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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

We study the structure of inter-industry relationships using networks of money flows between industries in 20 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.Comment: 14 pages, 7 figure

An obstacle to the widespread adoption of environmentally friendly energy technologies such as stationary and mobile fuel cells is their high upfront costs. While much lower prices seem to be attainable in the future due to learning curve cost reductions that increase rapidly with the scale of diffusion of the technology, there is a chicken and egg problem, even when some consumers may be willing to pay more for green technologies. Drawing on recent percolation models of diffusion by Solomon et al. [7], Frenken et al. [8] and Höhnisch et al.[9], we develop a network model of new technology diffusion that combines contagion among consumers with heterogeneity of agent characteristics. Agents adopt when the price falls below their random reservation price drawn from a lognormal distribution, but only when one of their neighbors has already adopted. Combining with a learning curve for the price as a function of the cumulative number of adopters, this may lead to delayed adoption for a certain range of initial conditions. Using agent-based simulations we explore when a limited subsidy policy can trigger diffusion that would otherwise not happen. The introduction of a subsidy policy seems to be highly effective for a given high initial price level only for learning economies in a certain range. Outside this range, the diffusion of a new technology either never takes off despite the subsidies, or the subsidies are unnecessary. Perhaps not coincidentally, this range seems to correspond to the values observed for many successful innovations.JEL Codes: C61, H23, O32, O33

Innovations are known to arrive more highly clustered than if they were purely random. Their distribution of importance is highly skewed and appears to obey a power law or lognormal distribution. Technological change has been seen by many scholars as following technological trajectories and being subject to 'paradigm' shifts from time to time.To address these empirical observations, we introduce a complex technology space based on percolation theory. This space is searched randomly in local neighborhoods of the current best-practice frontier. Numerical simulations demonstrate that with increasing radius of search, the probability of becoming deadlocked declines and the mean rate of innovation increases until a plateau is reached. However, for 'richer' technological environments, a 'trough' separates myopic from long-range search due to the e ect of R&D duplication. The distribution of innovation sizes is highly skewed and may resemble a Pareto distribution near the critical percolation probability. ? 2004 Elsevier B.V. All rights reserved. JEL classiÿcation: C15; C63; D83; O31

The research of Bart Verspagen has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.

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