Modeling the Knowledge Production Function Based on Bibliometric Information

An integral indicator of the development of society is the amount of knowledge, which can be measured by the number of accumulated publications in the form of patents, articles, and books. Knowledge production is examined on a global scale. We analyze existing econometric models and develop a generalized model that expresses the per capita knowledge production rate (called productivity) as a function of the amount of accumulated knowledge. The function interpolates two extreme cases, the first of which describes an underdeveloped society with very little knowledge and non-zero productivity, and the second, a highly developed society with a large amount of knowledge and productivity that grows according to a power law as knowledge accumulates. The model is calibrated using literature data on the number of patents, articles, and books. For comparison, we also consider the rapid growth in the global information storage capacity that has been observed since the 1980s. Based on the model developed, we can distinguish between two states of society: (1) a pre-information society, in which the knowledge amount is below a certain threshold and productivity is quite low, and (2) an information society with a super-threshold amount of knowledge and its rapid accumulation due to advanced computer technologies. An analysis shows that the transition to an information society occurred in the 1980s.