i (4)
In order to focus on spillovers, we concentrate on the results exclusive of self-citations, but we comment briefly on the very high degree of localization of self-citations.
We estimate Eq. 3 by non-linear least squares. Since the left-hand variable is an empirical frequency, the model is heteroskedastic. To improve efficiency and get the right standard errors, we weight the observations by the reciprocal of the estimated variance, ugX-N lt) ’ 8enera^ ^is weighting greatly improves the fit of the model, but does not alter the parameter estimates materially.


Complete results from the estimation of Eq. 3 are presented in Appendix B. The model has 82 parameters (y, base values of p, and p2; 24 cited country/citing country interactions for a; 4 technology field effects for a; 6 cited time period effects for a; 17 citing year effects for a; 24 cited country/citing country effects for p,; 4 technology field effects for P,). Overall, the model fits the data reasonably well. Because of the large sample size, the estimated standard errors are quite small. The base value for p, is about .2, suggesting a modal lag of about five years, which is not surprising based on Figure 1.

The estimate for the technology match parameter у is 99, which means that a patent is about 100 times more likely to cite a patent in the same patent class as it is to cite a random patent in some other class. In reality, of course, some classes are “closer” to each other than others in technology space, but it is not surprising that, on average, patents in the same class are much more likely to cite each other than to cite patents in any of the other classes.

Technology field effects are present in both the a’s and the p,’s, but the P, effects are not large. The a’s greater than 1 mean that all other fields receive more citations than Drug and Medical patents (the base group). The P,’s greater than 1 mean that other fields receive citations somewhat faster than Drugs. The cited time period and citing year effects are similar to what we have found before: the number of citations received rises in the 1970s and 1980s, and the number of citations made rises essentially throughout the whole period.