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

Silverberg, Gerald and Verspagen, Bart (2004). The size distribution of innovations revisited: an application of extreme value statistics to citation and value measures of patent significance. UNU-MERIT Research Memoranda. UNU-MERIT.

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  • Sub-type Working paper
    Author Silverberg, Gerald
    Verspagen, Bart
    Title The size distribution of innovations revisited: an application of extreme value statistics to citation and value measures of patent significance
    Series Title UNU-MERIT Research Memoranda
    Volume/Issue No. 21
    Publication Date 2004
    Publisher UNU-MERIT
    Language eng
    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.
    Keyword Returns to invention
    Patent citations
    Extreme-value statistics
    Skewed distributions
    Heavy tails
    JEL C16
    O31
    O33
    Copyright Year 2004
    Copyright type All rights reserved
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    Created: Fri, 13 Dec 2013, 12:39:57 JST