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Self-organization of R&D search in complex technology spaces

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  • Gerald Silverberg

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  • Bart Verspagen

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Abstract

We extend an earlier model of innovation dynamics based on invasive percolation by adding endogenous R&D search by economically motivated firms. The {0,1} seeding of the technol-ogy lattice is now replaced by draws from a lognormal distribution for technology ‘difficulty’. Firms are rewarded for successful innovations by increases in their R&D budget. We compare two regimes. In the first, firms are fixed in a region of technology space. In the second, they can change their location by myopically comparing progress in their local neighborhoods and probabilistically moving to the region with the highest recent progress. We call this the mov-ing or self-organizational regime. We find that as the mean and standard deviation of the log-normal distribution are varied, the relative rates of aggregate innovation switches between the two regimes. The SO regime has higher innovation rates, other things being equal, for lower means or higher standard deviations of the lognormal distribution. This results holds for in-creasing size of the search radius. The clustering of firms in the SO regime grows rapidly and fluctuates in a complex way around a high value which increases with the search radius. We also investigate the size distributions of the innovations generated in each regime. In the fixed one, the distribution is approximately lognormal and certainly not fat tailed. In the SO regime, the distributions are radically different. They are much more highly right skewed and show scaling over at least two decades with a slope of almost exactly one, independently of parame-ter settings. Thus we argue that firm self-organization leads to self-organized criticality. (Keywords: innovation, percolation, search, technological change, R&D, clustering, self-organized criticality.
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Suggested Citation

  • Gerald Silverberg & Bart Verspagen, 2007. "Self-organization of R&D search in complex technology spaces," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 195-210, December.
  • Handle: RePEc:spr:jeicoo:v:2:y:2007:i:2:p:195-210
    DOI: 10.1007/s11403-007-0023-1
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    References listed on IDEAS

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    1. 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.
    2. Winter, Sidney G., 1984. "Schumpeterian competition in alternative technological regimes," Journal of Economic Behavior & Organization, Elsevier, vol. 5(3-4), pages 287-320.
    3. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, vol. 139(2), pages 318-339, August.
    4. Dietmar Harhoff & Frederic M. Scherer & Katrin Vopel, 1997. "Exploring the Tail of Patented Invention Value Distributions," CIG Working Papers FS IV 97-27, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    5. Gerald Silverberg & Bart Verspagen, 2003. "Breaking the waves: a Poisson regression approach to Schumpeterian clustering of basic innovations," Cambridge Journal of Economics, Oxford University Press, vol. 27(5), pages 671-693, September.
    6. F. M. Scherer & Dietmar Harhoff & J, rg Kukies, 2000. "Uncertainty and the size distribution of rewards from innovation," Journal of Evolutionary Economics, Springer, vol. 10(1), pages 175-200.
    7. Nelson, Richard R. & Winter, Sidney G., 1993. "In search of useful theory of innovation," Research Policy, Elsevier, vol. 22(2), pages 108-108, April.
    8. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    9. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    10. 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.
    11. Silverberg, Gerald, 2002. "The discrete charm of the bourgeoisie: quantum and continuous perspectives on innovation and growth," Research Policy, Elsevier, vol. 31(8-9), pages 1275-1289, December.
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    15. F. M. Scherer, 1998. "The Size Distribution of Profits from Innovation," Annals of Economics and Statistics, GENES, issue 49-50, pages 495-516.
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    Cited by:

    1. Massimo Ricottilli, 2006. "Constraints and Freedom of Action: a fitness trade-off," Working Papers 580, Dipartimento Scienze Economiche, Universita' di Bologna.

    More about this item

    Keywords

    Innovation; Percolation; Search; Technological change; R&D; Clustering; Self-organized criticality; C15; C63; D83; O31;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives

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