Gerald Silverberg

Innovation, Diversity and Diffusion: A Self-organisation Model

A number of features of innovation diffusion are identified: appropriability, diversity, expectations, selection, learning, and spillover externalities. A dynamic model is formul ated to embed the diffusion question into a more general framework of disequilibrium competition. The model incorporates distinct vintage structures reflecting a change in technological trajectory, learning-by-using, a nd expectations-driven investment rules of thumb. Simulation studies reveal robust quasi-logistic curves, but a complicated pattern of net market share gains and losses. Uncertainty regarding the rationality of early or late adoption, it is argued, ensures that the requisite behavioral variety is present to generate these diffusion patterns. Copyright 1988 by Royal Economic Society.

The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance

This paper focuses on the analysis of size distributions of innovations, which are known to be highly skewed. We use patent citations as one indicator of innovation significance, constructing two large datasets from the European and US Patent Offices at a high level of aggregation, and the Trajtenberg (1990) dataset on CT scanners at a very low one. We also study self-assessed reports of patented innovation values using two very recent patent valuation datasets from the Netherlands and the UK, as well as a small dataset of patent license revenues of Harvard University. Statistical methods are applied to analyse the properties of the empirical size distributions, where we put special emphasis on testing for the existence of ‘heavy tails’, i.e., whether or not the probability of very large innovations declines more slowly than exponentially. While overall the distributions appear to resemble a lognormal, we argue that the tails are indeed fat. We invoke some recent results from extreme value statistics and apply the Hill (1975) estimator with data-driven cut-offs to determine the tail index for the right tails of all datasets except the NL and UK patent valuations. On these latter datasets we use a maximum likelihood estimator for grouped data to estimate the Pareto exponent for varying definitions of the right tail. We find significantly and consistently lower tail estimates for the returns data than the citation data (around 0.7 vs. 3-5). The EPO and US patent citation tail indices are roughly constant over time (although the US one does grow somewhat in the last periods) but the latter estimates are significantly lower than the former. The heaviness of the tails, particularly as measured by financial indices, we argue, has significant implications for technology policy and growth theory, since the second and possibly even the first moments of these distributions may not exist. (JEL Codes: C16, O31, O33 Keywords: returns to invention, patent citations, extreme-value statistics, skewed distributions, heavy tails.)

Evolutionary Theorizing on Economic Growth

The research project on Systems Analysis of Technological and Economic Dynamics at IIASA is concerned with modeling technological and organisational change; the broader economic developments that are associated with technological change, both as cause and effect; the processes by which economic agents -- first of all, business firms -- acquire and develop the capabilities to generate, imitate and adopt technological and organisational innovations; and the aggregate dynamics -- at the levels of single industries and whole economies -- engendered by the interactions among agents which are heterogeneous in their innovative abilities, behavioural rules and expectations. The central purpose is to develop stronger theory and better modeling techniques. However, the basic philosophy is that such theoretical and modeling work is most fruitful when attention is paid to the known empirical details of the phenomena the work aims to address: therefore, a considerable effort is put into a better understanding of the stylized facts concerning corporate organisation routines and strategy; industrial evolution and the demography of firms; patterns of macroeconomic growth and trade. n nFrom a modeling perspective, over the last decade considerable progress has been made on various techniques of dynamic modeling. Some of this work has employed ordinary differential and difference equations, and some of it stochastic equations. A number of efforts have taken advantage of the growing power of simulation techniques. Others have employed more traditional mathematics. As a result of this theoretical work, the toolkit for modeling technological and economic dynamics is significantly richer than it was a decade ago. n nDuring the same period, there have been major advances in the empirical understanding. There are now many more detailed technological histories available. Much more is known about the similarities and differences of technical advance in different fields and industries and there is some understanding of the key variables that lie behind those differences. A number of studies have provided rich information about how industry structure co-evolves with technology. In addition to empirical work at the technology or sector level, the last decade has also seen a great deal of empirical research on productivity growth and measured technical advance at the level of whole economies. A considerable body of empirical research now exists on the facts that seem associated with different rates of productivity growth across the range of nations, with the dynamics of convergence and divergence in the levels and rates of growth of income, with the diverse national institutional arrangements in which technological change is embedded. n nAs a result of this recent empirical work, the questions that successful theory and useful modeling techniques ought to address now are much more clearly defined. The theoretical work has often been undertaken in appreciation of certain stylized facts that needed to be explained. The list of these facts is indeed very long, ranging from the microeconomic evidence concerning for example dynamic increasing returns in learning activities or the persistence of particular sets of problem-solving routines within business firms; the industry-level evidence on entry, exit and size-distributions -- approximately log-normal -- all the way to the evidence regarding the time-series properties of major economic aggregates. However, the connection between the theoretical work and the empirical phenomena has so far not been very close. The philosophy of this project is that the chances of developing powerful new theory and useful new analytical techniques can be greatly enhanced by performing the work in an environment where scholars who understand the empirical phenomena provide questions and challenges for the theorists and their work. n nIn particular, the project is meant to pursue an evolutionary interpretation of technological and economic dynamics modeling, first, the processes by which individual agents and organisations learn, search, adapt; second, the economic analogues of natural selection by which interactive environments -- often markets - winnow out a population whose members have different attributes and behavioural traits; and, third, the collective emergence of statistical patterns, regularities and higher-level structures as the aggregate outcomes of the two former processes. n nTogether with a group of researchers located permanently at IIASA, the project coordinates multiple research efforts undertaken in several institutions around the world, organises workshops and provides a venue of scientific discussion among scholars working on evolutionary modeling, computer simulation and non-linear dynamical systems. n nThe research focuses upon the following three major areas: (1) Learning Processes and Organisational Competence; (2) Technological and Industrial Dynamic; (3) Innovation, Competition and Macrodynamics.

Collective Learning, Innovation and Growth in a Boundedly Rational, Evolutionary World

We formulate a simple multiagent evolutionary scheme as a model of collective learning, i.e. a situation in which firms experiment, interact, and learn from each other. This scheme is then applied to a stylized endogenous growth economy in which firms have to determine how much to invest in R&D, where innovations are the stochastic product of their R&D activity, spillovers occur, but technological advantages are only relative and temporary and innovations actually diffuse, both at the intra and interfirm levels. The model demonstrates both the existence of a unique long-run growth attractor (in the linear case) and distinct growth phases on the road to that attractor. We also compare the long-run growth patterns for a linear and a logistic innovation function, and produce some evidence for a bifurcation in the latter case.

Long waves and ‘evolutionary chaos’ in a simple Schumpeterian model of embodied technical change

Abstract Since Schumpeter, an extensive debate has taken place concerning the relationship between innovation, diffusion, macrodynamics, and the purported existence of long Kondratieff waves of economic activity. Rosenberg and Fritschtak have rightly pointed out that until now no conceptually consistent model has been proposed that would allow a scientific discussion of the causalities involved. By generalizing a previous model of Schumpeterian competition and ‘creative destruction’ based on the Goodwin growth cycle these various elements can be related naturally in a simple dynamic model. Mathematically, the model is equivalent to a large-dimensional Lotka-Volterra system with stochastically perturbed coefficients. Allowing for the introduction of new techniques according to various possible stochastic processes such as time-homogeneous or inhomogeneous Poisson, computer experiments reveal an intriguing and robust pattern of distributed ‘long waves’. Application of the Grassberger-Procaccia correlation dimension suggests that we may be dealing with an unusual form of low-dimensional ‘deterministic’ chaos as an emergent property of a basically stochastic system. We have termed this phenomenon ‘evolutionary chaos’. Empirical analysis of several innovation time series indicates that innovations have been arriving stochastically, but at an exponentially growing rate and somewhat more clustered than Poisson.

Adoption and Diffusion of Technology as a Collective Evolutionary Process

Innovation diffusion occupies a special place in the economics of technological change. On the one hand it is empirically the best established and most intensively studied phenomenon in this area, and the logistic and other S-shaped curves have provided a sound mathematical, if somewhat phenomenological, inroad into a diverse range of applications. On the other, it still remains somewhat divorced from any microeconomically founded, overarching theory of the determinants of technological change which might constitute a central component of a general approach to economic dynamics and social evolution.

Network structure of inter-industry flows

We study the structure of inter-industry relationships using networks of money flows between industries in 45 national economies. We find these networks vary around a typical structure characterized by a Weibull link weight distribution, exponential industry size distribution, and a common community structure. The community structure is hierarchical, with the top level of the hierarchy comprising five industry communities: food industries, chemical industries, manufacturing industries, service industries, and extraction industries.

An evolutionary model of long term cyclical variations of catching up and falling behind

We generalize a single-country model of endogenous growth to the case of a multi-country world economy in which technology transfer and behavioral imitation are the possible means of interaction between countries. The model is evolutionary in the sense that the economies are disaggregated by behaviourally heterogeneous firms, market selection occurs, and the innovation process is uncertain and stochastic. We demonstrate that this structure leads to a complex process of convergence and divergence over time that can be characterized as 1/f noise. Spectral analysis of measures of convergence for six core OECD countries in the period 1870–1989 reveals a similar pattern in the empirical data.

Embodied Technical Progress in a Dynamic Economic Model: The Self-Organization Paradigm

A number of distinguished economists have pointed out that the theoretical approaches dominant today have yet to come to terms with the historical, irreversible, and heterogeneous nature of the industrial societies they purport to deal with.1 Indeed, there seem to be fundamental reasons for this failure. Neoclassical theory, in aggregating capital and presupposing a very special equilibrium process, seems more to obscure than illuminate what is actually going on at the microeconomic level from which its concepts ostensibly are taken. And the post-Keynesian tradition deriving from Sraffa and von Neumann, by working exclusively with so-called long run equilibrium prices, implicitly assumes a single technique over all of history and thereby rules out the analysis of processes of transition (which indeed are the only ones we have known until now in the history of industrial society) involving the appearance and disappearance, the coexistance and differential reproduction (replacement) of distinct capital and consumer goods, natural resources, etc., which in dynamic terms is the ultimate justification for introducing heterogeneity in the first place. The deeper insights of Schumpeter on the disequilibrium process of industrial evolution, and of Keynes, particularly regarding the relationship between expectations and effective demand, have largely failed to find entrance into the mainstream of analytical economics.

Long Memory and Economic Growth in the World Economy Since the 19th Century

We discuss the relevance of long memory for the investigation of long-term economic growth and then briefly review the state-of-the-art of statistical estimators of long memory on small samples and their application to economic datasets. We discuss theoretical mechanisms for long memory such as cross-sectional heterogeneity. We argue that this endogeneity should be explained endogenously and not simply assumed. Evolutionary models of growth appear to offer one natural explanation of such heterogeneity. Using the Maddison (1995) [1] data on 16 countries starting in 1870, supplemented by more recent data down to the year 2001, we then apply different estimators to test the hypothesis of long memory on individual country GDP and GDP per capita. These estimators are Beran’s FGN nonparametric test based on an approximate Whittle ML estimator, Robinson’s semiparametric log periodogram regressor, Sowell’s parametric ML ARFIMA estimator and the ML FAR estimator. The results are mixed and somewhat ambiguous between methods. Moving from the nonparametric to the parametric methods (i.e., controlling for short memory) we find less evidence of long memory. We find that Robinson’s semiparametric method also suffers from severe sensitivity to the cuto. parameters. We compare our results with those of Michelacci and Zaffaroni [2] and criticize their methodology. We conclude that the lack until now of a single test that deals successfully with all known problems (small sample bias, short memory contamination, specification error, parameter sensitivity) precludes the formulation of a definitive statement about long memory in economic growth.