Political Economy: Evolutionary Economics

1
Political Economy Evolutionary Economics

• Power Laws Evolutionary Modelling

2
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

3
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 gt 1
  (Lyapunov exponent)
• Evolutionary data systemic instability measure ?
  1
• the edge of chaos
• Why?

4
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

5
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

6
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

7
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

8
Power Laws an empirical regularity

• Example Earthquakes in S.E. USA

1000
10
Number/Year?
1
Richter scale?
9
Applied to Economics?

• Power law fit Dow Jones

Power law predicts6 10 daily movementsper
century
Actual number was 8
1 means 10110events per century
-1 means 10-110 daily change

• Does this tell us anything the EMH doesnt?

10
Applied to Economics?

• You betcha!

• Random walk prediction OK for small movements
• /-3 780 reality v 718 random prob.
• Hopeless for large
• /-6 57 v 1
• /- 8 11 v 1 in a million chance

-2 means 10-2 onesuch event predictedevery
century
11 lastcentury
10-6 1 event predictedevery 1 million centuries
Actual number 57
10-1.18 change
-1.2 means 10-1.26 daily change
11
Applied to Economics?

• Belief system is
• in equilibrium
• changes due to random shocks
• Results in prediction that huge events
  vanishingly rare
• Actual data manifestly different

12
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 arent 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

13
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 systems 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 (Per Bak 1996 18)

14
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 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 the theoretical
  justification for catastrophism. (Per Bak 1996
  32)
• Self-organized criticality?

15
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 camels 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

16
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

17
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

18
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 1st 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

19
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 cant get any
  of her preferences
• See if she can be swapped with someone whos
  already been allocated
• Sounds easy?

20
Procedural Programming

• While not at end of list of students
• While not at end of students preferences
• Select all tutorials preference in students 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 (students preferences)
• If student not allocated
• Select all students in all tutorials in students
  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? Heres the computer code

21
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.RECltTIME.PREFgt,VM)
  LEN(STUDENT.RECltTIME.PREFgt1,1)
• 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.RECltT
  IME.PREF,CURRENTPREFgt THEN
• NUMTUTS COUNT(TIMES.RECltTUT.TIMES.TUT.NO
  gt,VM) LEN(TIMES.RECltTUT.TIMES.TUT.NOgt1,1)
• 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.RECltTUT.TIMES.TUT.NO,CURRENTT
  UTgt THEN
• SIZE COUNT(TUTORIAL.RECltTUT.SNgt,VM
  ) LEN(TUTORIAL.RECltTUT.SNgt1,1)
• IF SIZE lt MAX.SIZE THEN
• IF SIZE lt TUT.CHOICEltTUT.SIZEgt OR
  TUT.CHOICE '' THEN
• TUT.CHOICEltTUT.NOgt
  TIMES.RECltTUT.TIMES.TUT.NO,CURRENTTUTgt
• TUT.CHOICEltTUT.SIZEgt SIZE
• END

22
Programming and Evolution

• Compared to evolution?
• Input energy matter
• Life appears (dont 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

23
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 100,000,000,000 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

24
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

25
Neural networks

• Training input neurones receive values from data
  set

• Fruit recognition program
• Colour
• Red .1 Blue .9
• Shape
• Sphere .1 Cylinder .9
• Texture
• Smooth .1 Spiky .9

.9 .1 .1
Wrong weights adjusted (a?)
.9
Apple
.3

• Fruit given arbitrary numerical value
• Apple .1
• Pineapple .9

.7?

• Process repeated till NN returns correct answers

26
Neural networks

• Sample Neural Network (written in Mathcad)
• See Advanced Finance lectures for explanation (if
  interested)

27
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

So how does this relate to economics?
I'm gettin' there!
28

• 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

29
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)

30
Genetic Programming

• Example program fragment
• ( 1 2 (IF (gt Time 10) 3 4))

• Computer executes program from inside parenthesis
  outwards

Before 10
After 10
True
False

• Program could be altering pay rates based on hour
  of day

(IF T 3 4)
(IF F 3 4)
3
4
( 1 2 3)
( 1 2 4)
6
8
31
Genetic Programming

• Program can be represented as tree (read bottom
  up)
• ( 1 2 (IF (gt Time 10) 3 4))

Rest ofprogram

• Fragment could be one of many such fragments
• Environment specifies desired outcome, e.g.
• Payrates after 6pm 1.5 times payrates before 6pm

6 or 8

3 or 4
IF
1
2
T or F
3
4
gt
Time
10
32
Genetic Programming

• Two such fragments could be

Swap these...

• Neither very fit for purpose

• But crossover of highlighted segments could
  produce descendants that were more fit

33
Genetic Programming
20 or 40
2 or 4
2
Mutate...

• LHS program less fit will die
• RHS fit enough to survive will reproduce/mutate

34
Genetic Programming

• Process continues for many generations until
  average level of fitness
• Conformity to condition
• Payrates after 6pm 1.5 times payrates before
  6pm
• Reaches acceptable levels
• Best of generation programs then implemented

So how does this relate to economics?
I'm gettin' there!
35
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-employee-part-ti
  me, Person-contractor,
• Define the operations relevant to each one
• Technical computing reasons for shift
• Side-effect modelling artificial worlds
• Multi-agent modelling (MAM)

36
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

So how does this relate to economics?
37
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

38
NN, GP, MAM, and Economics

• GP alone
• Standard GP works by having a target to evolve
  towards environment is conformity to
  pre-determined 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 cant be
  assumed to be optimisers
• Run system to see behaviour

39
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

40
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

41
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)

42
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 19th century trade cycle, inflation, interest
  rates)
• Evolve agents till systemic output resembles
  fitness function
• (No-one has tried this yet)

43
Whither Evolutionary Economics?

• Use insights and tailor dynamic models?
• The KISS approach
• Einsteins 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.

44
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 21st
  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.

45
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).