## INTERNATIONAL KNOWLEDGE FLOWS: Econometric issues and interpretation 2

The estimate of any particular a(k), say a(g=Chemical), is a proportionality factor measuring the extent to which the patents in the Chemical field are more or less likely to be cited over time vis a vis patents in the base category (Drugs). Thus, an estimate of a(g=Chemical) =1.5 means that the likelihood that a patent in the field of Chemicals will receive a citation is 50% higher than the likelihood of a patent in the base category, controlling for other factors. Notice that this is true across all lags; we can think of an a greater than unity as meaning that the citation function is shifted upward proportionately, relative to the base group. Hence the integral over time (i.e., the total number of citations per patent) will also be 50% larger. Similarly, if a ((= Japan, L=U.S.) is .72, this means that a Japanese patent is 28% less likely to get a citation from a random U.S. patent than is a random U.S. patent.
We can think of the overall citation intensity measured by variations in a as composed of two parts. Citation intensity is the product of the “fertility” (Caballero and Jaffe, 1993) or “importance” (Trajtenberg, Henderson and Jaffe, 1997) of the underlying ideas in spawning future technological developments, and the average “size” of a patent, i.e., how much of the unobservable advance of knowledge is packaged in a typical patent. Within the formulation of this paper, however, it is not possible to decompose the а-effects into these two components.

In the case of a(K), that is, when the multiplicative factor varies with attributes of the citing patents, variations in it should be interpreted as differences in the probability of making a citation, all else equal, for patents in a particular category vis a vis the base category. If, for example, a(e = U.S., L = Japan) is 0.76, this means that the average patent granted to Japanese inventors is three-quarters as likely as a patent granted to inventors residing in the U.S. to cite any given U.S. patent. Note that, just as variations in a across cited patents are composed of both variations in fertility or importance and variations in “patent size,” variations across citing patents can be caused by both variations in true “knowledge use” and variations in the “propensity to cite.” Because there are institutional reasons why the propensity to cite may vary across countries, this has important consequences for interpreting the results. We return to this issue below.