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

Abstract

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

Related Variety, Unrelated Variety and Technological Breakthroughs: An analysis of US State-Level Patenting

“…This approach is original, as most studies use exogenously fixed (identical across years and technologies) criteria to distinguish between breakthrough and regular innovations instead, by defining breakthroughs as the patents belonging to the top 5% or top 1% quantiles of the citations distributions. The statistical properties that spurred the initial application of the method were highlighted by SILVERBERG and VERSPAGEN (2007). They showed that a lognormal distribution fits most of the forward citations distribution for patents quite well, except for the tail: the numbers of received citations of highly cited patents rather follow a Pareto distribution.…”

“…Empirical examination of patent data shows that Pareto distributions are superior at matching the observed frequency distributions in the right tail of the distribution of the 'value' of innovations (SCHERER et al, 2000), also when the value is measured with the numbers of citations received by patents (SILVERBERG and VERSPAGEN, 2007).…”

“…Following SILVERBERG and VERSPAGEN (2007), they estimate the cut-off point by using an estimator for the essential parameter of the Pareto distribution. If the tail follows this distribution F(x) = 1 − x − α, a maximum likelihood estimator of the parameter α can be obtained using the Hill estimator (HILL, 1975).…”

“…A criterion based on the numbers of citations to a patent is used as included in subsequent patent documents (so-called forward citations) to operationalize the concepts of incremental innovation and breakthrough innovations (SILVERBERG and VERSPAGEN, 2007;CASTALDI and LOS, 2012). The dataset contains all utility patents granted by the US Patent and Trademark Office (USPTO) between 1977 and 1999, for which the first inventor resided in the United States.…”

Portfolio diversification under local and moderate deviations from power laws

“…As discussed by Nešlehova, Embrechts & Chavez-Demoulin (2006), tail indices less than one are observed for empirical loss distributions of a number of operational risks. Furthermore, Scherer, Harhoff & Kukies (2000) and Silverberg & Verspagen (2004) report the tail indices α to be considerably less than one for financial returns from technological innovations. Rachev et al (2005) discuss and review the vast literature that supports heavy-tailedness and Pareto distributions for equity and bond returns.…”