#### 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