Political Economy Evolutionary Economics Power Laws Evolutionary Modelling

Political Economy: Evolutionary Economics Power Laws & Evolutionary Modelling Steve Keen

Recap • Modern evolutionary economics Veblen/Schumpeter hybrid – Necessity of non-equilibrium, dynamic modelling – Chaos/complexity • Complex patterns from simple models • Evolution to “edge of chaos” – Simple tools for dynamic analysis – Difficult tools for evolutionary modelling… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 2

Chaos, Complexity & Evolution • Logistic difference equation (last week) typical chaotic system – Low value of parameter: Convergence to equilibrium – Medium value: regular cycles (2, 4, 8 cycles, etc. ) – Higher value: chaos (aperiodic cycles) • Chaos: measures of systemic instability > 1 (Lyapunov exponent…) • Evolutionary data: systemic instability measure 1… – “the edge of chaos” – Why? ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 3

Chaos, Complexity & Evolution • Chaotic models remain chaotic because parameters are fixed: – Tiny change in parameter, huge change in system – But same value, same outcome every time… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 4

Chaos, Complexity & Evolution • In evolutionary system, parameters change – Change seems to evolve systems to “edge of chaos” • Then system fluctuates either side of edge over time – Therefore, patterns of “edge of chaos” appear in all evolutionary systems • Self-similarity • Scale invariance • Power Laws • Self-organised criticality – Concepts from “self-organised criticality” may be used to interpret evolutionary systems that are currently too difficult to model… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 5

Power Laws: an empirical regularity • Empirical research shows many phenomena follow “power law” distribution: – Number of size X events X raised to some power • Result of statistical relation: a “straight line” between size of event and event frequency when graphed on log-log plot: • “Log of number of events of size X = -a times log(X)” • Rule applies to huge range of phenomena… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 6

Power Laws: an empirical regularity • “Log of number of earthquakes of size X is a times log of X” • “Log of number of species extinctions of size X is a times log of X” • “Log of number of meteor impacts of size X is a times log of X” • And, if economic systems are evolutionary, – “Log of number of stock market movements of size X is a times log of X” – “Log of number of recessions of size X is a times log of X” – “Log of number of firms of size X in an industry is a times log of X”… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 7

Power Laws: an empirical regularity • Example: Earthquakes in S. E. USA: Number/Year 1000 10 1 Richter scale ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 8

Applied to Economics? • Power law fit Dow Jones: Power law predicts 6 10% daily movements per century 1 means 101=10 events per century • Does this tell us anything the EMH doesn’t? ©Steve Keen 2005 Actual number was 8 -1 means 10 -1=10% daily change Advanced Political Economy, Economics & Finance, University of Western Sydney 9

Applied to Economics? • You betcha! • “Random walk” prediction OK for small movements • +/-3% 780 -2 means 10 -2: one reality v 718 such event predicted random prob. every century • Hopeless for -6: 1 event predicted 10 large every 1 million centuries • +/-6%: 57 v 1 10 -1. 1: • +/- 8%: 11 v 8% change 1 in a million -1. 2 means 10 -1. 2=6% daily change chance… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 11 last century Actual number 57 10

Applied to Economics? • Belief system is – in equilibrium – changes due to random shocks • Results in prediction that huge events vanishingly rare • Applies to all economics; e. g. firms: • Actual data – Rather than “monopoly” & “perfect manifestly competition”, real industries have different: power law distribution of firms… some very big, many small… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 11

Applied to Economics? • Key insights w. r. t. neoclassical economics – Scale-invariance: no “typical size” of anything • Earthquakes of all scales occur – Many more small ones than large ones – But large ones aren’t “vanishingly rare” • Bubbles in bubble bath (try it!) • Daily movements in stock exchange – Any size crash feasible – Likelihood far higher than predicted by random/equilibrium model – “Crashes” not aberrations but normal behaviour ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 12

Irrelevance of Equilibrium… • ‘General equilibrium theory, assumes that perfect markets, perfect rationality, and so on bring economic systems into stable Nash equilibria in which no agent can improve his situation by any action. In the equilibrium state, small perturbations or shocks will cause only small disturbances, modifying the equilibrium state only slightly. The system’s response is proportional to the size of the impact… Small freak events can never have dramatic consequences. Large fluctuations in equilibrium systems can occur only if many random events accidentally pull in the same direction, which is prohibitively unlikely. Therefore, equilibrium theory does not explain much of what is actually going on, such as why stock prices fluctuate the way they do…’ do (Per Bak 1996: 18) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 13

Normality of cycles/catastrophic change… • ‘We must accept instability and catastrophes as inevitable in biology, history, and economics Because the outcome is contingent upon specific minor events in the past, we must also abandon any idea of detailed long-term determinism or predictability… Large catastrophic events occur as a consequence of the same dynamics that produces small ordinary everyday events… events [unlike] the usual way of thinking about large events, which … looks for specific reasons … to explain large cataclysmic events. Even though there are many more small events than large ones, most of the changes of the system are associated with the large, catastrophic events Self-organized criticality can be viewed as theoretical justification for catastrophism. ’ (Per Bak 1996: 32) – “Self-organized criticality”? ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 14

Self-organized criticality • One of several attempts to explain power law phenomena – Evolutionary change leads to system reaching point at which small changes can have dramatic consequences • “Straw that broke the camel’s back” – May be possible to model evolutionary systems by • Using dynamic modelling techniques – Where dynamic model displays same statistical characteristics • Unstable equilibria • Instability “critical” rather than overwhelming • On border between order and chaos ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 15

Modelling evolutionary systems • Dynamic models may simulate evolved systems • Relatively easy to do – Characterise macro, tops-down behaviour – Develop dynamic model to suit • Can use dynamic insights of great economists – Reproduce qualitative behaviour of data • Model using well-developed, easy to use technology… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 16

Modelling evolutionary systems • To model actual evolution – Must be “bottoms up” model • Define behaviour of each organism • Define relationships between them • Define adaptive behaviour – Simple: adaptive parameter change – Advanced: • Reproduction/Birth/Death • Crossover/imitation • Mutation/innovation • Spontaneous development of new species… – Model as computer program… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 17

Programming and Evolution… • Essence of Standard Programming – Take a problem • E. g. , doing inventory of warehouse – Describe process in minute detail • Enter warehouse • Start in 1 st aisle – Record product code of first product – While code remains same • Add one to count of products – Move to next product & repeat • Move to next aisle and repeat • Leave warehouse • End program ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 18

Programming and Evolution… • Essence of procedure is – Develop successful algorithm • Set of minute procedures that achieves desired outcome – Code algorithm into computer language • For success, programmer must exactly specify algorithm that achieves overall objective • Example: algorithm to allocate students to tutorials… – Allocate students on basis of preferences – If get to point where one student can’t get any of her preferences – See if she can be swapped with someone who’s already been allocated – Sounds easy? ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 19

Procedural Programming • While not at end of list of students – While not at end of student’s preferences • Select all tutorials preference in student’s list • While not at end of list of tutorials – Check capacity of tutorial – If tutorial has room, place student in tutorial – Else check next tutorial • End while (tutorials) – End while (student’s preferences) – If student not allocated • Select all students in all tutorials in student’s list • While not at end of list of students – Check preferences of student – If has another preference that can be fulfilled, swap… – … and on it goes • Sounds a bit less easy? Here’s the computer code: ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 20

Procedural Programming LOOP | TUT. CHOICE = "" | READNEXT ID USING CURSOR ELSE EOF = TRUE$ UNTIL EOF = TRUE$ DO | READ STUDENT. REC FROM STUDENT. FILE, ID THEN | | NUMPREFS = COUNT(STUDENT. REC<TIME. PREF$>, VM$) + LEN(STUDENT. REC<TIME. PREF$>[1, 1]) | | * WHILE statement stops a student being entered into additional tutorials once he/she has already been allocated to one. | | FOR CURRENTPREF = 1 TO NUMPREFS WHILE TUT. CHOICE = "" | | | READ TIMES. REC FROM TIMES. FILE, STUDENT. REC<TIME. PREF$, CURRENTPREF> THEN | | NUMTUTS = COUNT(TIMES. REC<TUT. TIMES. TUT. NO$>, VM$) + LEN(TIMES. REC<TUT. TIMES. TUT. NO$>[1, 1]) | | * While condition repeated to stop students being allocated to several tutorials at the same time. | | FOR CURRENTTUT = 1 TO NUMTUTS | | | READ TUTORIAL. REC FROM TUTORIAL. FILE, TIMES. REC<TUT. TIMES. TUT. NO$, CURRENTTUT> THEN | | | SIZE = COUNT(TUTORIAL. REC<TUT. SN$>, VM$) + LEN(TUTORIAL. REC<TUT. SN$>[1, 1]) | | | IF SIZE < MAX. SIZE THEN | | | | IF SIZE < TUT. CHOICE<TUT. SIZE$> OR TUT. CHOICE = '' THEN | | | | TUT. CHOICE<TUT. NO$> = TIMES. REC<TUT. TIMES. TUT. NO$, CURRENTTUT> | | | | TUT. CHOICE<TUT. SIZE$> = SIZE | | | | END | | | | | END ELSE | | | MSG('ST 102', 'UB', '', TIMES. REC<TUT. TIMES. TUT. NO$, CURRENTTUT>) | | | END | | NEXT CURRENTTUT | | | END ELSE | | MSG('ST 101', 'UB', '', STUDENT. REC<TIME. PREF$, CURRENTPREF>) | | | END | | NEXT CURRENTPREF | END ELSE | | MSG('ST 100', 'UB', '', ID) | END | IF TUT. CHOICE THEN | | GOSUB UPDATE | END ELSE | | GOSUB REALLOCATION | END | STU. COUNT += 1 | GOSUB STATUS. LINE REPEAT ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 21

Programming and Evolution… • Compared to evolution? – Input energy & matter… – Life appears (don’t know how—& may never) – Lifeforms adapt (crossover/mutation/selection…) – life/matter/energy feedbacks change environment… – No end goal, no tops-down design… • At basic level, programming & evolution incompatible • But recent (1990+) developments in programming emulate of evolution/adaptation/learning – Neural networks (brain analogy: adapt by learning) – Genetic programming (evolution analogy)… – Multi-agent simulations (species interaction analogy) • Used to model “simple” evolutionary problems… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 22

Neural networks • Brain regarded as most complex product of evolution • Neural networks “mimic” brain by mimicking structure – Human brain complex network of neural structures • About 100, 000, 000 neurones • Each neurone has about 1000 connections with other neurones • Inputs from 1000 input neurones determine whether and how much a neurone will “fire” – Some connections inhibit, others enhance firing • Learning seems to involve changing significance attached to connections between neurones ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 23

Neural networks • Structure mimicked by neural network (NN) software – 3 or more interconnected layers of “neurones” • Input level simulates sensory processing • “Hidden layer(s)” simulates brain reasoning • Output layer simulates brain response – Initial random relationships between neurones – NN trained on test data • Initial answers wrong • Difference between actual & desired answers used to alter weights • NN gradually converges to correct answer… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 24

Neural networks • Training: input neurones receive values from data set • Fruit recognition. 1 Wrong: weights. 1 program adjusted (a ). 1 – Colour. 3. 1 • Red: . 1 … … Yellow. 9 • Fruit given. 7? – Shape arbitrary • Sphere. 1 … numerical Cylinder. 9 value – Texture • Apple. 1 • Smooth. 1 … • Pineapple. 9 Spiky. 9 • Process repeated till NN • … returns correct answers… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 25

Neural networks • Sample Neural Network (written in Mathcad) • See Advanced Finance lectures for explanation (if interested…) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 26

Neural networks • “Evolutionary” aspects: origin of metaphor (brain) via evolution; adaptive nature of program learning • Most developed software approach – Commercial NN programs available – Basic structure of NNs easily programmed – Used extensively in game software, optical character recognition, medical diagnosis… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 27

Genetic Programming • More truly evolutionary approach is “Genetic Programming” – Simulates (neo-Darwinian) evolution • Environment (desired outcomes/data to explore) • Variation of population of randomly generated programs • Survivors from one generation selected via fitness function related to desired outcome • Reproduction via crossover/Mutation • New generation produced and evaluated against criteria; process repeated… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 28

Genetic Programming • Standard programming – Carefully detail problem to solve – Write exact algorithm to solve problem • Genetic programming (GP) – Carefully detail problem to solve – Evolve population of random programs towards solution • Huh? … – Programs can be considered as organisms – Sub-units of programs can be • Swapped (cross-over/sexual reproduction) • Altered (mutation) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 29

Genetic Programming • Example program fragment: – (* 1 2 (IF (> Time 10) 3 4)) Before 10 After 10 True False (IF T 3 4) (IF F 3 4) 3 4 (* 1 2 3) (* 1 2 4) 6 8 ©Steve Keen 2005 • Computer executes program from inside parenthesis outwards • Program could be altering pay rates based on hour of day… Advanced Political Economy, Economics & Finance, University of Western Sydney 30

• Program can be represented as tree (read bottom up) – (+ 1 2 (IF (> Time 10) 3 4)) Rest of program Genetic Programming • Fragment could be one of many such fragments • Environment specifies desired outcome, e. g. : • Payrates after 6 pm 1. 5 times payrates before 6 pm 6 or 8 * 1 or 4 2 r. F o T IF 3 > Time ©Steve Keen 2005 3 4 10 Advanced Political Economy, Economics & Finance, University of Western Sydney 31

Genetic Programming • Two such fragments could be: 11 or 11. 5 + 10 1 * or 1. 5 IF r. F o T 1 1. 5 > Time 6 or 8 10 1 • Neither very “fit” for purpose Time 3 2 > r o T or 4 IF F 3 4 10 • But “crossover” of highlighted segments could produce “descendants” that were more fit… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 32

Genetic Programming 2. 5 or 3. 5 20 or 40 30 or 40 + * 1 > 1 or 1. 5 2 IF r. F o T Time 1 10 or or 4 4 IF r. F o T 3 2 4 > 2 10 1. 5 Time 3 10 • LHS program less fit; will “die” • RHS fit enough to survive; will reproduce/mutate… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 33

Genetic Programming • Process continues for many generations until average level of “fitness” – Conformity to condition: • “Payrates after 6 pm 1. 5 times payrates before 6 pm” • Reaches acceptable levels • “Best of generation” programs then implemented ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 34

Multi-agent modelling • “In the beginning” programs were “procedure oriented” – Define the operations to be done • “Pay payroll” – Apply them to data • “Full-time employees”, “Part-time”, “Contractors”, “Consultants” • Modern programming is “object oriented” – Define the objects/entities • Person-employee-full-time, Person-employeepart-time, Person-contractor, … – Define the operations relevant to each one • Technical computing reasons for shift – Side-effect: modelling “artificial worlds” – Multi-agent modelling (MAM) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 35

Multi-agent modelling • Define agents, behaviour – E. g. , Insects • Move, Forage, Eat • Define environment – Landscape – Food items – Poison items • Evolve. . – Insects that eat poison die – “Avoid poison” behaviour evolves… ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 36

NN, GP, MAM, and Economics • Several possible ways – “Data mining” • NNs and GPs used extensively (and often secretly) to find patterns in economic data • Pattern then exploited by trained NN/GP – See, e. g. , Colin (2000): GP used to profit from foreign exchange volatility – Pricing strategy • Analyse past pricing behaviour • Derive pricing strategy that “beats” past competitors – See, e. g. , Marks (2000) & references ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 37

NN, GP, MAM, and Economics – GP alone • Standard GP works by having a target to evolve towards: “environment” is conformity to predetermined objective • In economics? No such thing… – MAMs with GPs & NNs • Build “artificial economy” – Workers, capitalists, firms, factories • NN or GP can be used to simulate decision processes of agents • Agents in evolutionary model of economy can’t be assumed to be optimisers • Run system to see behaviour ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 38

NN, GP, MAM, and Economics • Problems: – Extremely difficult to build such models – Technical • Need knowledge of dynamics, computer programming, etc. – Systemic • Properties of system known at “emergent” level – Aggregate behaviour of stock market: Bear & Bull markets – Aggregate behaviour of macro-economy: booms and busts • Difficult to know what (unknown) agent level behaviour will generate this (known) macro behaviour ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 39

NN, GP, MAM, and Economics • As a result, existing evolutionary models – Capture only very limited range of phenomena of real economy – Often fail due to agent initial parameter values that turn out to be inappropriate – Very difficult to design • Models written in programming languages like Swarm (specialist MAM extension to C++), Lisp (object-oriented list processing language [source of previous examples]) • Programs as difficult to construct as conventional programs • So that ‘Twenty years after the publication of these pioneering contributions [Nelson & Winter]…’ ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 40

Whither Evolutionary Economics? … • ‘it is fair to say that the great expectations of some observers have only become substantiated slowly and partially. There are, of course, many reasons for this, but two related reasons seem to have special importance. First, it is obvious that there are significant barriers to entry for students and researchers who want to explore and extend evolutionary models by simulation; you simply have to master a great many skills to be able to combine evolutionary theorising and simulation in a fruitful way Second, there is a lack of cumulativeness of the efforts of developing evolutionary analysis with the help of computer simulation; instead many entrants to the field seem to build their efforts from scratch. ’ (Anderson & Valente: 44) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 41

Whither Evolutionary Economics? … • Feasible future directions – Persist with MAM modelling? • Improve tools (see e. g. Andersen & Valente 2002) • Develop Simulink/Vissim-like Graphical User Interface? – Take GP approach? • Design agents with GP/NN behaviours • Make fitness function past economic data (e. g. , US 19 th century trade cycle, inflation, interest rates) • Evolve agents till systemic output resembles “fitness function” – (No-one has tried this yet) ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 42

Whither Evolutionary Economics? … • Use insights and tailor dynamic models? – The KISS approach • Einstein’s “Keep it as simple as possible, but no simpler” – Statics too “simple” • Will lead to erroneous answers to the wrong questions – Dynamics with “self-organised criticality”, “highly optimised tolerance” etc. might be both simple and not too simple • Key insight of EE: Economic theory should explain why the economy keeps changing, not model a system in which change must end. ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 43

Conclusion • The economy is dynamic, and our modelling of it must be (cannot be static) • The economy is evolutionary, and our modelling of it… – Has to be aware of evolutionary process – Has to capture nature of evolutionary data • Power laws, etc. – May not be able to be truly evolutionary until techniques (GPs, MAM, etc. ) develop in 21 st century… • Key insights of founders – Dynamic instability (Veblen) – Creative destruction (Schumpeter) – Remain true as “vision” of economic process – Can be melded with “vision” of Marx, Post Keynesians, etc. … ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 44

References • Andersen, E. S. , & Valente, M. , (2002). “Model Exploration and Extension in the Laboratory for Simulation Development”, Artificial Economic Evolution. • Bak, P. (1996). How Nature Works, Copernicus, New York • Barnett, W. , Chiarella, C. , Keen, S. , Marks R. , & Schnabl, H. , (eds. ), Commerce, Complexity & Evolution, Cambridge University Press, New York. • Colin, A. , (2000). “A genetic programming-based approach to the generation of foreign exchange trading models”, in Barnett et al. (2000). • Koza, J. R. , (1992). Genetic Programming, MIT Press, Cambridge MA. • Marks, R. , (2000). “Evolved Perception and the Validation of Simulation Models”, in Barnett et al. (2000). ©Steve Keen 2005 Advanced Political Economy, Economics & Finance, University of Western Sydney 45