Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

Adam B. Jaffea,b and
Manuel Trajtenbergc

^aBrandeis University and National Bureau of Economic Research, Department of Economics, Waltham, MA 02254-9110; and ^cTel Aviv University and National Bureau of Economic Research, Department of Economics, Tel Aviv 69978, Israel

Abstract

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.

Footnotes

↵ b To whom reprint requests should be addressed. e-mail: jaffe{at}binah.cc.brandeis.edu.
This paper was presented at a colloquium entitled “Science, Technology, and the Economy,” organized by Ariel Pakes and Kenneth L. Sokoloff, held October 20–22, 1995, at the National Academy of Sciences in Irvine, CA.
↵ d By “United States patents,” we mean in this context patents granted by the United States Patent Office. All of our research relies on United States patents in this sense. Currently, about one-half of United States patents are granted to foreigners. Hence, later in the paper, we will use the phrase United States patents to mean patents granted to residents of the United States, as opposed to those granted to foreigners.
↵ e The city and state are reported for United States inventors, the country for inventors outside the United States.
↵ f There are, presumably, university patents before 1965, but we do not have the ability to identify them as such.
↵ g In previous work (6), we showed that university patents applied for up until about 1982 were more highly cited than corporate patents, but that the difference has since disappeared.
↵ h The approximation involved is that log(1 + β₂/β₁) ≈ β₂/β₁. Our estimations all lead to β₂/β₁ on the order of 10⁻⁶, and indeed the approximation holds to five significant figures for lags up to 30 years.
↵ i We exclude cells for which t = T, where the model predicts that the number of citations is identically zero. In fact, the number of citations in such cells is almost always zero.
↵ j About two-thirds of the zero citation observations are for cells associated with either Canada or Rest of World.
↵ k As noted above, α is not separately identified from β₁ and β₂. Hence, we do not estimate a “base” value for the parameter α; it is implicitly unity.
↵ l The base group for each effect is: Cited time period (tp), 1963–1965; Cited field (g), “All Other”; Type of Cited Institution (i), Corporate; Citing year (T), 1977; Citing region (L), United States.
↵ m Caballero and Jaffe (7) attempt to identify the size of patents by allowing exponential obsolescence to be a function of accumulated patents rather than elapsed calendar time. We intend to explore this possibility in future work.