
d
KC2( t)
dt
KC1( t)
QC10
d
LC1( t)
dt
PC1( 0)
PK2( t)
FDC1( t)
pr prC( t ) PK1( t)
d
QC1( t)
dt
1
1
KC10
LK1( t) LK2( t) LC1( t) LC2( t) LA1( t) LA2( t) LE1( t) LE2( t)
aK( 0)
Pop ( t)
QK
PK20
d
PK2( t)
dt
W M0
QC1( 0)
LK20
d
LK2( t)
dt
0
d
aK( t)
dt
Energy
FDC20
FDA1( 0)
Consumption 1
d
KC1( t)
dt
KK2( t)
QK20
LK2( 0)
QK1( t)
LK1( t)
LK
aK( t)
1
FDK2( t)
pr prK( t) PK2( t)
d
QK2( t)
dt
LK10
W M ( 0)
Technical Change
Agriculture
FDC2( 0)
KK20
d
KK2( t)
dt
KK1( t)
QK10
d
PK1( t)
dt
( 0)
KK2( 0)
pr prK( t) PK1( t)
d
LK1( t)
dt
Consumer Goods
FDC10
Agriculture 1
d
QK1( t)
dt
Capital Goods
FDK20
FDC1( 0)
FDE1( t) rD FDE1( t) AE LA1( t) W M ( t) EA LE1( t) W M ( t) CE LC1( t) W M ( t) EC LE1( t) W M ( t) EE LE1( t) W M ( t) EE LE2( t) W M ( t) KE LK1( t) W M ( t)
2 CWE
QK1( 0)
Employment Rate
FDK10
FDK2( 0)
Capital 2
KK10
d
KK1( t)
dt
Wages
FLE20
FDA1( t) rD FDA1( t) AA LA1( t) W M ( t) AA LA2( t) W M ( t) AC LA1( t) W M ( t) CA LC1( t) W M ( t) AE LA1( t) W M ( t ) EA LE1( t) W M ( t) KA LK1( t) W M ( t)
KK1( 0)
Prices
FLE2( 0)
FDE2( t)
FLE2( t)
FLE2( t)
BI( t)
FDA2( t)
FDE2( t)
FDC2( t)
FDE2( t)
FDE1( t)
FDE2( t)
FDK2( t)
W D( t)
rL FLE2( t ) LE2( t) W M ( t)
FDE2( t) rD FDE2( t) AE LA2( t) W M ( t) EA LE2( t) W M ( t) CE LC2( t) W M ( t) EC LE2( t) W M ( t) EE LE1( t) W M ( t) EE LE2( t) W M ( t) KE LK2( t) W M ( t)
pr prE( t)
RL prE( t)
NM prE( t)
2 CBE
CAE
CEA
CCE
CEC
CEE
CEE
CKE
2 CWE
Capital 1
Employment
FLE10
FDC2( t) rD FDC2( t) AC LA2( t) W M ( t) CA LC2( t) W M ( t) CC LC1( t) W M ( t) CC LC2( t) W M ( t) CE LC2( t ) W M ( t) EC LE2( t) W M ( t) KC LK2( t) W M ( t)
BI( t)
BI( t)
BI( t)
d
BI( t) rL FLA1( t) rL FLA2( t) rL FLC1( t) rL FLC2( t) rL FLE1( t) rL FLE2( t) rL FLK1( t) rL FLK2( t)
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) W D( t) rD W D( t)
CBA
CBC CBE
dt
Production system
Output
FLA20
FLE1( 0)
FDA2( t)
FLA2( t )
FLA2( t)
BI( t)
FDA1( t)
FDA2( t)
FDA2( t)
FDC2( t )
FDA2( t)
FDE2( t)
FDK2( t)
W D( t )
rL FLA2( t) LA2( t) W M ( t)
FDA2( t) rD FDA2( t) AA LA1( t) W M ( t) AA LA2( t) W M ( t) AC LA2( t) W M ( t) CA LC2( t) W M ( t) AE LA2( t) W M ( t ) EA LE2( t) W M ( t) KA LK2( t) W M ( t)
pr prA ( t)
RL prA ( t)
NM prA ( t)
2 CBA
CAA
CAA
CAC
CCA
CAE
CEA
CKA
2 CWA
W D( t)
W D( t)
W D( t)
LA1( t) W M ( t) LA2( t) W M ( t) LC1( t) W M ( t) LC2( t ) W M ( t) LE1( t) W M ( t) LE2( t) W M ( t) LK1( t) W M ( t) LK2( t) W M ( t)
W D( t) rD W D( t)
CWA
CWC CWE
Capital Stock
FLA10
FLA2( 0)
W D( 0)
d
FDA1( t)
dt
FLC20
FDE2( 0)
FDK2( t) rD FDK2( t) KA LK2( t) W M ( t) KC LK2( t) W M ( t) KE LK2( t) W M ( t)
CKE
RR prC( t)
FLC10
FLC2( 0)
d
FDC2( t)
dt
FLK20
FLC1( 0)
FDK1( 0)
FDC1( t)
FLC1( t)
FLC1( t)
BI( t)
FDA1( t)
FDC1( t)
FDC1( t )
FDC2( t)
FDC1( t)
FDE1( t)
FDK1( t )
W D( t)
rL FLC1( t ) LC1( t) W M ( t)
FDC1( t) rD FDC1( t) AC LA1( t) W M ( t) CA LC1( t) W M ( t) CC LC1( t) W M ( t) CC LC2( t) W M ( t) CE LC1( t ) W M ( t) EC LE1( t) W M ( t) KC LK1( t) W M ( t)
RR prC( t)
pr prC( t)
RL prC( t)
NM prC( t )
2 CBC
CAC
CCA
CCC
CCC
CCE
CEC
CKC
2 CWC
BR( t)
FLK2( 0)
FLA1( 0)
NM prA ( t)
FLE2( t)
FLA2( t)
BR( 0) BR0
FLK1( 0) FLK10
2 BR( t)
RR prA ( t )
NM prE( t)
FLA1( t)
FLE1( t)
RR prK( t)
NM prA ( t)
NM prC( t)
2 BR( t)
d
FDC1( t)
dt
d
W D( t)
dt
BR( t)
RL prC( t)
RR prE( t)
FLC1( t)
BR( t)
RR prK( t)
FLK2( t )
RL prK( t)
d
FDK1( t)
dt
RL prK( t)
2 BR( t)
FLK1( t )
BR( t)
d
FLA1( t)
dt
RR prC( t)
BR( t)
d
FLC1( t)
dt
2 BR( t)
aE0
W M( t)
aE( t) 1 s E
PE2( t)
A Multi-sectoral monetary model
• Notional Sectors in system shown here:
– Capital Goods
– Consumer Goods
– Agriculture
– Energy
• Generates complex endogenous cycles in income shares,
output, credit, employment—just like actual economy
– No need for “exogenous shocks”
• Though can also be added in future
• Not yet fitted to empirical data
– But qualitative behaviour of model matches “stylised
facts” of (credit-driven) business cycle
A Multi-sectoral monetary model of production
• Endogenous cycles...
Real Rate of Economic Growth
The Rate of Profit in a Monetary Multisectoral Model of Production
8
15
6
Profit/Capita (Percent)
Percent p.a.
10
4
2
5
0
Capital Goods
Consumer Goods
Agriculture
Energy
0
2
20
5
25
30
35
0
20
40
60
40
Years
• Cycles similar to stylised facts of business cycle
• Long accelerating boom
• Sudden slump
• Tepid recovery before next boom
80
100
A Multi-sectoral monetary model of production
10.0
Unemployment Rate
Dynamic Path
9.0
Steady State Path
8.0
7.0
6.0
5.0
4.0
Mar-80
Mar-83
Mar-86
Mar-89
Mar-92
Mar-95
Mar-98
Mar-01
Real Rate of Economic Growth
Change in Nominal Credit and Nominal GDP
60
Projection
11.0
% of Labour Force
• With equilibrium models
– History cyclical
– The future equilibrium...
• With non-equilibrium
model, projections look like
history
• Cycles in past & future
History
12.0
8
40
GDP
Debt
6
40
20
Percent p.a.
Percent change p.a.
30
4
2
20
10
0
0
20
25
30
35
0
40
2
0
20
40
60
80
Mar-04
Mar-07
Mar-10
A Multi-sectoral monetary model of production
• Crucial role of credit
– Change in credit leads cycle
Debt and Growth Dynamics
7
6
40
Rate of Growth
Change in Debt Ratio (RHS)
8
150
Rate of Growth
Debt Ratio (RHS)
30
5
20
4
10
3
0
2
10
6
100
4
2
1
20
0
30
1
40
2
20
25
30
35
50
0
50 2
40
20
25
30
35
0
40
A Multi-sectoral monetary model of production
• Income distribution cycles...
Distribution of National Income
80
10
70
0
85
Wages
Profit (RHS)
Interest (RHS)
Rate of Growth (RHS)
90
95
10
100
100
30
95
25
90
20
85
15
80
10
75
5
70
0
65
5
60
10
55
94
96
98
100
Employment Rate
Wages
Profit
Interest
102
15
104
Capitalist & Banker Shares
20
Wages Share of Output
Wages Share
90
60
80
Income Distribution Limit Cycles
30
Profit & Interest Share and Rate of Growth
100
A Multi-sectoral monetary model of production
• Crucial role of monetary variables
Bank Assets & Liabilities
110
15
110
14
110
13
110
12
110
11
110
10
Bank Assets & Liabilities
110
8
Loans
Bank Reserves
Deposits
110
7
Loans
Deposits
Bank Reserves (RHS)
110
7
110
6
110
6
110
5
110
5
9
110
8
110
7
110
6
110
5
110
10000
1000
100
0
20
40
60
80
100
20
25
30
• Simulation show here generates “stable instability”
• Cycles but not breakdown
• Different parameters can generate
• Convergence to stability; or
• Financial collapse (Great Depression)
35
10000
A Multi-sectoral monetary model of production
• Crucial characteristic that cycles are endogenous
– General Disequilibrium as hallmark of a good model
• “Instability is an observed characteristic of our economy.
• For a theory to be useful as a guide to policy for the
control of instability, the theory must show how
instability is generated.
• The abstract model of the neoclassical synthesis cannot
generate instability...”
– (Minsky, “Can "It“ Happen Again? A Reprise”)
Future development of model
• First “meteorological” model of capitalism
– Causal dynamics rather than equilibrium assumptions
– Realistic non-equilibrium multi-sectoral production
– Designed for rising realism/complexity over time
• Parameter calibration of nonlinear, disequilibrium model
– Two approaches to data fitting feasible
• Fit functions and selected empirical data
• Fit overall model and generate realistic nonlinear
functions, lags, etc. from that
• Develop to generate alternative scenarios
– All will include cyclical, non-equilibrium future
• Enable automatic generation of higher-dimensional
multisectoral models