Fame and Obsolescence: Disentangling growth and ageing dynamics of patent citations

Abstract: We present an analysis of citations accrued over time by patents granted by the United States Patent and Trademark Office in 1998. In contrast to previous studies, a disaggregation by technology category is performed, and exogenously caused citation-number growth is controlled for. Our approach reveals an intrinsic citation rate that clearly separates into an -- in the long run, exponentially time-dependent -- ageing function and a completely time-independent preferential-attachment-type growth kernel. For the general case of such a separable citation rate, we obtain the time-dependent citation distribution analytically in a form that is valid for any functional form of its ageing and growth parts. Good agreement between theory and long-time characteristics of patent-citation data establishes our work as a useful framework for addressing still open questions about knowledge-propagation dynamics, such as the observed excess of citations at short times.