Political Economy: Evolutionary Economics

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Political Economy Evolutionary Economics

• Complexity self-organisation

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Recap

• Veblen Schumpeter two different directions for
  evolutionary economics
• Veblen anti-neoclassical
• statics must be abandoned
• but no model
• Schumpeter pro-neoclassical
• statics can co-exist with disequilibrium
  transformational growth
• a model
• Modern evolutionary political economy combines
  VB
• Veblenian rejection of (neoclassical) statics
• Schumpeterian model of transformational growth

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Why the hybrid?

• Incompatibility of static dynamic/evolutionary
  reasoning
• Neoclassical economists tend to think
• Evolution leads to optimising behaviour
• Dynamics explains movement from one equilibrium
  point to another
• So statics is long run dynamics
• also believed by Sraffian economists
• implicit in Post Keynesian or Marxian analysis
  using comparative static or simultaneous equation
  methods

Statics
Dynamics
Evolution
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Why the hybrid?

• Modern mathematics reverses this
• Field of evolution larger than dynamics
• Dynamics larger than statics
• Results of evolutionary analysis more general
  than dynamics
• But two generally consistent
• Results of dynamics more general than statics
• GENERALLY INCONSISTENT
• Dynamic results correct if actual system
  dynamic/evolutionary

Evolution
Dynamics
Statics

• An example supply and demand analysis

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Supply Demand Analysis

• Typical supply demand exercise
• Demand a decreasing linear function of quantity
• Supply an increasing linear function of quantity
• Equate the two to find equilibrium Q P

• Two equations return same result

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Supply Demand Analysis

• An example
• D(Q)1000-2/10000000 Q
• S(Q)-1001/10000000 Q

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Supply Demand Analysis

• X marks the spot!
• (Are neoclassical economists really just
  frustrated pirates?)

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Supply Demand Analysis

• What if initial price isnt equilibrium price
  how does it get there?
• Dynamic analysis
• Demand price and supply price as functions of
  time
• Producers plan output based on last years prices
• Consumers react to todays prices
• Convergence to equilibrium over time

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Supply Demand Analysis

• Confirming that this gives the same result as
  static analysis

• Try with initial quantity 10 more than Qe

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Supply Demand Analysis

• Convergence
• So Statics is long run dynamics?
• Lets try another demand supply pair

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Supply Demand Analysis

• D(Q)10005/100000000 Q
• S(Q)-1001/10000000 Q

• Meaningful (non-negative) equilibrium price
  quantity as before
• The dynamic answer?

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Dynamic Instability

• Whoops!
• Quantity unstable
• Cause slope of supply curve steeper than demand
• But also unrealistic negative quantities
• Dynamic model must be wrong then?

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Dynamic Instability

• Model of single Market
• Converges to equilibrium if bgtd
• Consumers more responsive than suppliers
• Diverges from equilibrium if bltd
• Suppliers more responsive than consumers
• Two possibilities
• Either consumers are more volatile than suppliers
• Contradicted by the data
• Or the model is wrong somehow
• Similar debate occurred in IS-LM modelling

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Dynamic Instability

• Hicks (father of IS-LM analysis) on instability
• Harrod welcomes the instability of his system,
  because he believes it to be an explanation of
  the tendency to fluctuation which exists in the
  real world. I think, as I shall proceed to show,
  that something of this sort may well have much to
  do with the tendency to fluctuation. But
  mathematical instability does not in itself
  elucidate fluctuation. A mathematically unstable
  system does not fluctuate it just breaks down.
  The unstable position is one in which it will not
  tend to remain. (Hicks 1949)
• I.e., models must have stable equilibria

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Dynamic Instability

• Kaldor analysed dynamics of IS-LM model
• Stable if slope of Sgt slope of I
• any disturbances would be followed by the
  re-establishment of a new equilibrium, this
  assumes more stability than the real world, in
  fact, appears to possess. (80)
• Unstable if slope of Igt slope of S
• the economic system would always be rushing
  either towards a state of hyper-inflation or
  towards total collapse this possibility can be
  dismissed (80)
• Since thus neither of these two assumptions can
  be justified, we are left with the conclusion
  that the I and S functions cannot both be
  linear. (81)
• I.e. models must have nonlinear functions

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Dynamic Instability

• 1st set of insights not known to Schumpeter
• Simple (non-evolutionary) models of market can
  fail to converge to equilibrium under realistic
  conditions (suppliers more responsive than
  consumers, investors more responsive than savers)
• Models can have unstable dynamics and not break
  down if functions nonlinear
• Underlying static partial equilibrium model need
  not converge to equilibrium
• What about general equilibrium?
• 2nd insight not known to Schumeter (or many
  economists today!)
• General equilibrium is unstable

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Dynamic Instability

• Schumpeters faith in equilibrium tendency of
  non-evolutionary markets derived from Walras
• Walras believed market system would find
  equilibrium prices and quantities bytatonnement
  (groping) process
• Start with randomly chosen starting point
• Adjust prices iteratively
• Increase price where demand gt supply
• Decrease price where demand lt supply
• Converge to equilibrium prices quantities
• In Walras words

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Dynamic Instability

• Once the prices have been cried at random,
  each party will offer those goods or services
  of which he thinks he has relatively too much,
  and he will demand those articles of which he
  thinks he has relatively too little the prices
  of those things for which the demand exceeds the
  offer will rise, and the prices of those things
  of which the offer exceeds the demand will fall.
  New prices now having been cried, each party to
  the exchange will offer and demand new
  quantities. And again prices will rise or fall
  until the demand and the offer of each good and
  each service are equal (Walras 1874)
• Convergence to general equilibrium over time?

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General Disequilibrium

• General equilibrium requires stable output
  prices
• Yt Yt-1 Ye (or with growth) Yt (1g) Yt-1
• Where Y vector of all commodities in economy
• Pt Pt-1 Pe
• Where P vector of relative prices of all
  commodities in economy
• Constant relative prices
• Modern maths shows these two inconsistent
• Either prices stable quantities unstable, or
• prices unstable quantities stable
• But not both (Jorgenson 60,61 McManus 63,
  Blatt 83)
• So general equilibrium will never converge to
  equilibrium, so that

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General Disequilibrium

• There exist known systems, therefore, in which
  the important and interesting features of the
  system are essentially dynamic, in the sense
  that they are not just small perturbations around
  some equilibrium state, perturbations which can
  be understood by starting from a study of the
  equilibrium state and tacking on the dynamics as
  an afterthought.
• If it should be true that a competitive market
  system is of this kind, then No progress can
  then be made by continuing along the road that
  economists have been following for 200 years. The
  study of economic equilibrium is then little more
  than a waste of time and effort Blatt (1983
  5-6)

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General Dynamics

• Schumpeters evolutionary economics was done by
  starting from a study of the equilibrium state
  and tacking on evolution as an afterthought
• We now know this cant be done
• So modern evolutionary economics
• Veblenian anti-equilibrium, Schumpeterian models
• Builds dynamic models add evolution later or
• Builds evolutionary models from the outset
• Former approach more common
• Easier (potentially dangerous reason!)
• Can incorporate vision of given economic theory
  (Marx, Keynes,)
• Close match to slowly evolving systems
• Insights from complex systems to evolution

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In summary

• Summarising validity of analytic techniques
  relations between them

• Now insights on evolution from complex systems

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Complexity Evolution

• Previous supply demand model linear
• Variables added together
• Only variables and constants
• Kaldors insightreal world cannot be this simple
• Variables must interact in more complex ways than
  simple addition
• Models with nonlinear relations between variables
  generate complex behaviour from even simple
  models
• Two examples
• Discrete logistic model of population
• Lorenzs quasi-quadratic weather model

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Complexity Evolution

• Logistic population model
• Simplest population model is
• This years population
• Equals last years
• Multiplied by growth rate

• Model predicts population grows to infinity
• But real-world populations will hit constraints
• Simplest constraint
• Cow tramples grass another cow could have eaten
• Interaction reduces life expectancy
• Interaction function of number of animals squared

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Complexity Evolution

• Ratio a/b gives equilibrium population
• For b0, exponential growth of population forever

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Complexity Evolution

• For bgt0, population first rises at accelerating
  rate and then slowly tapers to equilibrium level

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Complexity Evolution

• For a2 (2 births per animal per cycle), a
  2-cycle results
• Population overshoots carrying capacity
• Interactions reduce population to below carrying
  capacity
• And so on forever

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Complexity Evolution

• For agt2.7, chaos
• Population bounces around in unpredictable way
• Cycles never quite repeat (aperiodic) but never
  cease either
• But behind the apparent disorder, structurehence
  complexity rather than chaos theory

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Complexity Evolution

• Another example Lorenzs weather model simple
  system 3 equations, 3 unknowns, 3 constants

• Just 2 semi-quadratic nonlinear terms z.x and x.y

x displacement
y displacement
temperature gradient

• Model has 3 equilibria
• All 3 are unstable
• Generates incredibly complex cycles that are
• Highly sensitive to initial conditions but
• Have underlying common structure

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Complexity Evolution

• x,y,z values bounce around like crazy

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Complexity Evolution

• Small change in initial conditions has huge
  impact on eventual system path

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Complexity Evolution

• Behind the apparent chaos, an incredibly
  intricate structure
• Basic feature system never even approaches
  equilibria

Equilibrium 2
Equilibrium 1
Equilibrium 3
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Complexity Evolution

• Equilibrium highly unstable start just next to
  it and get propelled away instantly
• Strange role of equilibria in nonlinear
  dynamics/evolution

Start near equilibrium 3
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Complexity Evolution

• Systems almost always have unstable equilibria
• Many technical ways to measure degree of
  stability of dynamic system
• Dominant eigenvalue, Lyupanov exponent, Hurst
  exponent,
• Basic idea of all measures
• Greater than one value, system diverges from
  equilibrium (eigenvalue)
• Greater than another, initial starting points
  spread apart in timesensitive dependence on
  initial conditions, butterfly effect
• Greater than another, system inherently unstable
  fluctuations not only due to random shocks but
  also inherent instability of system feedbacks

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Edge of chaos

• Fixed dynamic system like Logistic is either one
  side or the other of measures
• Dominant eigenvalue lt 1, stable equilibrium
• Dominant eigenvalue gt 1, unstable equilibrium
• Lyapunov exponent gt 1, chaos
• Evolutionary systems (e.g., when parameters a b
  can change over time) tend to the edge of chaos
• System oscillates between stability and chaos
• Small change in parameters either way shift from
  stable to unstable and vice versa.
• Living systems appear to dynamic systems that
  evolve to edge of chaos
• Other insights from complexity analysis

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Emergent behaviour

• Group behaviour occurs that is not predictable
  from properties of individuals in it but depends
  on relationships between them
• Relationships may evolve as much as individuals
• E.g., individual sparrows easily fall prey to
  Hawk
• Sparrows that fly together increase chances of
  survival
• Relationship of flying together evolves
• Flocking results
• Intuitions
• Macro outcomes can be very different to micro
  level behaviour
• Similar conclusion reached by some neoclassicals

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Emergent behaviour

• Failure to derive coherent market demand curves
  from individual demand curves led to conclusion
  that
• If we are to progress further we may well be
  forced to theorise in terms of groups who have
  collectively coherent behaviour. Thus demand and
  expenditure functions if they are to be set
  against reality must be defined at some
  reasonably high level of aggregation. The idea
  that we should start at the level of the isolated
  individual is one which we may well have to
  abandon. (Kirman 1989)

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Dynamic Evolutionary Modelling

• Dynamic modelling mature field
• Mathematical techniques well-known
• Computer simulation tools sophisticated
• Evolutionary modelling relatively immature
• No mathematical tools
• Computer simulation tools complicated to use
• Basic methods in both
• Specify characteristics of entities
• Specify relationships between entities
• Specify adaptive processes
• change in number, size of entities

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Dynamic Evolutionary Modelling

• Differences
• Dynamic modelling
• Behaviour of entities remains constant
• Parameters of relationships remain constant
• Evolutionary modelling
• Behaviour alters via mutation/adaptation
• Parameters of relationships alter

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Dynamic Evolutionary Modelling

• Basic tools of dynamic modelling
• System of difference equations
• Property now some nonlinear function of
  properties in previous time period

• System of differential equations
• Rate of change of property now nonlinear
  function of properties now (or lagged)

• Differential equations more general
• Approximate behaviour of large numbers
• Discrete technical change by each firm sums to
  near continuous technical change by industry

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Dynamic Evolutionary Modelling

• Final, closed form solutions cant be specified
• With equilibrium comparative statics, can
  conclude, e.g.

• With single differential equation, can conclude,
  e.g.

• With 3 or more coupled nonlinear differential
  equations
• No closed form solution exists
• Must simulate
• On which, advanced dynamic tools

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Dynamic Evolutionary Modelling

• Advanced tools
• Specialised mathematical programs
• Mathcad, Mathematica, Matlab, Maple
• Much more powerful, flexible than spreadsheets

• Flowchart tools Simulink, Vissim, IThink
• E.g., stockmarket model

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Dynamic Evolutionary Modelling

• Stock market with fundamental trades, bandwagons,
  collective optimism/pessimism panics

Matlab/Simulink
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Dynamic Evolutionary Modelling

• Contra Efficient Markets Hypothesis, model
  generates realistic bull/bear cycles, crashes
• But no alteration of behaviour over time

• Sufficient for description of systemic dynamics
• Insufficient for evolution of individual
  systemic behaviour over time

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Dynamic Evolutionary Modelling

• Evolutionary modelling
• Entities and relationships specified
• at individual level (agents)
• in discrete form (aggregation gives collective
  emergent behaviour)
• Adaptive formula for change in parameters of
  entities/relationships specified
• Parameters altered adaptively each time step
• Sometimes
• Rules for death, crossover, mutation
• Spontaneous appearance of new entities (products,
  firms)
• Only feasible tool at present computer
  programming
• On which, more next week!

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References

• Blatt, J.M., (1983). Dynamic Economic Systems, ME
  Sharpe, Armonk.
• Hicks, J.R., (1949). Mr Harrods Dynamics,
  Economic Journal 68-75
• Jorgenson, D. W., (1961). Stability of a dynamic
  input-output system, Review of Economic Studies
  28 105-116.
• Stability of a dynamic input-output system a
  reply, Review of Economic Studies 30 148-149.
• Kaldor, N., (1940). A model of the trade cycle,
  Economic Journal 78-92
• Kirman, A., (1989). The intrinsic limits of
  modern economic theorythe emperor has no
  clothes, Economic Journal 99 126-139.
• McManus, M., (1963), Notes on Jorgenson's
  Model, Review of Economic Studies 30 141-147.
• Walras, L., (1874). Elements of Pure Economics,
  Augustus M Kelley, Farfield

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General Disequilibrium

• Most basic model of production is input-output
• It takes ½ ton of steel and 5 tons of coal to
  make 1 ton of steel etc.
• Can be represented as matrix equation
• YtA Yt-1
• Where A is matrix of input-output coefficients
• Single number can be derived from A
• Yt l Yt-1
• Just like Yt(1g) Yt-1

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Technical stuff