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

TL;DR

This paper analyzes the citation dynamics of US patents granted in 1998, revealing an intrinsic citation rate that separates into ageing and growth components, providing a theoretical framework for understanding knowledge propagation.

Contribution

It introduces a separable model of patent citation dynamics, distinguishing ageing from growth, and derives an analytical expression for the citation distribution applicable across different functional forms.

Findings

Intrinsic citation rate separates into ageing and growth components.

Analytical citation distribution matches long-term patent data.

Model explains short-term citation excess phenomena.

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.