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

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

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

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

4. “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

5. 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 understandone ends up with TWO systems that one does not understand:the initial one and its computer copy.

6. Solution: • Start with solvable multi-agent modelswhich keep only theindividual features involved in amplification micro->macro • Autocatalytic (“procyclic”, self-reinforcing) feedback loops • Still obtain and understand • macroscopic resulting features • while neglect the microscopic clutter.

7. 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.

8. Types of Autocatalytic Feedback loops (described and explained in the sequel): - Between firm and itself (e.g. self-regulation rich get richer , poor get poorer) - Between interactingfirms (e.g. domino, spill-over, diffusion) - Between firms and the system as such (similar to Minsky accelerator)

9. Between interactingfirms (e.g. domino, spill-over, diffusion) Social percolation modelsS Solomon, G Weisbuch, L de Arcangelis, N Jan and D Stauffer Physica A: 277 (1-2) (2000) 239Market percolation J. Goldenberg; , B. Libai , S. Solomon, N. Jan , D. Stauffer Physica A 284 (2000) 335{347

10. 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.

11. Total number of Ponzi contaminated to failure N=1+N(1) +N(2) +N(3) +… N(t) N=1+(K-1)rPONZI+[(K-1)rPONZI]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1

12. Dynamics of Ponzi contamination to failure N=1+N(1) +N(2) +N(3) +… N(t) N=1+(K-1)rPONZI+[(K-1)rPONZI]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1 N=1+ 1 + 1 + 1 +… 1 Nfailed for (K- 1)rPONZI=1 1 TIME

13. Total number of Ponzi contaminated to failure N=1+N(1) +N(2) +N(3) +… N(t) N=1+(K-1)rPONZI+[(K-1)rPONZI]2+[(K-1)rPONZI]3+…[(K-1)rPONZI]t-1 Nfailed(t) = { [(K-1)rPONZI ]t-1} /{[(K-1) rPONZI ]-1} Nfailed for (K-1)r PONZI > 1 for (K- 1)rPONZI=1 For (K-1)r PONZI < 1 1 TIME

14. 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)] -1for r -> rcritical =1/(K-1): Nfailed-> ∞ phase transition from a microscopic localized disruption to a system size crisis: Nfailed= [1-rPONZI /rCRITICAL]-g

15. CRISIS PERCOLATION PHASE TRANSITION Until nowfirms hadsimilar size. We make them heterogeneous later

16. N FAILED 100 High Leverage (High Ponzi Density) rPONZI >> 0+ High Connectivity (Many trade partners) K>>1 rPonzi=1/15 rPonzi=1/20 rPonzi=1/30 Increase the probability of failure By favoring contagion avalanches 10 Crisis Percolation PhaseTransition 1 K 0 3 6 9 12 15 18 21 24 27 30

17. 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. N FAILED 100 rPonzi=1/15 rPonzi=1/20 rPonzi=1/30 If you are in a boom or in the process of adopting new technologies , large K will amplify / accelerate them too. 10 Large rPONZI and large Kare dangerous only if they lead to a large number of pairs of Ponzi being connected => chain reaction. 1 K 0 3 6 9 12 15 18 21 24 27 30

18. 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.12When the collective acts on its components: economic crisis autocatalytic percolation

19. Minsky Accelerator: loop System <-> components m = Pareto exponentof debt distribution (Takayasu et al 2000) resilience rn= the level r of interest rate Above which n would turn into Ponzi: r > rn = earningsn / debtn rn ~ n 1/m resilience Interest rate r n NPONZI ~ rm

20. Minsky Accelerator: loop System <-> components rn= Interest rate that turns n into Ponzi(interest > earnings) rn ~ n 1/m r=Interest rate = r0NPONZIa ; a~1/2 Latane(72) resilience r0=Initial Interest Rate NPONZI ~ rm

21. If a >1/m

22. Minsky Accelerator loop System <-> components rn= Interest rate that turns n into Ponzi(interest > earnings) rn ~ n 1/m r=Interest rate = r0NPONZIa resilience NPONZI ~ rm rPONZI

23. Minsky Accelerator +Network 15 min NOT ALL PONZI FAIL: ONLY BY DIRECT CONTAGION rn~ n 1/m r=Interest rate ~ r0 (NFAILED)a ~ r0(1-NPONZI/ NC)-g a resilience r=Interest rate r0NPONZIa NPONZI ~ rm

24. Minsky Accelerator+Network NOT ALL PONZI FAIL: ONLY BY DIRECT CONTAGION rn~ n 1/m Systemic Crisis r=Interest rate ~r0(NFAILED)a ~ r0(1-NPONZI/ NC) -g a resilience STOP OR DELAY NPONZI ~ rm LIMITED LOCAL CRISIS

25. Nstart Faiures =Initial number of Exogenous Failures Stop Very solid core N=(Mr0-m)1/(1-am) N=(Mr0-m)1/(1-am) Minsky Instability Stable Nno return =(r0/rc )a Ncrisisoffset =(r0/rc )a Crisis PROPAGATES N hung-up = N0 (1+1/amg)g stop MICRO CRISES N0 Indpendent Crisis centers r0c= rc N0a(amg +1)1/m (1+1/amg)ag Initial interest rate r0

26. Feedback loops between unit and Itself • Exogenous Financial Changes=> changes in the Real Sector Firms functioning Microscopic Study Reveals the Singular Origins of GrowthG 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

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

28. J-Shape after Shock GDP EXACT TIME OF REFORMS

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

30. Scaled Real GDP of the United Kingdom

31. Fractal Exponent of Timefluctuations (~instability in the industrial index) Pareto Exponent (of wealth Distributrion) b a Quantitative Finance, M Levy and S 2003

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