On the long-run evolution of technological knowledge

This paper revisits the debate about the appropriate differential equation that governs the evolution of knowledge in models of endogenous growth. We argue that the assessment of the appropriateness of an equation of motion should not only be based on its implications for the future, but that it should also include its implications for the past. We maintain that the evolution of knowledge is plausible if it satisfies two asymptotic conditions: Looking forwards, infinite knowledge in finite time should be excluded, and looking backwards, knowledge should vanish towards the beginning of time (but not before). Our key results show that, generically, the behavior of the processes under scrutiny is either plausible in the future and implausible in the past or vice versa, or implausible at both ends of the time line.