Fame and obsolescence: Disentangling growth and aging 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-aging 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 aging 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.

Ex-ante measure of patent quality reveals intrinsic fitness for citation-network growth

“…For comparison, we include in the same figures also fits of the quantity ∆k i (t + ∆t)/∆t representing the uncontrolled-for-fitness average citation rateλ i ≡ A(t) f (k i ) considered before [12,14,15]. In agreement with previous results [12] obtained using the technologyclassification scheme from Ref. [13], we observe A(t) to be exponential in the long run while significantly exceeding the exponential behavior extrapolated to short times.…”

“…[13], we observe A(t) to be exponential in the long run while significantly exceeding the exponential behavior extrapolated to short times. Fits to the data forλ also establish the form [12] f (k) = k α + f 0 , with α >α.…”

“…Our construction of a technologydependent single quality score for individual patents from a broad range of patent-quality measures that are exogenous to citations and available at the time of grant is shown to quantify the innate attractiveness of patents to be cited in the future. The ability to account for inherent quality as a driver of citation dynamics enables better observation of other important influences, including the time scale for knowledge obsolescence [12].Empirically, the average rateλ at which the number of citations k accrued by patents [13] increases over time t is observed [12,14,15] to follow an aging-tempered [16] preferential-attachment-type [17][18][19] growth modelλ = A(t) f (k). The asymptotic form f (k) ∼ k α for large k with α > 0 embodies a rich-gets-richer feedback loop whereby more highly cited patents are more likely to gain future citations.…”

“…Our construction of a technologydependent single quality score for individual patents from a broad range of patent-quality measures that are exogenous to citations and available at the time of grant is shown to quantify the innate attractiveness of patents to be cited in the future. The ability to account for inherent quality as a driver of citation dynamics enables better observation of other important influences, including the time scale for knowledge obsolescence [12].…”

“…(1) depends on k and t. More specifically, we consider the time evolution of the fraction n(0, t) of uncited patents. Expanding its expression [12,28]…”