Assessing the value of patent portfolios: an international country comparison

Abstract

Patent counts have been extensionally used to measure the innovative capacities of countries. However, since economic values of patents may differ, simple patent counts may give misleading rankings, if the patents of one country are on average more valuable than those of another. In the literature several methods have been proposed, which shall adjust for these differences. However, often these do not possess a solid economic micro-foundation and therefore are often ad-hoc and arbitrary procedures. In this paper, we intend to present an adjustment method that is based on the analysis of renewal decisions. The method builds on the theoretical model used in Schankerman and Pakes (1986) and Besson (2008) but goes beyond both approaches in that it recovers the important long tail of the value distribution. It also transfers Besson’s (2008) econometric methodology (applicable to the organisational structures of the US Patent and Trademark Office) also to the European Patent Office which is necessary, since each application here may split up into several national patent documents. The analysis is performed for 22 countries. Exemplarily, we find that in the cohort of 1986 patent applications, Danish patents are about 60% more valuable than the average patent. German patents are a bit below average. Japanese patents are of least value. In the cohort of 1996, Danish patents lose some of their lead but are still more valuable than the average. While German are a bit above average, Japanese patents even fall further behind (possibly due to the economic downturn in since the mid of 1990ies).

Appendix

Define $\bar{r}_{j}$ to be the initial return rate associated with a specific patent. The return rate can basically measure any return, no matter if they accrue from selling a protected product or blocking a competitor. Assume that the (non-discounted) return rate at a future point in time τ > 0 can be calculated by $\overline{{r_{j} }} \cdot \text{e}^{ - d\tau }$, where d ≥ 0 is a deprecation rate. That is we assume that returns resulting from a patent are exponentially damped. Suppose that there are discrete points in time t _i , i = 1, 2,…K, where the owner of a patent has to decide, whether he wants to renew. Denote by PV _j the total value of patent j and by PV _i,j the return that is attributable to the period [t _i , t _i+1], that is between any two dates, where renewal decisions are necessary. Letting r ^m be the internal rate of return (possibly but not necessarily equal to observable interest rates), then we can calculate the net present value of a patent accruing to the period [t _i , t _i+1] as follows:

$$ \begin{aligned} PV_{j,i} &= \int\limits_{{\tau = t_{i}}}^{{t_{i + 1} }} {\overline{{r_{j} }} {e}^{{ - \left( {r^{m} + d}\right)\tau }} d\tau }\\ &= \overline{{r_{j} }} \left({\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau - \int\limits_{{\tau = t_{i + 1} }}^{\infty} {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{\tau = 0}^{{t_{i} }} {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau } \right)\\ &= \overline{{r_{j} }}\left( {\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} +d} \right)\tau }} } d\tau - \int\limits_{{\tau = t_{i + 1}}}^{\infty } {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{\tau = 0}^{\infty } {{e}^{{ - \left( {r^{m} + d}\right)\tau }} } d\tau + \int\limits_{{\tau = t_{i} }}^{\infty }{{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau } \right)\\&= \overline{{r_{j} }} \left( {\int\limits_{{\tau = t_{i}}}^{\infty } {{e}^{{ - \left( {r^{m} + d} \right)\tau }} } d\tau -\int\limits_{{\tau = t_{i + 1} }}^{\infty } {{e}^{{ - \left({r^{m} + d} \right)\tau }} } d\tau } \right)\\ &=\overline{{r_{j} }} \left( {\frac{{{e}^{{ - r^{m} t_{i} }} -{e}^{{ - r^{m} t_{i + 1} }} }}{{r^{m} + d}}} \right)\\\end{aligned} $$

(3)

Because the returns are steadily decreasing in time (by assumption) and the renewal fees are steadily increasing (as a matter of fact), a patent is renewed, if and only if $PV_{j,i} \ge c_{i} \text{e}^{{ - r^{m} t_{i} }}$, where c _i is the renewal fees to be paid in period i.

Now, suppose a patent is renewed in time t ^* but not in the next period, we trivially have $PV_{j,i^{*} } \ge c_{i^{*} } \text{e}^{{ - r^{m} t_{j,i^{*}} }}$ and $PV_{j,i^{*} + 1} \le c_{i^{*} + 1} \text{e}^{{ - r^{m} t_{j,i^{*} + 1} }}$. Therefore, if the periods t _i and t _i+1 are close together, then both PV _j,i* and PV _j,i*+1 do not differ by much, and we do not lose much in replacing both conditions by the following relationship:

$$ PV_{j,i^{*} } \approx c_{i^{*} } \text{e}^{{ - r^{m} t_{j,i^{*} } }} $$

(4)

Using 3 and 4, setting t ₁ = 0 and solving for the initial return rate yields

$$ \overline{{r_{j} }} = \left\{ {\begin{array}{*{20}c} {\left( {c_{1} \frac{{r^{m} + d}}{{1 - \text{e}^{{ - r^{m} t_{2} }} }}} \right)} & {lapsed} & {after} & {t_{1} } \\ {\left( {c_{2} \text{e}^{{ - r^{m} t_{2} }} \frac{{r^{m} + d}}{{\text{e}^{{ - r^{m} t_{2} }} - \text{e}^{{ - r^{m} t_{3} }} }}} \right)} & {lapsed} & {after} & {t_{2} } \\ \ldots & \ldots & \ldots & \ldots \\ {\left( {c_{K} \text{e}^{{ - r^{m} t_{K} }} \frac{{r^{m} + d}}{{\text{e}^{{ - r^{m} t_{K} }} - \text{e}^{{ - r^{m} t_{K + 1} }} }}} \right)} & {lapsed} & {after} & {t_{K} } \\ \end{array} } \right. $$

(5)

Plugging Eq. 5 into Eq. 3 yields Eq. 1 in Chapter 3.