## INTERNATIONAL KNOWLEDGE FLOWS: MODELING 2

The citation frequency (the likelihood that any particular patent К granted in year T will cite some particular patent к granted in year t) is assumed to be determined by the combination of an exponential process by which knowledge diffuses and a second exponential process by which knowledge becomes obsolete. That is:

where (3, determines the rate of obsolescence and p2 determines the rate of diffusion. The parameter a is a shift parameter that depends on the attributes of both the patent к and the patent K. D(k,K) is a dummy variable, set equal to unity if the patent к is in the same patent class as the patent K, and zero otherwise. Thus, the parameter у measures the overall increase in citation frequency associated with the two patents matching by patent class. The dependence of the parameters a and Pj on к and К is meant to indicate that these could be functions of certain attributes of both the cited and citing patents. In this paper, we consider the following as attributes of the cited patent к that might affect its citation frequency:

• t, the grant year of the potentially cited patent,

• C, the “location” of the cited inventor (U.S., Great Britain, France, Germany or Japan),

• g= 1… 5, the technological field of the potentially cited patent.

As attributes of the potentially citing patent К that might affect the citation likelihood we consider:

• T, the grant year of the potentially citing patent, and

• L=\ …5, the location of the potentially citing patent.
Additional insight into this parameterization of the diffusion process can be gained by computing the lag at which the citation function is maximized (“the modal lag”), and the modal probability of citation. A little calculus shows that the modal lag is approximately equal to 1/p^ increases in P, shift the citation function to the left. The maximum value of the citation frequency is approximately determined by P2/PL Increases in P2 holding p! constant increase the overall citation intensity,7 and are roughly equivalent to increasing the citation frequency proportionately at every value of (T-t). That is, variations in P2, holding P, constant are not separately identified from variations in a.