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Patents in the Knowledge-Based Economy
Similarly, Q(Xc) = L(Xc)/[L(Xc) + M(Xc)]. Solving for M and substituting, we get the result:
P(Xc) = Q(Xc)/[K(1 – Q(Xc))] (A.3.1)
Population Marginal Effects
For each characteristic Xk, the population marginal effect is
∂P(Xc)/∂Xkc = [dP(Xc)/dQ(Xc)] ∂Q(Xc)/∂Xkc
The last term is the sample marginal effect computed from the probit regression. From the expression for P(Xc) we get
dP(Xc)/dQ(Xc) = 1/K[1 – Q(Xc)]2
Measuring Q(Xc) by the sample probability of litigation in the class, Q, we get the result:
dP(Xc)/dQ(Xc) ≈ P/Q(1 – Q)
We measure P for each class as follows. For the denominator, we take the total number of patents in the class during 1978-1995. In the numerator we use the number of infringement or declaratory judgment suits that can be directly identified as such and include all others as infringement suits. These are inflated for underreporting and for truncation as described in Appendix 1. We then calculate marginal adjustment factors by USPC groups, infringement and declaratory judgment suits. Separate classes defined by cohort are not needed because of the maintained hypothesis that the litigation model applies to all cohorts, making nonsystematic sampling in this dimension unimportant. Results are at the bottom of Table 9. Because dP(Xc)/dQ(Xc) is the same for all Xk for a given class c, all sample marginal effects are adjusted by the same factor to convert them to population marginals.