The paper, R&D, Invention and Economic Growth: An Empirical Analysis, by Professor Hulya Ulku shows that patents, per capita GDP, and spending on research and development are closely correlated.  Figure 2 of the paper shows a straight line relationship between per capita GDP and per capita patents for 20 OECD countries.  The data is based on the number of US patents issued to inventors in the 20 OECD between 1981 and 1997.

The paper discusses the endogenous/exogenous invention and growth debate and concludes:

The fact that the effect of invention on per capita output is the largest in higher income countries implies that rich countries are not constrained by stagnant output growth, as implied by exogenous growth models.  These results support endogenous growth theories which predict that countries’ R&D efforts may foster economic growth.

The paper does not support the patent thicket (tragedy of the anticommons) theory that patents inhibit research and development.  It shows that those countries with the most patents are most likely to undertake the most research and development expenditures.