Power Law Distributions of Patents as Indicators of Innovation

TL;DR

This paper investigates the distribution of patents among applicants in OECD countries, revealing power law patterns that correlate with innovation indicators and economic development levels.

Contribution

It demonstrates that patent distributions follow power laws with varying exponents and links these exponents to innovation metrics and economic development.

Findings

Patent distributions follow power laws with exponents from 1.66 to 2.37.

Lower exponents correlate with higher innovation indicators.

More advanced economies have smaller exponents, indicating more patents by large firms.

Abstract

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Here we present evidence that the distribution of patents amongst applicants within many OECD countries is well-described by power laws with exponents that vary between 1.66 (Japan) and 2.37 (Poland). Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as R&D intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.