Do more equal societies produce more patents? Some very preliminary data

Do more equal societies produce more patents? Well - leaving aside whether patent applications can measure "creativity" or "use of human resources" - first, what is a "more equal society"? Let's assume a society with a more equal income distribution, as measured by the Gini index (also called the Gini coefficient). You can find a list of countries ranked according to their Gini index (or other measures) here.
WIPO publishes as statistic on the number of patent [corr.] applications per resident; the latest (more or less complete) figures are from 2005.
To check for a relationship without using sophisticated statistical analysis, we can display the data using a scatter plot; plotting the Gini index on the y-axis and the number of patent applications per million residents on the x-axis. The result looks like this (click for larger version):

This graph is pretty useless. Because the variability of the number of patent applications is so much larger than the variability of the Gini index, most countries are concentrated in a small area on the left hand side. A logarithmic transformation of the data yields this:There does not seem to be much of a (linear) relationship between number of patent applications per resident and the Gini index as measurement of income equality. But the professor (allegedly) said

If you look at patents per head of population in the rich countries, it's the more equal ones that do better, partly because more unequal societies are wasting their talent.

So you have to compare rich countries only. "Rich countries" is also a relative term. I took the EU member states, plus USA, Canada, Australia, New Zealand, Switzerland, Iceland, Japan and South Korea. Most people would agree that these are relatively rich countries. The plot looks like this:Again, the data points are all over the place. There does not seem to be much of a (linear) relationship between the equality of income distribution and the number of patent applications per resident. Admittedly, this is not a sophisticated statistical analysis, but if there was a trend in the data, you should be able to see it in the scatter plots [the authors of "The Spirit Level" maintain that "There is a weak but statistically significant tendency for more equal societies to gain more patents per head than less equal ones"; this can't be disproved with the plots in this post. The key word here is "weak".]

What is definitely noteworthy are the extreme outliers of Japan and South Korea - they just have a lot more patent applications per capita than anyone else, including the USA.

Correction 2 Feb 2010: the WIPO data concerns patent applications, not granted patents. The post has been amended accordingly.