## 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).

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## Notes

- 1.
- 2.
There is probably no use in employing more recent data, because the majority of patents expire after 13–14 years (see Table 2). Moving closer to the present will therefore result in a severe increase of the share of censored patent values.

- 3.
Note that Bessen focuses on the initial return rate. But since this is a somewhat fuzzy concept, we prefer rather to make assumption about the patent value.

- 4.
Note, however, one subtlety. We do not impose a fixed censoring limit (for example the observed initial return rate is censored, if it takes a value y), but we allow patents to have different censoring values. This more general statement is necessary, because the total renewal costs and thus the according patent values differ by patent office.

- 5.
This number should roughly correspond to the number of patents that were finally granted, because the number of patents that were granted by the EPO but never appeared at European Patent office should be low.

- 6.
The latest ISI high-tech list (Legler and Frietsch 2007) provides a classification of both sectors (based on NACE) and goods (based on SITC) according to their technology-intensiveness. Based on the SITC goods classification a concordance to the International Patent Classification (IPC) can be constructed. This concordance table contains 35 particularly technology-intensive fields. The dummies used on this study are fractionalised, which results from the fact that each patent can have several IPC classifications. Suppose for example that a patent has two classification in high-tech-field 1 (HT1), one classification in high-tech-field 2 (HT2) and one classification in a field that does not belong to the ISI high-tech list (LOWTECH), the fractionalised dummy for HT1 would be 0.5, for HT2 it would be 0.25 and for LOWTECH 0.25. The sum over all dummies is therefore unity.

- 7.
This number is quite large, because the Inpadoc family does not only contain patent documents at different national offices referring to the same invention but also different patents that somehow belong together, e.g., when patents are split up later on in the patenting process.

- 8.
If we do that by country, e.g., for France, then

*μ*_{ xβ }and \( \sigma_{x\beta }^{2} \) are replaced with the corresponding mean and variance in the subsample of French patents. - 9.
We should note, however, that using the value adjustment factors to reweight simple patent counts is retrospective, in that they extrapolate structures from the past: they critically depend on both the explanatory variables

*x*as well as the estimated coefficients β. Therefore, whenever either the distribution of the explanatory variables in one country changes (e.g. French patents may be cited more frequently) or the structure of the regression model expressed by the coefficients changes, then the value adjustment factor needs to be re-estimated. In any case, looking at Table 3 tells us that coefficients appear to not to change excessively. Thus, it seems not too critical to extrapolate them to the present. More likely is that changes in the distributions of the explaining variables account for differences in the value adjustment factor. If we, for example, would like to deduce the VAF for patents with priority year 2005, we could take the coefficients from the regression model corresponding to the data from 1996. We would then use them to derive predicted values for 2005. With these at hand, we again use Eq. 2 to derive value adjustment factor. This procedure clearly implies the constancy of coefficients but it allows for changes in the distributions of the explaining factors. In any case, we cannot exclude the existence of a structural change after 1996. It is well known that this is the time of the patent-surge, which might have induced more severe changes in the regression model. However, this remains to be seen when more recent data becomes available.

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## Acknowledgments

Financial project support of the German Expert Commission Research and Innovation for the work underlying this article is kindly acknowledged. Helpful comments on an earlier version of this article from the 10th EPO-PATSTAT Conference in Vienna are also acknowledged. I am grateful to Nicolai Mallig for the help that he provided on collecting the necessary patent data from the PATSTAT database. Lastly, I would also like to thank an anonymous referee for his valuable suggestions that helped to improve the article.

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## Appendix

### 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:

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:

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

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Schubert, T. Assessing the value of patent portfolios: an international country comparison.
*Scientometrics* **88, **787 (2011). https://doi.org/10.1007/s11192-011-0454-2

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### Keywords

- Patent count
- Value
- Adjustment
- Renewal fees