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Autocatalytic Mechanisms (feedback-loops) Amplify Individual Financial Interactions to Systemic Economic Crises

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Prof David Bree Guy Kelman Prof Leanne Ussher Prof Andrzej Nowak Prof Damien ChalletDr Sonia Emsalem Prof Natasa Golo Dr Simona Cantono Prof. Moshe Levy Dr Marco Lamieri Prof Gerard Weisbuch Prof Dietrich Stauffer

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Dr Gur Yaari Dr. Sarit Moldovan 3 Julia Aronson Prof Jacob Goldenberg Prof Lucilla de Arcangelis Dr Yaniv Dover Dr Sabine Pitnauer Prof Nadav Shnerb Prof Yoram Louzoun

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“ 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

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- 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

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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 understand macroscopic resulting features while neglect the microscopic clutter. Solution:

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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.

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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)

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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)

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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 rate or r=interest rate>earnings/debt We assume a Ponzi will fail by contagion if one of its debtors fail.

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Total number of Ponzi contaminated to failure N=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

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TIME N failed N=1+ 1 + 1 + 1 +… 1 for (K- 1) PONZI =1 1 Dynamics of Ponzi contamination to failure N=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

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TIME N failed N failed (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 failure N=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

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N failed ( ∞ ) = [1- (K-1)] -1 for critical (K-1) : N failed ∞ phase transition from a microscopic localized disruption to a system size crisis: N failed = [1- PONZI CRITICAL ] - Total number of Ponzi contaminated to failure N=1+ N(1) +N(2) +N(3) +…N(t) +…. N=1+ (K-1) +[(K-1) ] 2 + [(K-1) ] 3 +…[(K-1) ] t-1 +…

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CRISIS PERCOLATION PHASE TRANSITION Until now firms had similar size. We make them heterogeneous later

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3015 03691221182724 K Ponzi =1/30 Ponzi =1/15 Ponzi =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 failure By favoring contagion avalanches Crisis Percolation PhaseTransition

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3015 03691221182724 K Ponzi =1/30 Ponzi =1/15 Ponzi =1/20 100 10 1 N FAILED Mainstream 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.

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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

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resilience r n = the level r of interest rate Above which n would turn into Ponzi: r > r n = earnings n / debt n Interest rate r rnrn = Pareto exponent of debt distribution (Takayasu et al 2000) Minsky Accelerator: loop System components PONZI ~ r ~ n n resilience

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r=Interest rate = r 0 PONZI ; Latane(72) r 0 =Initial Interest Rate Minsky Accelerator: loop System components r n ~ n PONZI ~ r r n = Interest rate that turns n into Ponzi (interest > earnings) resilience

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If >1/

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PONZI r n ~ n PONZI ~ r r=Interest rate = r 0 PONZI r n = Interest rate that turns n into Ponzi (interest > earnings) Minsky Accelerator loop System components resilience

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r n ~ n r=Interest rate ~ r 0 ( FAILED ) ~ r 0 PONZI / C ) NOT ALL PONZI FAIL: Minsky Accelerator PONZI ~ r r=Interest rate r 0 PONZI +Network 15 min ONLY BY DIRECT CONTAGION resilience

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r n ~ 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 ~ r 0 ( FAILED ) ~ r 0 PONZI / C ) resilience

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N0N0 N no return =(r 0 /r c ) Crisis PROPAGATES stop Stop N=(Mr 0 ) N start Faiures =Initial number of Exogenous Failures Initial interest rate r 0 Minsky Instability MICRO CRISES N 0 (1+1/ ) N hung-up = Indpendent Crisis centers Very solid core N=(Mr 0 ) N crisis offset =(r 0 /r c ) Stable r 0c = r c N 0 ( +1) (1+1/ )

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

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TIME NEWOLD TOTAL EXPONENTIAL + EXPONENTIAL Financial Shock Real Economic Sector Size Emergent Collective objects (economic growth clusters ) Analytic Solution: Master Equation Renormalization group Shnerb, Louzoun, Bettelheim, Solomon (PNAS 2000)

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EXACT TIME OF REFORMS J- Shape after Shock GDP

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exploding deficit systemic banking crisis GDP - became a net debtor nation -austerity program - adjust fiscal imbalances Financial Shock J-shape in Real Sector of Economy

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Scaled Real GDP of the United Kingdom

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Pareto Exponent (of wealth Distributrion) Quantitative Finance, M Levy and S 2003 Fractal Exponent of Time fluctuations (~instability in the industrial index)

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Conclusion Agent Based Models with Autocatalytic Feedback Loops lead to: Understanding Analytic tractability Predictability

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Complexity Emergence in Economics Sorin Solomon, Racah Institute of Physics HUJ Israel Scientific Director of Complex Multi-Agent Systems Division, ISI.

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