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Behavioural Finance
Lecture 12 Part 2
The Global Financial Crisis
Empirical Data & Modelling
Modelling financial instability
• Financial Instability Hypothesis only theory that makes
sense of this data
• Model in previous lecture
– Had only “implicit” money
– Omitted Ponzi Finance
– Omitted role of deflation
• This lecture
– Model with Ponzi finance
– Combining Minsky and the Circuit
• Full monetary model of capitalism
Modelling financial instability
• Firstly: last week’s Goodwin model in equations
K
• Causal chain: capital determines output
Y
• Output determines employment
v
Y
L
a
• Employment rate determines rate of
change of wage (Phillips curve PH)
1 d
L
PH   
w
w dt
N 
• Wages (w.L) determine profit P
Y w L  P
• Profit P determines investment = rate
of change of capital
I P     K 
d
K
dt
1d
1 d
• Population growth & technical change
a  ;
N
a dt
N dt
drive the system:
Modelling financial instability
• System has 4 “differential
equations”:
• Some calculus needed to work
out other terms:
d
Y  g Y
dt
d
Wage level:
w  PH     w
dt
d
Productivity:
a   a
dt
d
Population:
N   N
dt
Growth rate:
 I  r 

1 d
1 d K 1 d
1
g
Y

K    I  r   Y    K   
 
K dt v K dt
Y dt
K
 v

v
• Full system is…
Modelling financial instability
• 4 differential equations & 7 algebraic relations
System States
Algebraic Relations
d
Y( t)
dt
g ( t)  Y( t)
Y( 0)
Y0
P( t)
Y( t)  W ( t)
P( 0)
P0
d
w ( t)
dt
PH(  ( t) )  w ( t)
w ( 0)
w0
W ( t)
w ( t)  L( t)
W ( 0)
W0
d
a( t )
dt
d
N ( t)
dt
 a( t)
  N ( t)
a( 0)
N ( 0)
a0
N0
L( t)
 ( t)
( t )
 r( t)
Y( t)
a( t )
L( t)
N ( t)
w ( t)
a( t )
P( t)
v  Y( t)
 I r( t)   
g ( t) 
  
 v  
L( 0)
L0
 ( 0)
0
( 0)
0
 r( 0)
g ( 0)
 r0
g0
• Simulating this, gives same cyclical pattern as last week’s
“systems engineering” model
Modelling financial instability
• Cyclical growth…
Output
• Limit Cycles
cycle
in wages
& employment
in employment
and wages
6000
110
4000
90
80
2000
70
0
Employment Rate %
Wages share %
0
20
40
60
80
100
Income & Employment Limit Cycle
0
20
40
60
80
Years
• Then add in debt…
1
0.9
0.8
0.7
0.6
0.8
60
Year
1.1
Wages Share of Output
Real output
100
0.85
0.9
0.95
Employment Rate
1
1.05
100
Modelling financial instability
• Firms borrow when desired investment exceeds profits:
Change in debt:
d
D I P
dt
• Profit now net of interest payments
P  Y W  r D
D
• A new system state: debt to GDP ratio d 
Y
• Very different dynamics but stable system
110
Employment vs wages share
110
100
Wages share %
100
90
80
80
70
70
60
90
60
80
0
20
40
60
80
85
90
95
100
Employment Rate %
Employment %
Wages share %
100
105
Modelling financial instability
• Now add in Ponzi Finance
– Borrowing $ to speculate on rising asset prices
– Adds to debt without adding to productive capital
• Modelled as a function of rate of economic growth
– Higher rate of growth, higher level of speculation
Ponzi Finance:
1 d
P    g 
Y dt
• Aggregate debt now includes Ponzi Finance
d
Change in debt:
D  I  P  P
dt
Modelling financial instability
• Now a six-dimensional model:
System States
Algebraic Relations
d
Y( t)
dt
g ( t)  Y( t)
Y( 0)
Y0
P( t)
Y( t)  W ( t)  r( t)  ( D( t) )
d
w ( t)
dt
PH(  ( t) )  w ( t)
w ( 0)
w0
W ( t)
w ( t)  ( L( t) )
d
a( t )
dt
d
N ( t)
dt
d
D( t)
dt
d
P( t)
dt
 a( t)
a( 0)
  N ( t)


I  r( t)  Y( t)  P( t)  P( t)
Ponzi ( g ( t) )  Y( t)
N ( 0)
D( 0)
P( 0)
a0
N0
D0
P0
L( t)
 ( t)
( t )
 r( t)
g( t)
Y( t)
a( t )
L( t)
N ( t)
W ( t)
Y( t)
P( t)
v  Y( t)
 I  r( t)   

  
 v  
d( t)
• Very different dynamics…
Y( t)
• With Ponzi switch set to zero, same as before
• With Ponzi “on”…
P( 0)
P0
W ( 0)
W0
L( 0)
L0
 ( 0)
0
( 0)
0
 r( 0)
 r0
g ( 0)
g0
d ( 0)
d0
D( t)
Modelling financial instability
• Dynamics
– Borrow money to finance investment during a boom
• Repay some of it during a slump
– Debt/ Income ratio rises in series of booms/busts
– Eventually one boom where debt accumulation passes
“point of no return”…
Employment Rate
Real Output
1500
No Speculation
Ponzi Finance
100
Per cent
1000
90
500
80
No Speculation
Ponzi Finance
70
0
0
10
20
30
40
0
10
20
30
50
Years
40
50
Modelling financial instability
• Driving force is debt to GDP ratio…
Debt to GDP Ratio
1200
No Speculation (LHS)
Ponzi Finance (RHS)
Per cent of GDP
0
1000
 20
800
 40
600
 60
400
 80
200
 100
 120
0
0
10
20
30
40
 200
50
Per cent of GDP
20
Are We “It” Yet?
• Can summarise model’s equations in 4 “stylised facts”
– Employment rises if growth exceeds productivity +
population increase
– Wages share grows if wage rises exceed productivity
– Bank lend money to finance investment & speculation
– Speculation rises when growth rises
• Same model in flowchart form (with different
parameters)…
Are We “It” Yet?
+
• Minsky: Ponzi
finance
extension to
Keen 1995
Investment
Capital
Output
Plot
Speculative to Productive Debt
Output
6
5
Cyclical Growth
2000
4
1000
3
2
0
0
10
20
30 40 50
Time (Years)
60
70
1
0
WageShare
Click here to
download Vissim
viewer program
Output
0
10
30
40
Time (Years)
50
60
70
Cyclical Growth
Debt
Ratios
Wages share of output
Employment Rate
1.0
.5
0
On
DebtInModel
On
Off
Ponzi
InitialBoom
Plot
Debt to Output Ratios
0
10
20
30
40
50
Time (Years)
60
70
6
Total Debt
Productive
Speculative
5
Cyclical Growth
4
1.1
Employment
• Click on icon to
run simulation
after installing
Vissim Viewer
20
3
.9
2
.7
1
.5
.3
.5
EmploymentRate
+
Profit
+
.7
.9
Wages
*
1.1
Employment
InterestRate
TotalDebt
0
0
10
+
+
20
30
40
Time (Years)
Productive
Debt
Speculative
Debt
50
60
Profit
Investment
RateOfGrowth
70
Are We “It” Yet?
• Weakness of previous model
– Implicit money only—deflationary process ignored
– No explicit treatment of aggregate demand
• Overcome by blending Minsky with the Circuit
– Lay out basic macro operations in accounts table
• See “Roving Cavaliers of Credit” for basic approach
• Also “Circuit Theory & Post Keynesian Economics”
– Generate financial flows dynamics
– Couple with Goodwin cycle model
Are We “It” Yet?
• The financial flows table:
"Type"
0
0
1
1
1


"Account"
"Bank
Capital"
"Bank
P/L
(B.PL)"
"Firm
Loan
(FL)"
"Firm
Deposit
(FD)"
"Worker
Deposit
(WD)"




"Symbol"
B.C( t)
B.PL( t)
F.L( t)
F.D( t)
W .D( t)


"Compound Debt"
0
0
A
0
0




"Pay Debt"
0
B
0
B
0


"Record Payment"
0
0
B
0
0


"Debt-financed Investment"
0
0
C
C
0


M.1 


"Wages"
0
0
0
D
D


"Interest"
0
( E  F)
0
E
F



"Consumption"
0
G
0
G H
H



"Debt repayment"
I
0
0
I
0


0
0
I
0
0
 "Record repayment"

 "Lend from capital"

J
0
0
J
0


"Record Loan"
0
0
J
0
0


• Nonlinear functions
for placemarkers C, I
and J:


C  Inv  r( t)  PC( t)  Yr( t )
I 
J 
FL( t)

 RL  r( t)

BC( t)

 LC  r( t)

Are We “It” Yet?
• Fully specified Phillips function for wage setting:
– Employment
– Rate of change of employment
– Rate of inflation adjustments
d
W ( t)
dt


 Phillips
 1   Inv  r( t)


1 
W ( t)

W ( ( t) )  Ph(  ( t) )  Rate
  of
v  change ofemployment
   (    )  
 1  Inflation

v
 v  

   Pc  a( t)  ( 1  s )  PC( t) 
 Curve
Wages and Employment Rate
Percent change in money wages
20
15
  
100 Ph

 100 
10
5
0
5
90
92
94
96

Employment Rate
98
100
Are We “It” Yet?
• Investment, debt repayment and money relending
functions:
Investment & Profit Rate
Loan Repayment and Money relending
50
20
Loan repayment
Money relending
40



 100 
100 Inv
r
30
Years
Percent of GDP
15
20
 x 
 LC

 100 
10
5
10
0
5
 x 

 100 
 RL
0
5
r
Profit Rate %
10
0
 10
5
0
x
Rate of Profit
5
10
Are We “It” Yet?
Financial Sector
• Overall model:
14 equations (11
ODEs, 3
algebraic)
• 5 equations for
financial sector
• 1 for prices
• 1 for wages
• 7 for physical
economy
d
BC( t)
dt
d
BPL( t)
dt
FL( t)

 RL  r( t)

BC( t)


 LC  r( t)

rL FL( t)  rD FD( t)  rD W D( t ) 
BC( t)
FL( t)
BPL( t)
B


d
FL( t)
dt
 LC  r( t)
d
FD( t)
dt
BC( t )
FL( t)
BPL( t)
W D( t )
W ( t)  Yr( t)
rD FD( t)  rL FL( t) 



 PC( t )  Yr( t)  Inv  r( t ) 
 LC  r( t )
 RL  r( t)
B
W
a( t )
d
W D( t)
dt




 RL  r( t )

 PC( t)  Yr( t )  Inv  r( t)

rD W D( t) 
W D( t)
W






W ( t)  Yr( t )
a( t )
Physical output, labour and price systems
Level of output
Rate of Profit
v
Yr( t)
PC( t)  Yr( t )  W ( t) 
 rL FL( t)
a( t )
 r( t )
Rate of employment
v  PC( t)  Yr( t )
d
 ( t)
dt
Rate of real economic growth
Rate of change of wages
Kr( t)
Yr( t )
g( t)
d
W ( t)
dt


 1   Inv  r( t)


 ( t )    v  
    (    )
v
v
  



Inv  r( t)

v




 1   Inv  r( t)


1 
W ( t)

W ( ( t) )  Ph (  ( t) )     v  
    (    )  
 1 

v
a( t )  ( 1  s )  PC( t) 
 v  

  Pc
Rate of change of prices

d
PC( t )
dt
Rate of change of capital stock
d
Kr( t )
dt
Rates of growth of population and productivity
d
a( t )
dt

1
 Pc
 PC( t) 

W ( t)


a( t )  ( 1  s ) 
Kr( t)  g ( t)
 a( t )
d
N ( t)
dt
  N ( t)


Are We “It” Yet?
• Same system in QED:
Are We “It” Yet?
• Integrating Minsky & the Circuit
– Debt-deflationary dynamics in strictly monetary
Minsky-Circuit model
– “The Great Moderation”, then “The Great Crash”
Bank Accounts
Debt to Output Ratio
5
110
5
4
110
Years to repay debt
4
$
1000
100
Bank Equity
Bank Transactions
Firm Loan
Firm Deposit
Worker Deposit
10
1
0
10
20
30
Year
40
3
2
1
0
50
0
10
20
30
Year
40
50
Are We “It” Yet?
• Stability is destabilizing...
Rate of employment and rate of profit
Real growth rate
10
20
15
5
90
0
Percent p.a.
100
Percent p.a.
Percent of workforce
110
5
100 (    )
0
80
Employment
Profit
70
10
0
10
5
20
30
5
50
40
0
10
20
30
40
50
Employment and wage share dynamics
120
Year
Inflation Rate
Percent p.a.
40
20
0
0
Worker share of GDP
60
100
80
60
 20
 40
40
0.7
0
10
20
30
40
50
0.8
0.9
Employment rate
1
1.1
Are We “It” Yet?
• Income inequality
– Not worker vs capitalist but worker vs banker
Income Distribution
110
Workers
Capitalists
Bankers
100
90
Percent of GDP
80
70
60
50
40
30
20
10
0
 10
0
10
20
30
Year
40
50
Are We “It” Yet?
rl
• Can
government
policy save
us?
• Simple model
with fiat
injection
implies can
succeed
against credit
crunch alone:
Bank Assets
1500
Bank Liabilities (Deposits)
Loans
Unlent Reserves
1250
1500
1000
1000
750
750
500
500
250
250
0
0
10
20
Firms
Households
Banks
1250
30
Time (Years)
40
50
60
URate
0
0
10
InfRate
20
B_D
H_D
Unemployment
25
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
NoStimulus
Production
System
StimBank
0
60
-10.0
0
10
20
3
Debt to Output Ratio
Magnitude of Crunch
25
30
Time (Years)
25
No Stimulus
Bank Injection
Borrowers Injection
20
C_size
tCC
15
StimFirm
StimFirm
F_L
Y
l
r
/
100
10
1.
5
D:0 S:1
60.
0
0
10
20
30
40
Time (Years)
50
60
Are We “It” Yet?
• My expectation: best outcome of government policy alone
will be Japanese Stalemate
– Government monetary injections neutralise private
sector deleveraging
– Outcome “Turning Japanese”:
• Long-term stagnation and borderline deflation
• Need debt abolition & real financial reform
– Cancel debts that should never have been issued
– Cauterise financial sector in the process
– Reform assets to minimise chance of future bubbles
• Shares on secondary market expire in 30 years
• Property leverage limited to 10 times annual rental