  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.
