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Evolutionary modelling and theLaboratory for Simulation Development

PhD Eurolab on Simulation of Economic Evolution (SIME)University of Strasbourg, April 2004

Esben Sloth AndersenDRUID and IKE, Aalborg University, Denmark

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KISS and TAMAS: Conflicting principles?

KISS = Keep It Simple, Stupid! A slogan from the US army during World War II Generally acknowledged by scientific modellers

TAMAS = Take A Model, Add Something! Variant for Lsd modellers:

TAMAM = Take A Model, Add Marco! Principle for cumulative modelling

KISS = TAMAS? Not when the initial model is complex and ill structured! In this case we need a new principle!

TAMAKISS = Take A Model And Keep It Simpler, Stupid!

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The history of evolutionary economics

1. Old evolutionary economics: No KISS and TAMAS Adam Smith, Marx, Menger, Marshall, Schumpeter, Hayek, …

2. The “dark ages”: KISS and TAMAS kill evolution! Crowding out by the formalist revolution from about 1930

3. Starting new evolutionary economics with KISS and TAMAS

Breakthrough I: Nelson and Winter’s book on An Evolutionary Theory of Economic Change (1982)

Breakthrough II: The follow-up on Maynard Smith’s book on Evolution and the Theory of Games (1982)

Breakthrough III: The computational study of evolving dynamical systems (e.g. the Santa Fe Institute)

4. Developing new evolutionary economics Normal evolutionary science with TAMAS or new start with

TAMAKISS?

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Population thinking as the starting point

Typological thinking is anti-evolutionary It suggests that heterogeneity is not essential – just

disturbing It wants to find the common type or the “representative

agent” Population thinking is pro-evolutionary

Here heterogeneity is the driver of evolution The outliers are of crucial importance The “representative firm” must be supplemented by

population statistics (including the variance of behaviour) Literature

Population thinking is explained by Ernst Mayr (evolutionary biologist) and Stan Metcalfe (evolutionary economist)

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Nelson and Winter’s population thinking

Nelson and Winter’s evolutionary synthesis including:

Behavioural patterns and their transmission Creation of new behavioural patterns Different types of selection mechanisms

More specifically, they combined: Simon’s work on routines and satisficing behaviour Nelson’s and other Schumpeterian work on

innovation and imitation Alchian’s and Winter’s work on natural selection

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The structure of the Nelson-Winter book

Part I: Overview and Motivation Part II: Organization-Theoretic Foundations of Economic

Evolutionary Theory The part that has made Nelson and Winter famous in leading

business schools and in leading business economics journals Part III: Textbook Economics Revisited

Includes KISS models of the selection process Part IV: Growth Theory

Micro-founded endogenous growth theory, but no KISS Part V: Schumpeterian Competition

Core contribution to evolutionary theory and to a realistic industrial dynamics, but no KISS

Part VI: Economic Welfare and Policy Part VII: Conclusion

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The Nelson-Winterfamily of simulation models NWch6, NWch7 and NWch10: Theoretical KISS models of the

selection process

NWch9 reproduces Solow’s growth data in a more ‘realistic’ way than through Solow’s own growth model

NWch12: the competition between innovators and imitators in a

process of 'Schumpeterian competition' (Schumpeter Mark II)

NWch13: how concentration and macroproductivity are influenced by the conditions of innovation and imitation, and by investment strategies

NWch14: the trade-off between static efficiency and dynamic efficiency (based on some degree of market power)

XNW1984: Winter’s study of Schumpeterian competition in alternative technological regimes

XNW1999: history-friendly modelling of the computer industry

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The basic set-up of Nelson-Winter models

State at time t

A1t ,, Ajt ,, Ant

K1t ,,K jt ,,Knt

State at time t + 1

A1,t1,,A j,t1,, An ,t1

K1,t1,,K j,t1,,Kn ,t1

Complex transition rule with stochastic change of A and deterministic change of K Determined by a lot of decision 'routines' (parameters), e.g. R&D intensity per unit of capital, capacity utilisation etc.

The models can be extended by introducing new evolving variables into the state space

• E.g. R&D intensity in the models by Silverberg and Verspagen

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Naive simulation of the Nelson-Winter model of Schumpeterian competition

2 4 6 8 10 12 14 160.15

0.2

0.25

0.3

0.35

0.4

0.45

market shares (total = 1.0)

time

2 4 6 8 10 12 14 160.15

0.2

0.25

0.3

0.35

0.4

output/capital ratio

time

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The structure of the transformationmechanism in Nelson-Winter models

1. Short-run process

2. Capital accumulation

3. Technical change

Ki

Ai

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The need for simulation tools

The areas of simulation Simple models (like replicator dynamics) can be

studied by mathematical analysis But simulation helps mathematical intuition Complex models can only be studied by simulation

The need for tools To perform the simulations The present the results graphically To perform statistical analysis of the results To document the simulation model and share it with

others

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Typical simulation tasks - I

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Tasks - II

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First step: install and start Lsd

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Second step: select a model

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Third step: start the model

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Fourth step (a): load configuration file

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Fourth step (b): inspect configuration file

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Fourth step (c): revise configuration file

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Fifth step: run simulation and study plot

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Sixth step: make data analysis

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Seventh step (a): automatic documentation

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Seventh step (b): Lsd equations as model specification

Equations are written in a rather simple language and in an arbitrary sequence

Example:EQUATION("Q")

/*

Q(t) = K(t-1) * A(t-1)

Quantity is is computed as capital times

productivity, both with lagged values

*/

RESULT(VL("K",1)*VL("A",1))

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How to do it in practice?

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Rethinking simulation models:The avoidance of the monopolistic trend

The core of the Nelson-Winter model Replicator dynamics in a

homogeneous selection environment Such dynamics lead to monopoly It is even worse when we include cumulative innovation

NW solution: monopolistic investment restraint

In the end selection is more or less switched off Variance is sustained and innovation dominates Not a fully satisfactory solution! Alternatives are the introduction of market niches

and/or large spin-offs from large firms (inheriting the productivity level from the mother firm)

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Step-wise analysis of the transformation mechanism in Nelson-Winter models

Define four regime parameters Regime_inno

Determines whether and how innovation takes place

Regime_imi Determines whether and

how imitation takes place Regime_restraint

Determines whether investment restraint is present

Regime_fission Determines whether spin-offs

from large firms takes place

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Specifying the regimes Regime_imi - Imitative regime of the industry 0: no imitation

1: imitation of industry's best productivity 2: imitation of industry's mean productivity

Regime_inno - Innovative regime of the industry 0: no innovation

1: innovation from industry's mean productivity 2: innovation from firm's present productivity Regime_restraint - Monopolistic behaviour O: no monopolistic behaviour 1: monopolistic restraint due to mark-up pricing Regime_fission - Splitting of large firms 0: no fission of large firms 1: fission of large firms

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Defining and calculating statistics

Population information for two points of time Initial capacity share of each firm Reproduction coefficient of each firm Productivity of each firm and its change

Simple statistics Mean reproduction coefficient (abs. fitness) Change in mean productivity Variance of productivities Covariance of reproduction coefficients and

productivities

Regression of reproduction coefficients on productivities

( , )t t

is/i i iw x x

,i iz z

i iw s wz

2Var( ) ( )i i iz s z z Cov( , ) ( )( )i i i i iw z s w w z z

( , ) Cov( , ) / Var( , )i i i i i iw z w z w z

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George Price’s interpretation of the statistics

Developed in biology in the beginning of the 1970s

Surprisingly fruitful for any evolutionary analysis

The format of Price’s equation (identity) Total evolutionary change

Selection effect + Innovation effect

Metcalfe (2002): “For some years now evolutionary economists

have been using the Price equation without realising it.”

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Price’s definition of evolutionary change

Total evolutionary change with respect to a particular characteristic of a population = the change in the mean of the individual values of that characteristic, i.e.

This definition is directly applicable to simple population analysis and multi-level population analysis

z

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Definition of selection by covariance

Selection effect = the covariance of relative reproduction coefficients and values of the characteristic

The meaning of this definition of selection: The exploitation of variance in pre-selection population to

change the mean characteristic of post-selection population Elements of pure selection (i.e. no innovation)

Basically selection is seen as the covariance between relative reproduction coefficients (fitnesses) and characteristics

The efficiency of selection is the regression of fitnesses on characteristics

w

zzw

w

zwz iiiii )Var(),(),Cov(

Cov( / , )i iw w z

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Definition of innovation by a mean effect

Innovation effect = the mean of the product of the change of the values of the characteristic and the relative reproduction coefficients, i.e.

Measuring pure innovation (i.e. no selection)

e.g. the weighted mean of the firm-internal change in productivity

“Innovation” is any local change in the “units of selection”

It includes imitation among units and learning within units It can often be decomposed into within-unit selection and low-

level innovation

E( / ) ii i i i i i

wz z w w s z s z

w

E( / )i iz w w

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Price’s partitioning of evolutionary change

Total evolutionary change Selection effect + Innovation effect

Alternative formulation for further partitioning

Remark that the LHS is structurally like the RHS expectation

The innovation effect is often the outcome of both selection and innovation within higher-level “units of selection”

Selection Innovation

Cov( , ) E( )i i i iw z w z w z

w

zw

wz iizw ii )E(Cov( ),

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The meaning of Price’s equation

The innovation effect is the creative part It takes place within the units, e.g. the firms It may be due to innovation, imitation, learning, … It may also be due to intra-firm selection, e.g. of plants

The selection effect means that some entities are promoted while other entities shrink

It represents Schumpeter’s “creative destruction” Firms may try to avoid selection by imitation and

learning The selection pressure sets the agenda for firms

The Price equation ignores ecological effects Thus it is a form of short-term evolutionary analysis But short-term evolution is the starting point!

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Understanding Nelson-Winter models through the TAMAKISS principle

The simplest situation: No innovation/imitation and no monopolistic

restraint Then we have a simple replicator dynamics Result: Monopoly of the productivity leader

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The movement of mean productivity

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The movement of capital shares

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The covariance between reproduction coefficients and productivity

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The regression of reproduction coefficients on productivity

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Introducing monopolistic restraint

The monopoly paradox in evolutionary models Not really a paradox in the highly simplified

environment with a homogeneous product, etc. But in reality monopolies are seldom

We also would like some permanent competition for using the model for exploring evolution

Nelson-Winter solution: monopolistic restraint Large firms recognise that they do not maximise

profits by expanding capacity But a full monopoly would be more profitable! Alternative solution: new firms by spin-offs

but presently we shall stick to N&W

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The movement of mean productivity

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The movement of capital shares

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The regression of reproduction coefficients on productivity

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Introducing innovation intosimple replicator dynamics

Innovation strengthens monopolistic tendencies Innovation is costly, so in the short run it reduces

capital accumulation In the long run, innovation is more profitable for large

than for small firms Reason 1: There are fixed probabilistic costs of

producing an innovation, but large firms have a larger effect of the innovation (it is immediately used throughout the firm)

Reason 2: Under the cumulative regime, productivity leaders have better innovations than others

Consequence There are further reasons to introduce

monopolistic restraint (see below)

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The movement of productivities

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The movement of capital shares

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Innovation and monopolistic restraint

Monopolistic restraint totally change the outcome

It means that firms moves profits away from capital accumulation within the industry

Therefore, they make room for other firms Oligopoly

The result is an oligopoly, since only a limited number of firms can survive in the productivity race

Productivity growth is smaller than in (unrealistic)replicator dynamics with innovation

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The movement of productivities

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The movement of capital shares

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Results about the monopoly paradox

The core of the Nelson-Winter model Replicator dynamics in a homogeneous selection

environment Such dynamics lead to monopoly It is even worse when we include cumulative innovation

Stabilisation of diversity by investment restraint A simple solution that creates an environment in which

many evolutionary processes can be tested Not a fully satisfactory solution Alternatives are the introduction of market niches

and/or large spin-offs from large firms (inheriting the productivity level)

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Introducing fission in replicator dynamics

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Andersen’s early lack of TAMAKISS

Building on complex rather than simple simulation models Not making a demand specification for his model version Not making a sufficiently detailed model design

Although lots of verbal descriptions, flow charts, pseudo-code, ... Not developing the program step by step

Much too often the simulation program did not run correctly! Not performing systematic simulation experiments Not making deep statistical analysis Not making a cumulative an extensive documentation

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Overcoming the difficulties and failures

Development of TAMAKISS versions of Nelson-Winter models and AL models starting from replicator dynamics

Complexity is introduced in a step-wise manner Development of concrete models to explain concrete

phenomena Like macroeconomic demand satiation and the stylised

history of the software industry Use of the Lsd system for simulation models

Makes gradual model development and statistical analysis easy

Gives easy tools for model documentation and distribution Use Price’s evometrics to understand the dynamics of

simulations and to start exploration of empirical data