Autocatalytic Mechanisms(feedback-loops)

AmplifyIndividual Financial Interactions

toSystemic Economic Crises

Prof David Bree Guy Kelman Prof Leanne Ussher

Prof Andrzej Nowak

Prof Damien Challet Dr Sonia EmsalemProf Natasa Golo

Dr Simona CantonoProf. Moshe Levy

Dr Marco Lamieri

Prof Gerard Weisbuch

Prof Dietrich Stauffer

Dr Gur Yaari

Dr. Sarit Moldovan

3

Julia Aronson Prof Jacob Goldenberg

Prof Lucilla de Arcangelis

Dr Yaniv DoverDr Sabine PitnauerProf Nadav Shnerb

Prof Yoram Louzoun

“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 maximizeexplanatory or predictive power.”

HARRY MARKOWITZ Nobel Laureate in Economics

- lose explanatory power : which of the myriads of microspopic features is responsible for the macroscopic effects?

TWO systems that one does not understand:the initial one and its computer copy.

Agent Models with too many details =>

- lose predictability: can predict anything you wish to by tuning many uncalibrable parameters.

- By representing exactly in the computer a system that one does not understand one ends up with

Start with solvable multi-agent models which keep only the individual features involved in amplification micro->macro

Autocatalytic (“procyclic”, self-reinforcing) feedback loops

Still obtain and understandmacroscopic resulting features

while neglect the microscopic clutter.

Solution:

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 firms and the system as such (similar to Minsky accelerator)

- Between interacting firms (e.g. domino, spill-over, diffusion)

- Between firm and itself (e.g. self-regulation rich get richer , poor get poorer)

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

Between interacting firms (e.g. domino, spill-over, diffusion)

Feedback loop between firms• Market Percolation: (e.g. Trade Credit)

• Each firm has K trade partners

• Fraction PONZI of firms susceptible to failure contagion

“Ponzi”= firm who cannot pay the interest on its debt from its earnings:earnings < debt x interest rateor 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 failureN=1+N(1) +N(2) +N(3) +… N(t)

N=1+(K-1)PONZI+[(K-1)PONZI]2+[(K-1)PONZI]3+…[(K-1)PONZI]t-1

TIME

Nfailed

N=1+ 1 + 1 + 1 +… 1

for (K- 1)PONZI=1

1

Dynamics of Ponzi contamination to failureN=1+N(1) +N(2) +N(3) +… N(t)

N=1+(K-1)PONZI+[(K-1)PONZI]2+[(K-1)PONZI]3+…[(K-1)PONZI]t-1

TIME

Nfailed

Nfailed(t) = { [(K-1)PONZI ] t -1} /{[(K-1) PONZI ] -1}

For (K-1) PONZI < 1

for (K-1) PONZI > 1

for (K- 1)PONZI=1

1

Total number of Ponzi contaminated to failureN=1+N(1) +N(2) +N(3) +… N(t)

N=1+(K-1)PONZI+[(K-1)PONZI]2+[(K-1)PONZI]3+…[(K-1)PONZI]t-1

Nfailed(∞) = [1-(K-1)] -1

for critical (K-1):

Nfailed ∞

phase transition from a microscopic localized disruptionto a system size crisis:

Nfailed= [1-PONZI CRITICAL]-

Total number of Ponzi contaminated to failureN=1+ N(1) +N(2) +N(3) +…N(t) +….

N=1+ (K-1) +[(K-1) ]2 + [(K-1) ]3 +…[(K-1) ]t-1+…

CRISIS PERCOLATION PHASE TRANSITION

Until nowfirms hadsimilar size.We make them heterogeneouslater

1

10

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

K=5=0.25

K=4=0.33

K=3=0.50

3015 0 3 6 9 12 2118 2724K

Ponzi

=1/30Ponzi

=1/15Ponzi

=1/20

100

10

1

N FAILED

High Leverage (High Ponzi Density) PONZI >> 0 + High Connectivity (Many trade partners) K>>1

Increase the probability of failureBy favoring contagion avalanches

Crisis Percolation PhaseTransition

1

10

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

K=5=0.25

K=4=0.33

K=3=0.50

3015 0 3 6 9 12 2118 2724K

Ponzi

=1/30Ponzi

=1/15Ponzi

=1/20

100

10

1

N FAILEDMainstream economics maintains that diversification (K>>1) is always good. According to our very simple model (refined later) diversification (K>>1) by itself is neither good or bad : it depends on the state of the economy.If you are in a boom or in the process of adopting new technologies , large K will amplify / accelerate them too.

Large PONZI and large K

are dangerous only if they lead to a large number of pairs of Ponzi being connected => chain reaction.

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

resilience rn

= the level r of interest rateAbove which n would turn into Ponzi: r > rn = earningsn / debtn

Interest rate r

rn

= Pareto exponentof debt distribution(Takayasu et al 2000)

Minsky Accelerator: loop System <-> components

PONZI ~ r

~ n

n

resi

lien

ce

r=Interest rate = r 0

PONZI ;

Latane(72)

r0=Initial Interest Rate

Minsky Accelerator: loop System <-> components

rn ~ n

PONZI ~ r

rn= Interest rate that turns n into Ponzi(interest > earnings)

resi

lien

ce

If >1/

PONZI

rn ~ n

PONZI ~ r

r=Inte

rest r

ate = r 0

PONZI

rn= Interest rate that turns n into Ponzi(interest > earnings)

Minsky Accelerator loop

System <-> components

resi

lien

ce

rn~ n

r=Interest rate ~ r0 (FAILED)

~ r0

PONZI/C)

NOT ALL PONZI FAIL:

Minsky Accelerator

PONZI ~ rr=Interest rate r 0

PONZI

+Network 15 min

ONLY BY DIRECT CONTAGION

resi

lien

ce

rn~ n NOT ALL PONZI FAIL:ONLY BY DIRECT CONTAGION

Minsky Accelerator+Network

PONZI ~ r

STOP OR DELAY

Systemic Crisis

LIMITED LOCAL CRISIS

r=Interest rate ~ r0 (FAILED)

~ r0 PONZI/C

)

resi

lien

ce

N0

Nno return =(r

0 /rc ) Crisis

PROPAGATES

stop

Stop

N=(Mr0)

Nstart Faiures

=Initial number of Exogenous Failures

Initial interest rate r0

Minsky Instability

MICRO CRISES

N0 (1+1/)N hung-up =

Indpendent Crisis centers

Very solid core

N=(Mr0)

Ncrisis

offset =(r0 /r

c )

Stable

r0c= rc N0 ( +1) (1+1/)

Feedback loops between unit and Itself

• Exogenous Financial Changes=> changes in the Real Sector Firms functioning

Dover, Moulet, Yaari,S, Risk and Decision Analysis 2009

Challet, Yaari, Solomon, Economics 2009 “The Universal Shape of

Economic Recession and Recovery after a Shock “

Microscopic Study Reveals the Singular Origins of Growth G Yaari, S Solomon, K Rakocy, A Nowak, European Physics Journal B 62 4, p505 2008,.

TIME

NEWOLD TOTAL

EXPONENTIAL + EXPONENTIAL

Financial Shock

Real Economic Sector Size

Emergent Collective objects

(economic growth clusters)

Analytic Solution: Master Equation

Renormalization groupShnerb, Louzoun,

Bettelheim, Solomon (PNAS 2000)

EXACT TIME OF

REFORMS

J-Shape after Shock

GD

P

exploding deficit

systemic banking crisis

GD

P-became a net debtor nation-austerity program-adjust fiscal imbalances 

Financial Shock

J-shape in Real Sector of Economy

Scaled Real GDP of the United Kingdom

Pareto Exponent (of wealth Distributrion)

Quantitative Finance, M Levy and S 2003

Fractal Exponent of

Time fluctuations(~instability in the industrial index)

Conclusion

• Agent Based Models with Autocatalytic Feedback Loops lead to:

• Understanding

• Analytic tractability

• Predictability