Transcript Autocatalyic Crisis Percolation

Autocatalytic Mechanisms
(feedback-loops)
Amplify
Individual Financial Interactions
to
Systemic Economic Crises
Prof Natasa Golo Prof Gerard WeisbuchProf Damien Challet Dr Sonia Emsalem
Prof David Bree
Guy Kelman
Prof Leanne Ussher Dr Marco Lamieri
Prof Dietrich Stauffer Prof. Moshe Levy Dr Simona Cantono
Prof Andrzej Nowak
3
Dr Gur Yaari
Prof Yoram Louzoun
Prof Nadav Shnerb
Dr Sabine Pitnauer
Prof Jacob Goldenberg
Dr Yaniv Dover
Julia Aronson
Prof Lucilla
de
Arcangelis
Dr. Sarit Moldovan
“Levy, Levy and Solomon’s
’Microscopic Simulation of
Financial Markets’
points us towards the
future of financial economics.
If we restrict ourselves to models
which can be solved analytically,
we will be modelling for our mutual
entertainment, not to maximize
explanatory or predictive
power.”
HARRY MARKOWITZ
Nobel Laureate in
Economics
Agent Models with too many details =>
- lose predictability: can predict anything
you wish to by tuning many uncalibrable
parameters.
- lose explanatory power : which of the
myriads of microspopic features is
responsible for the macroscopic effects?
- By representing exactly in the computer
a system that one does not understand
one ends up with
TWO systems
that one does not understand:
the initial one and its computer copy.
Solution:
 Start with solvable multi-agent models
which keep only the individual features
involved in amplification micro->macro
Autocatalytic (“procyclic”, selfreinforcing) feedback loops
Still obtain and understand
macroscopic resulting features
while neglect the microscopic clutter.
Plan for the next 15 min:
-Examples of Autocatalytic Feedback loops
- Their effects
- Models where these loops interact
- Their Predictions
- Quantitative Empirical validation of the
predictions.
Types of Autocatalytic Feedback loops
(described and explained in the sequel):
- Between firm and itself (e.g. selfregulation rich get richer , poor get poorer)
- Between interacting firms
(e.g. domino, spill-over, diffusion)
- Between firms and the system as such
(similar to Minsky accelerator)
Between interacting firms
(e.g. domino, spill-over, diffusion)
Social percolation models
S Solomon, G Weisbuch, L de Arcangelis, N Jan and D Stauffer
Physica A: 277 (1-2) (2000) 239
Market percolation
J. Goldenberg; , B. Libai , S. Solomon, N. Jan , D. Stauffer
Physica A 284 (2000) 335{347
Feedback loop between firms
• Market Percolation: (e.g. Trade Credit)
• Each firm has K trade partners
• Fraction rPONZI of firms susceptible to
failure contagion
“Ponzi”= firm who cannot
pay the interest on its debt
from its earnings:
earnings < debt x interest rate
or
r=interest rate>earnings/debt
We assume a Ponzi will fail
by contagion if one of its
debtors fail.
Total number of Ponzi contaminated to failure
N=1+N(1)
N=1+(K-1)r
+N(2)
PONZI
+[(K-1)r
+N(3)
PONZI
+… N(t)
]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1
Dynamics of Ponzi contamination to failure
N=1+N(1)
N=1+(K-1)r
N=1+ 1
1
+N(2)
PONZI
+[(K-1)r
+
1
+N(3)
PONZI
+… N(t)
]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1
+
1
+…
1
Nfailed
for (K- 1)rPONZI=1
TIME
Total number of Ponzi contaminated to failure
N=1+N(1)
N=1+(K-1)r
+N(2)
PONZI
+[(K-1)r
+N(3)
PONZI
+… N(t)
]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1
Nfailed(t) = { [(K-1) rPONZI ] t -1} /{[(K-1) rPONZI ] -1}
1
Nfailed
for (K-1)r PONZI > 1
for (K- 1)rPONZI=1
For (K-1)r PONZI < 1
TIME
Total number of Ponzi contaminated to failure
N=1+ N(1) +N(2)
+N(3)
+…N(t)
+….
N=1+ (K-1)r +[(K-1)r ]2 + [(K-1)r ]3 +…[(K-1)r ]t-1+…
Nfailed(∞) =
[1-r (K-1)] -1
for r -> rcritical =1/(K-1) :
Nfailed -> ∞
phase transition
from a microscopic localized disruption
to a system size crisis:
Nfailed= [1-rPONZI /rCRITICAL]-g
CRISIS PERCOLATION
PHASE TRANSITION
Until now
firms had
similar size.
We make them
heterogeneous
later
N FAILED
100
High Leverage (High Ponzi Density) rPONZI
100
rPonzi
+
rPonzi
rPonzi
K=3
K=4
K=5
=0.50
=0.33
=1/15
=1/20
=0.25
>> 0
=1/30
High Connectivity (Many trade partners) K>>1
Increase the probability of failure
10
By favoring contagion avalanches
10
Crisis Percolation
PhaseTransition
11
0
0
0.05
3
0.1
6
0.15
9
0.2
0.25
12 15
0.3
18
0.35
21
0.4
24
0.45
27
0.5
30
K
Mainstream
N
economics maintains that
FAILED
100
diversification (K>>1) is always good.
According to our very simple
rPonzi model
rPonzi (refined
rPonzi later)
=1/20
=1/30
diversification (K>>1)=1/15
by itself
is neither good or bad :
itIf depends
state or
of the
economy.
you are on
in atheboom
in the
process of
100
K=3
K=4
K=5
=0.50
=0.33
=0.25
10
10
adopting
new technologies ,
large K will amplify / accelerate them too.
Large rPONZI and large K
are dangerous only if they lead to a large
number
of pairs of Ponzi being connected
1
K
0
3
6
9
12 15 =>
18 chain
21
24reaction.
27 30
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Feedback loop between
firms and the system:
• The collective reacting
on its own components
• Similar to Minsky accelerator
• Top-down+bottom-up
S Cantono and S Solomon 2010 New J. Phys. 12
When the collective acts on its components:
economic crisis autocatalytic percolation
Minsky Accelerator: loop System <-> components
m = Pareto exponent
resilience r
n
= the level r of interest rate
Above which n would turn into
Ponzi:
of debt distribution
(Takayasu et al 2000)
rn~ n 1/m
resilience
r > rn = earningsn / debtn
Interest
rate r
N PONZI ~
rm
n
Minsky Accelerator: loop System <-> components
r0=Initial Interest Rate
N PONZI ~ rm
rn ~ n 1/m
resilience
rn= Interest rate that
turns n into Ponzi
(interest > earnings)
If a >1/m
Minsky Accelerator loop
System <-> components
rn ~ n 1/m
resilience
rn= Interest rate that
turns n into Ponzi
(interest > earnings)
m
N
~
r
r PONZI
Minsky Accelerator +Network
15 min
NOT ALL PONZI FAIL: ONLY BY DIRECT CONTAGION
resilience
rn~ n 1/m
Minsky Accelerator+Network
NOT ALL PONZI FAIL:
ONLY BY DIRECT
CONTAGION
rn~ n 1/m
LIMITED
LOCAL
CRISIS
STOP
OR
DELAY
resilience
Systemic
Crisis
Nstart Faiures
=Initial
number of
Exogenous
Failures
Stable
Very solid core
Minsky
Instability
Crisis
PROPAGATES
N hung-up = N0 (1+1/amg)g
N0
Indpendent Crisis centers
MICRO
CRISES
r0c= rc N0a (amg +1)1/m (1+1/amg)ag
Initial interest rate r0
Feedback loops between
unit and Itself
• Exogenous Financial Changes
=>
changes in the Real Sector Firms functioning
Microscopic Study Reveals the Singular Origins of Growth
G Yaari, S Solomon, K Rakocy, A Nowak, European Physics Journal B 62 4,
p505 2008,.
Challet, Yaari, Solomon, Economics 2009 “The Universal Shape of
Economic Recession and Recovery after a Shock
“
Dover, Moulet, Yaari,S, Risk and Decision Analysis 2009
Real Economic Sector
Size
EXPONENTIAL + EXPONENTIAL
OLD
Financial
Shock
TOTAL
NEW
TIME
Analytic Solution:
Emergent Collective objects
Master Equation
(economic growth clusters)
Renormalization group
Shnerb, Louzoun,
Bettelheim, Solomon
(PNAS 2000)
GDP
JShape
after
Shock
EXACT TIME
OF
REFORMS
GDP
-became a net debtor nation
exploding -austerity program
deficit
-adjust fiscal imbalances
systemic
banking crisis
Financial Shock
J-shape in Real Sector of Economy
Scaled Real GDP of the United Kingdom
Pareto Exponent
(of wealth
Distributrion)
Fractal Exponent of
Time fluctuations
(~instability in the
industrial index)
b
a
Quantitative Finance, M Levy and S 2003
Conclusion
• Agent Based Models with
Autocatalytic Feedback Loops
lead to:
• Understanding
• Analytic tractability
• Predictability