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1
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
2
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!
3
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?
4
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)
5
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
6
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
7
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
8
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
9
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
10
The structure of the transformationmechanism in Nelson-Winter models
1. Short-run process
2. Capital accumulation
3. Technical change
Ki
Ai
11
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
12
Typical simulation tasks - I
13
Tasks - II
14
First step: install and start Lsd
15
Second step: select a model
16
Third step: start the model
17
Fourth step (a): load configuration file
18
Fourth step (b): inspect configuration file
19
Fourth step (c): revise configuration file
20
Fifth step: run simulation and study plot
21
Sixth step: make data analysis
22
Seventh step (a): automatic documentation
23
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))
24
How to do it in practice?
25
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)
26
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
27
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
28
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
29
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.”
30
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
31
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
32
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
33
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( ),
34
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!
35
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
36
The movement of mean productivity
37
The movement of capital shares
38
The covariance between reproduction coefficients and productivity
39
The regression of reproduction coefficients on productivity
40
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
41
The movement of mean productivity
42
The movement of capital shares
43
The regression of reproduction coefficients on productivity
44
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)
45
The movement of productivities
46
The movement of capital shares
47
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
48
The movement of productivities
49
The movement of capital shares
50
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)
51
Introducing fission in replicator dynamics
52
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
53
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