Correlating gdp to scientific productivity is a reasonable proxy for progress
If growth is related to the number of new ideas generated per unit of time, it is possible to associate growth to the number of ideas generated by the scientific community[@bloom2020Are Ideas Getting Harder to Find?]. This, however, may be slightly restrictive because it neglects the growth generated by non scientific-based new ideas, but proposes as well another interesting thought: high value ideas are based on research and science.
Looking at GDP, however, has an extra complication, since it is susceptible to external factors (commodity price fluctuations, for example) that have nothing to do with innovation. Discovering oil may produce a jump of the GDP even without any investment in science and research. On the other hand, being able to exploit non-conventional reservoirs can be the product of innovation.
It is also important to note that calculating the gdp of a country should include the unpaid work done by women because there is a massive amount of unpaid work done by women. If this has been changing over time, it is possible that GDP was simply very poorly measured.
In the case of research funded through public money, it could be possible to measure the success of technology transfer from universities by using the total number of patents, licenses and spin-offs, although it may not be the best metric since patents and spin-offs do not have the same added value.
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