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Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics

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  • Emerson G. Escolar
  • Yasuaki Hiraoka
  • Mitsuru Igami
  • Yasin Ozcan

Abstract

Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. We propose a new method to characterize firms' inventive activities via topological data analysis (TDA) that represents high-dimensional data in a shape graph. Applying this method to 333 major firms' patents in 1976--2005 reveals substantial heterogeneity: some firms remain undifferentiated; others develop unique portfolios. Firms with unique trajectories, which we define and measure graph-theoretically as "flares" in the Mapper graph, perform better. This association is statistically and economically significant, and continues to hold after we control for portfolio size, firm survivorship, industry classification, and firm fixed effects. By contrast, existing techniques -- such as principal component analysis (PCA) and Jaffe's (1989) clustering method -- struggle to track these firm-level dynamics.

Suggested Citation

  • Emerson G. Escolar & Yasuaki Hiraoka & Mitsuru Igami & Yasin Ozcan, 2019. "Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics," Papers 1909.00257, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:1909.00257
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    References listed on IDEAS

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    5. Josh Lerner & Amit Seru, 2017. "The Use and Misuse of Patent Data: Issues for Corporate Finance and Beyond," NBER Working Papers 24053, National Bureau of Economic Research, Inc.
    6. Zvi Griliches, 1984. "R&D, Patents, and Productivity," NBER Books, National Bureau of Economic Research, Inc, number gril84-1, July.
    7. Adam B. Jaffe & Manuel Trajtenberg & Rebecca Henderson, 1993. "Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 577-598.
    8. repec:fth:harver:1473 is not listed on IDEAS
    9. Mitsuru Igami & Jai Subrahmanyam, 2019. "Patent Statistics as an Innovation Indicator? Evidence from the Hard Disk Drive Industry," The Japanese Economic Review, Japanese Economic Association, vol. 70(3), pages 308-330, September.
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