The dynamics of innovations and citations

- Patent citations occur as new ideas are produced by combining existing ideas.
- Ideas are intervals in a variety space.
- Interval lengths determine the likelihood of citation.
- The model derives exponential aging of patents, which fits the data very well.
- Endogenous aging sets the model apart from preferential attachment models.

We present a model in which patent citations occur as new ideas are produced from combinations of existing ideas. An idea's usability in this process is represented as an interval in a variety space of ideas, whose length determines the likelihood of citation. This process endogenously derives exponential aging of patents, which is consistent with empirical observations. The endogeneity of aging sets our process apart from the standard preferential attachment literature.