Current Research Interests

1
Current Research Interests

• Complex models of innovation on rugged technology
  landscapes
• Endogenous evolutionary models of economic
  growth, and comparison with neoclassical rational
  expectations models with learning
• Applied econometrics of complex systems
• Long memory
• Skewed, fat-tailed distributions (e.g. Pareto vs.
  Lognormal)
• Spatio-temporal clustering
• Graph-theoretic properties of technological
  trajectories
• Risk management in a Paretian universe

2
Percolating Complexity Generating the Complex
Patterns of the Innovation Process from a Simple
Probabilistic Lattice, with some Empirical
Illustrations

• Gerald Silverberg
• MERIT, Maastricht University

based on joint work with Bart Verspagen ECIS,
Eindhoven University of Technology
Lyon Exystence Thematic Institute, June 2003
3
What is Complexity, and What is a Complex
Dynamics Model?
Negative definitions Dick Day (1994) Something
not generated by a point attractor or a limit
cycle, i.e., highly unpredictable with classical
deterministic methods. If we add noise and think
about it observationally Something that is not
Gaussian and short-memory (i.e., stable ARMA
process) or does not consist solely of a finite
number of sharp spectral peaks above background
noise. Positive, heuristic definitions A
complex spatio-temporal structure with
significant clustering or long-range
correlations Examples 1/f noise, power laws,
fractals, long memory, intermittancy Possible
modeling approaches exploit extended critical
systems such as percolation, self-organized
criticality (sandpiles, etc.)
4
Stylized Facts About Technological Change
  1. Technical change is cumulative new
technologies build on each other.   2.  Technical
change follows relatively ordered pathways, as
can be measured ex post in technology
characteristics space (see the work of Sahal,
Saviotti, Foray and Gruebler, etc.). This has led
to the positing of natural trajectories (Nelson),
technological paradigms (Dosi), and technological
guideposts (Sahal).   3.  The arrival of
innovations appears to be stochastic, but more
highly clustered than Poisson (overdispersion).
  4.  The size of an innovation is drawn from
a highly skewed distribution (as evidenced e.g.
by citation and co-citation frequencies compiled
by Tratjenberg and van Raan).   5.  Technological
trajectories bifurcate and also
merge.   6.  There appears to be a certain
arbitrariness in the path actually chosen, which
could be the result of small events (path
dependence or neutral theory?) and cultural and
institutional biases (social construction of
technology?).   7.  Incremental improvements tend
to follow upon radical innovations according to
rather regular laws (learning curves).
5
Raw data and four fitted regression models for
supersample data. Pure Poisson models are
rejected against negative binomial
(overdispersed) models
6
Innovation Size Distributions
Frequency distributions of CT scanner patent
citations. Linear scale above, double log plot by
rank above right, with self-citation left. Data
source Tratjenberg (1990).
7
Scherer et al. Analysis of Innovation Returns
Source Scherer, Harhoff and Kukies, 2000,
Uncertainty and the size distribution of rewards
from innovation, JEE, 10 175-200.
8
Scherer et al. continued
9
Hill Estimator Consider n observations of a
random variable Xi, and denote by Xi the order
statistics X1?X2? ?Xn. Then the Hill
estimator is defined as follows
Hill estimator applied to Harvard University
patent portfolio data used in Scherer (1998)
(left), and to Trajtenbergs (1990) patent
citation data (right).
10
Percolation diagram in technology-performance
space. Lattice sites are filled at random. A site
is viable when it connects to the baseline.
11
Probability of a random site being on the
infinite cluster P as a function of the
percolation probability q
12
Convergence, divergence and shortcuts, and two
methods of defining a technology's
competitiveness.
13
New innovations are generated with probability p
in a region d units above and below the
technological frontier.
14
Near disjoint regions represent inventions, far
off discoveries science, and clusters that can
never be connected to the baseline science
fictions.
15
A cluster of simultaneous invention occurs when a
disjoint island of invention is suddenly joined
to the frontier by a single 'cornerstone'
innovation.
16
Screen Shot of Run with Search Radius 8
17
Deadlocking Statistics
Number of runs, which deadlock out of batches of
ten for different values of the search radius.
q0.593.
Number of deadlocked runs out of ten as a joint
function of the search radius and the percolation
probability q.
18
The mean height of the BPF attained after 5000
periods as a function of the search radius and
percolation probability q.
19
Size distribution of innovations (left) and
rank-order distribution (right, double-log
scale), q0.603, m10.
20
Hill Estimators q0.6, 0.645
Hill estimator of Pareto ? for innovation
distribution generated with q0.6 and m5 plotted
on a double-log scale for values of k up to 90
of number of observations.
Hill estimator of Pareto ? for innovation
distribution generated with q0.645 and m5
plotted on a double-log scale for values of k up
to 90 of number of observations
21
Hill Estimator q0.695
Hill estimator of Pareto ? for innovation
distribution generated with q0.695 and m5
plotted on a double-log scale for values of k up
to 90 of number of observations.

• LD Plot q0.6

LD plot for innovation distribution generated
with q0.60 and m5 (original data and aggregated
data in blocks of 10, 100 and 200 observations).
22
LD Plots q0.645, 0.695
LD plot for innovation distribution generated
with q0.645 and m5 (original data and
aggregated data in blocks of 10, 100 and 200
observations).
LD plot for innovation distribution generated
with q0.695 and m5 (original data and
aggregated data in blocks of 10, 100 and 200
observations).
23
Temporal clustering Innovation count time series
for a threshold of 2 (left) and 10 (right) for a
run with search radius 5.
24
Arrival rate and overdispersion index for search
radius m and threshold theta for radical
innovations
25
Space-time plot of innovations Moran clustering
index highly significant
Technology space
time
26
Space-time clustering of cylinder sizes of
Cornish steam engines (Nuvolari and Verspagen
2003)
27
Conclusions

• We can maximize our ignorance of technology space
  by percolating it with an exogenous percolation
  probability q
• We can impose the cumulativeness condition by
  requiring viable technologies to trace a path
  back to the baseline
• We can impose blindness and localness of the RD
  search process by using m-neighborhoods of the
  BPF with uniform prob of testing sites
• Nevertheless we obtain, instead of a completely
  random innovation process, spatial and temporal
  clustering of innovations
• Innovation size distributions are highly skewed
  and possibly fat tailed. Near the critical q they
  appear to be Pareto, for higher q probably
  lognormal
• Outlook
• Endogenize RD effort and targeting using
  agent-based model
• Endogenize q along lines of Bak-Sneppen model