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

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  • Silverberg, Gerald
  • Verspagen, Bart

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 Keywords: returns to invention, patent citations, extreme-v

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 139 (2007)
Issue (Month): 2 (August)
Pages: 318-339

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Handle: RePEc:eee:econom:v:139:y:2007:i:2:p:318-339

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Simon Kuznets, 1962. "Inventive Activity: Problems of Definition and Measurement," NBER Chapters, in: The Rate and Direction of Inventive Activity: Economic and Social Factors, pages 19-52 National Bureau of Economic Research, Inc.
  2. Bronwyn H. Hall, Adam Jaffe and Manuel Trajtenberg., 2000. "Market Value and Patent Citations: A First Look," Economics Working Papers E00-277, University of California at Berkeley.
  3. Silverberg, Gerald & Verspagen, Bart, 2005. "A percolation model of innovation in complex technology spaces," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 225-244, January.
  4. Adam B. Jaffe & Manuel Trajtenberg & Michael S. Fogarty, 2000. "The Meaning of Patent Citations: Report on the NBER/Case-Western Reserve Survey of Patentees," NBER Working Papers 7631, National Bureau of Economic Research, Inc.
  5. De Vany, Arthur S. & Walls, W. David, 2004. "Motion picture profit, the stable Paretian hypothesis, and the curse of the superstar," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1035-1057, March.
  6. Manuel Trajtenberg, 1990. "A Penny for Your Quotes: Patent Citations and the Value of Innovations," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 172-187, Spring.
  7. Dietmar Harhoff & Francis Narin & F. M. Scherer & Katrin Vopel, 1999. "Citation Frequency And The Value Of Patented Inventions," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 511-515, August.
  8. Scherer, F. M. & Harhoff, Dietmar, 2000. "Technology policy for a world of skew-distributed outcomes," Research Policy, Elsevier, vol. 29(4-5), pages 559-566, April.
  9. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
  10. Thomas Lux, 2001. "The limiting extremal behaviour of speculative returns: an analysis of intra-daily data from the Frankfurt Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 11(3), pages 299-315.
  11. F. M. Scherer, 1998. "The Size Distribution of Profits from Innovation," Annales d'Economie et de Statistique, ENSAE, issue 49-50, pages 495-516.
  12. Silverberg, G. & Verspagen, B., 2003. "Brewing the future: stylized facts about innovation and their confrontation with a percolation model," Working Papers 03.06, Eindhoven Center for Innovation Studies.
  13. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
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