Input-Output Modelling and Simulation of Scientometric Indicators: A Focus on Patents 1

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1 Input-Output Modelling and Simulation of Scientometric Indicators: A Focus on Patents 1 R. D. Shelton * and Sam D. Monbo, Jr. ** * shelton@wtec.org WTEC, 4600 N. Fairfax Dr. #104, Arlington, VA (USA) ** sam@everybuilder.net EveryBuilder LLC Inc, A. B. Tolbert Rd./Weaver Av., Paynesville (Liberia) Abstract Input-output models for indicators can provide insight into the policies that can encourage better national performance. Prior work has identified input resources that are most effective in encouraging scientific paper and patent outputs. Delays between research funding and paper publication are less significant than one might expect. However, delays between research funding and patent grants are substantial and have a profound impact on this process. Here improved models for patents are developed that incorporate this system memory in two stages: (1) between input resources and patent applications, and (2) between applications and patent grants. Modelling and simulation are then used to provide quantitative insight into policies that can enhance national patenting performance. Simulation forecasts a dire future for the U.S. Patent and Trademark Office, and thus for U.S. innovation, and suggests reforms. Introduction As neatly summarized by Godin (2001), scientometric indicators differ from mere data about science in four ways: (1) they measure a phenomenon to follow the state of society. (2) they must be recurrent, not just a single snapshot in time. (3) they normally consist of a set of associated data, not just a single measurement, and (4) an indicator rests on a model an attempt to associate cause and effect. (Holton, 1978). Price (1978) similarly said, To be meaningful, a statistic must be somehow anticipatable from its internal structure or its relation to other data (...). It means the establishment of a set of relatively simple and fundamental laws. A nation s science and technology (S&T) establishment (or innovation ecosystem) can be considered to be an economic system that needs inputs of resources like labour and capital to produce outputs such as jobs and exports, which contribute to national prosperity. Inputs to and outputs from such a system can be measured using indicators. Previous publications have shown that there is a strong relation between input and output in S&T establishments. Leydesdorff (1990) regressed world share of publications in the Science Citation Index (SCI) as output on Government Expenditure for R&D (GERD) data as an input. Later, the measurement was refined by focusing on components of GERD funding as independent variables (Leydesdorff & Gauthier, 1996; Leydesdorff & Wagner, 2009a; Zhou & Leydesdorff, 2006). Shelton (2008) extended this work to build input-output models for paper publication as a function of national investments in R&D to help explain the causes of the well-known European 1 Funding from NSF coop agreement ENG is much appreciated.

2 Paradox (Foland & Shelton, 2010) and a similar American Paradox. Independently, both Shelton and Foland (2009) and Leydesdorff and Wagner (2009) predicted that China would soon surpass the United States in the SCI, if recent trends continue. Shelton and Leydesdorff (2012) further extended this analysis using multiple linear regression to show that the resource inputs that were most effective in encouraging paper and patent outputs were complementary. For example, government R&D funding best encouraged papers, while industrial funding best encouraged patents. They also found that regression is useful in identifying the input IVs that are most predictive of output indicators, which then can be used to build individual models for the countries in question. Here the focus will be on providing new models for patents, and assessing their policy implications. Patents Patents are an important indicator of the output of a national S&T establishment. A considerable body of literature associates patents with downstream benefits like exports, for example (Soete, 1987). Furthermore, there have been big changes in the international patent scene in recent years. Fig. 1 adapted from (Zhou & Stembridge, 2010) shows that China has suddenly emerged as a world power in patenting, much as it did a few years earlier in scientific paper publication. This curves show patent applications to the national patent offices in the U.S. (USPTO), Europe (EPO), Japan (JPO), and China (SIPO). These curves include both foreign and domestic applications to these offices. While Japan (JP) still led the world in 2008, extrapolation of these trends show that China (CN) should pass both Japan and the US to lead the world in about China's assumption of the lead in this indicator was confirmed in a press release in December by Thomson Reuters (2011). Total Patent Volume (X 1,000) JP US EP CN Figure 1. Patent applications to four offices. The dynamics of patent production differ greatly from those of papers. Cross-correlations show that the lag between resource inputs and paper outputs is small enough that accurate models can be memoryless. However, statistical analysis shows that there are substantial delays between R&D funding and patent applications. Furthermore, there are often very large delays in granting 757

3 of patents by patent offices, partly because of backlogs. Both of these delays require more complex models. Queuing theory provides a simple structure for such models, including the essential random nature of the processes. For example, one of the most interesting patent regimes is the U.S. Patent and Trademark Office (USPTO), which is important world-wide, because many international companies want these patents for the huge U.S. market. The USPTO has also made both input application and output grant data available over many years, by country of origin, which makes modelling much easier. (Modelling for papers would be much simpler if similar data were available for submissions of papers to journals!) It turns out that the USPTO can be viewed as an unstable queue since the arrival rate of applications is much greater than the service rate, and worse, the arrival rate is rapidly increasing, particularly from foreign sources. For such situations, simulation can provide more insight than attempts to derive formulaic results. Most importantly, modelling and simulation can illuminate the likely effects of national policy choices (Leydesdorff, 2006). For example, if present trends in inputs and present servicing policies continue, the USTPO can clearly be overwhelmed: delays and backlogs could expand without bound. The model also provides potential remedies: a faster service rate by hiring more patent examiners and by automation. USPTO Patents Worldwide Grants Applications Disposals Figure 2. USPTO applications and grants. Disposals are total output transactions, including grants and abandonments (rejections), calculated from posted allowance (grant/disposal) rates. Methods and Materials Data sources Input indicators considered here include: (1) The number of researchers in a country; (2) gross domestic expenditures on research and development (GERD); (3) two GERD funding components: government and industry. This investment data at the national level was used from OECD (2010) in Paris for its member countries and affiliates. 758

4 Output indicators considered here include: three kinds of patent indicators: (1) patent applications to the USPTO, (2) USPTO patent grants, and (3) triadic patent grants. The latter are patents that are registered in all of these three: the USPTO, the EPO, and the JPO. These are sometimes called high value patents, since this process is costly. Patent data was from USPTO (2012) and OECD (2010). Some countries are omitted as statistical outliers; e.g. U.S. data must be handled separately in the USPTO data because the home advantage effect makes its data point atypical (Criscuolo, 2006). Indicators may both be absolute numbers or relative, that is, percentage shares obtained by dividing by totals for a set of nations. Here we use a set called the OECD Group. This is the set of some 40 nations that have had a fairly complete set of data over many years (OECD, 2010). Broader data is available from the UNESCO Institute for Statistics in Montreal (UNESCO, 2010), which adds results from other countries, including some large countries like India and Brazil. However, the OECD nations account for more than 95% of USPTO applications. Instead of absolute numbers, percentage shares often provide the better values for national comparisons, particularly when one wishes to compare results for two or more time samples. Lags in time should also be considered. There can also be a considerable delay between the time of patent applications and their grants, and even more from the initial R&D funding that enabled the invention. However, most variables do not change rapidly from year to year, and strong correlations are obtained, even without lags. Regression and Interpretation While causality cannot be proven from correlations and regression models, here it is reasonable to assume that there is a causal connection between resource inputs on the one hand, and outputs like papers and patents on the other. Thus it is likely that the input resources that are most predictive of outputs are more effective investments than those that are less predictive. For example, a nation s paper share of the OECD Group can be predicted as the dependent variable (DV) with a regression line that accounts for more than 95% of the variation using a single independent variable (IV): government R&D investment (p < 0.001). A similar regression with two IVs, the government and industrial funding components, will show that the industrial component is not significant (p > 0.05) as another IV in comparison. It can then be suggested that government funding is probably more important than industrial funding in producing scientific papers, since this is consistent with the logic of the situation. Government funding tends to go to universities, where professors are highly motivated to publish (or perish). Industrial funding mostly goes to businesses that tend to produce other kinds of outputs, like patents. By regression over the OECD Group countries, Shelton (2008) identified some of the national inputs that were most important in encouraging papers; for example, the number of researchers was not significant compared to investment. From the structure of the publication process, he built a model for individual countries in terms of shares. This model suggested that changes in the GERD share have been the driver of changes in paper share, accounting for the rise of China since 2000 (Moed, 2002; Jin & Rousseau, 2005; Leydesdorff & Zhou, 2006), and the inevitable associated (but relative) decline of the US and EU. More accurate models were then developed that could account for Europe s rapid increase in efficiency during the 1990s (Foland & Shelton, 2010) (Shelton & Leydesdorff, 2012). It was shown that the government component of R&D funding is more effective in producing papers than the industrial component or overall GERD, and models based on this finding were successful in accounting for the EU passing the U.S. in SCI paper publication. 759

5 However, the opposite side of this coin is that industrial funding was shown to be much more effective in encouraging patents than government funding, and models can be better based on this input resource. As we have seen, the memory or time lags are essential for modelling the overall patenting process, so here the focus will be development of patent models that can better account for the substantial delays in the patenting process, and on the policy implications of those models. Most correlations are high and significant between any input resource on the one hand, and outputs like papers and patents on the other, partly because all these variables vary with the size of the respective countries. Thus, reasonable models with a single independent variable (IV) could be constructed from any one of these input resources. However, in a linear regression with two IVs, only the IV with the largest correlation will usually be found to be important, since it already accounts for the underlying size factor. For example the 2007 regression based on the capital (GERD) and labor (Researchers) components as IVs for USPTO patent applications (as DV) is: Apps07 = GERD Researchers (R 2 = 92.2%) [2] While both IVs are significant with p = 0.000, the investment variable (GERD) is more useful in predicting patent applications than the number of researchers. Not only is the sign of the Researchers IV negative, but its coefficient is very small. In the following models the significance level will be less than a tenth of one percent (p < 0.001) unless stated otherwise. Input-Output Model for Patent Applications Patents are an important output indicator of the performance of national research establishments. One complication is that many patents are awarded on a national rather than international basis. While some national offices, like the US Patent and Trademark Office (USPTO), receive many international applications, the United States itself dominates this dataset because of its home advantage. However, the USPTO data is useful for evaluating the performance of other countries because the US market is attractive for foreign inventors, making US patents desirable internationally (Narin & al., 1997). Indeed, in 2008 foreign patents granted by the USPTO exceeded US grants for the first time. However, in regressions one normally removes such outliers as the US data point in this case, as being atypical of the remainder of the data. Some international patent series are also available from the OECD. Triadic patents involve applications to all three: USPTO, EPO, and JPO. Since this process is expensive, one can assume that only the most promising inventions get this treatment, so the term high value patents, is sometimes used. Table 1, adapted from (Shelton & Leydesdorff, 2012), shows the correlations with several resource IVs. The US data has been removed from the USPTO columns. Among the IVs available, we focus here on those components that are most controllable by government policy: GERD, Researchers, the Government and Industrial funding components of GERD. 760

6 Table 1. Correlations for patent shares with various input resources. Triadic Triadic USPTO USPTO USPTO Grants Grants Apps Apps Grants Capital vs. Labor GERD Researchers Funding Components Industry Government Slight differences in the correlations for the components will usually lead to the one with the lower correlation being found to be less significant in a multivariate regression model. For example in all cases the component Researchers as IV has a lower correlation than GERD with all DVs. When regressions are made with this pair of IVs, the Researchers one will be found to be less significant compared to the GERD variable. Thus between these two, GERD seems not only to account for the country size factor, but to better account for other national factors. Also in all cases shown in Table 1, the Industry funding component of GERD is more highly correlated with patenting than the Government funding one. This provides some quantitative evidence for the logical expectation that industry is more effective than governments in producing patents. Table 1 also shows that the Industry component is slightly more predictive than overall GERD investment, so it will be explored in the models following. Let us first provide several models for USPTO patent applications. Industry funding of R&D seems to be much more effective in encouraging patent applications than government funding. Apps07 = Industry Government (R 2 = 79.3%) [3] While both IVs are significant, the Government one is less so with p = compared to p<0.001 for Industry. Also, the sign of the Government investment term is negative. With this insight we can focus on the Industry funding component as being most predictive of patent applications. A simple, single IV, regression model is: Apps07 = Industry (R 2 = 74.1%) [4] We will see, however, that there is a substantial time lag in the effectiveness of this R&D funding in producing patent applications. Table 2 provides the cross correlations of the industry R&D IV with two outputs, USPTO applications in 2007 and in The time lag for the peak correlation is substantial for both outputs. Indeed it happens to occur for both with the input in

7 Table 2. Correlations of Industrial R&D Funding by year ( ) with USPTO applications in 2007 and Industry R&D Applications07 w/o US Applications07 with US Applications10 w/o US I I I I I I I I I Using this insight a regression model with a 5-year time delay produces a far better fit for foreign applications in Apps07 = Industry (R 2 = 92.8%) [5] The similar correlation for foreign applications in 2010, the most recent data now available, also shows a peak for This is eight years earlier for this case. For consistency, we would prefer the same number of years of lag, but it is what it is. As shown in Table 2, these peaks are not very much greater than those for other nearby years, so the conclusion drawn here is simply that is a long delay, ranging from 4-8 years, in converting R&D into patent applications. The regression model for these 2010 applications is similar to the one for the 2007 case. Apps10 = 1.05 Industry (R 2 = 93.6%) [6] As shown in Table 2, adding the U. S. data causes the lag for the peak correlation to increase by a year or two. Thus the delay for the U. S. by itself might be better modelled by seven years compared to five for foreign applications. As shown by the R 2 values, the fit of these lagged models is quite good. Figure 3 shows the scatter diagram for the 2007 case. In Fig. 4 a log-log scale was used, just to show the fit over the wide range of country sizes. The U.S. point was not used in these calculations. 762

8 90000 Scatterplot of Apps10 vs I Apps I Figure 3. Scatterplot of USPTO applications in 2010 versus Industrial R&D in Linear plot with regression line. The U.S. is not included in this calculation; its point would be at ($106,000K, 242,000 applications). 5 Scatterplot of log Apps10 vs log I02 4 log Apps log I Figure 4. USPTO patent applications in 2010 versus Industrial R&D in 2002 on a log-log scale. The U.S., not shown, would be at (5.38, 5.02). 763

9 Table 3 summarizes some models for USPTO patent applications in As suggested by the cross correlations in Table 2, the best single IV model uses the industry funding component lagged by five years as an IV (Row 6). However, while some lag is clearly important, models for lags of five to seven years in Rows 6 and 7 do not greatly differ. Table 3. Summary of regression models for applications in 2007 (OECDg set, less US). IV1 IV2 Coeff1 Coeff2 Constant p1 p2 R 2 1 GERD07 Researchers % 2 Industry07 Government % 3 GERD % 4 Industry % 5 Industry % 6 Industry % 7 Industry % Input-Output Model for the USPTO Figure 5 shows a model for patent grants by the USPTO. The vertical branches on the left show the generation of patent applications as proportional to Industry R&D investment, with the delays that have been discussed. There is a separate branch for U.S. patent applications since they are modelled differently. Figure 5 then shows a queuing system in the horizontal branch to model the delay involved in converting an application into either a grant, or an abandonment (rejection) of an application. The USPTO provides considerable detail on its inner workings, including an R&D Dashboard showing the current pendency or delay in the system. (USPTO, 2012). Service actions usually involve a sequence of messages between inventor and examiner over a period of years, until either a grant or abandonment occurs. The USPTO itself has a servicing model, based on the throughput of the various levels of examiners. For our model we will suppress most of this detail. As an approximation, we will assume that the service rates for both grants and abandonments are the same. The overall service rate can be obtained from the disposals per year in Fig. 2, which shows it to have been in the vicinity of 250,000 per year until when it shot up to about 350,000. Since the rate of grants was nearly constant, this had to because of a much greater rate of abandonments (rejections). Figures 2 and 5 then show the predicament that the USPTO was in by It was an unstable queue with arrival rates well above the service rate. Worse, the arrival rate was increasing, but the overall service rate was not keeping up. Thus unless something changed, delays and backlogs would increase without bound. Since designers try to avoid this disastrous situation, the theory of unstable queues is less developed than that for stable queues. Simulation is a reasonable way of trying what-if remedies. Indeed one of those remedies occurred in 2010 when a new USTPO director was appointed, and the rate of grants shot up by 31% over 2009, to 220,000 grants, as the allowance rate A was suddenly increased to about 50%. While this change helps the queue performance, some worry about its effects on the quality of the patents granted, and it remains to be seen if it will really solve the backlog problem. There are funds available for increasing the service rate from application fees--but the U.S. Congress often raids these fees for the general treasury. 764

10 Figure 5. Model for patent applications and grants. Discrete simulation languages were developed long ago to model systems very much like this. Here GPSS/H was used to simplify consideration of the implications of this model, and various ways the underlying system might be improved. Often it is the modelling exercise itself that is most valuable, not whether the results are that accurate. Here the exercise immediately makes clear that outputs of the USPTO for many years to come can accurately be forecast. The reason is that the huge delays mean that the relevant inputs are already known for years to come. That is the number of grants in 2015 is mainly a function of Industry R&D investments in 2010, which we already know unless the system itself changes. The simulation confirms that the USPTO will experience rapidly increasing backlogs and delay times, unless its service rate can be increased. It also shows that foreign applications will come to dominate the output grants. This dilution of U.S. outputs coupled with the long delays involved mean that policies that affect R&D investment, such as the Obama Adminstration's goal to increase R&D investment to 3% of GDP, will take many years to have an effect on output U.S. grants. Indeed this analysis suggests that a much smaller investment in the USPTO might effect a more immediate improvement in U.S. innovation. Conclusions Models for patent indicators show that R&D funding from industry is a key input in encouraging patent applications. Models that include the substantial delays in patenting can be useful in predicting the effects of policy options. Discrete event simulations can provide further insight in some cases, such as unstable queues, where mathematical results are not so available. 765

11 One implication of the long delays in the patenting process is that one can forecast output patents for years to come, because the resource inputs that are most associated with those outputs are already known unless there is a marked change in the system itself. This also means that increased funding for R&D in a particular country will take many years to bear fruit in these output indicators unless the system itself is changed. The USPTO in particular needs reform to continue its role in international patenting. If present trends continue, these models show that it will be overwhelmed by applications, and its domestic patents will be frozen out of their own patent office. This outcome could be devastating for U.S. innovation, and for the sustainability of the patent office itself. References Criscuolo, P. (2006). The Home Advantage Effect and Patent Families. A Comparison of OECD Triadic Patents, the USTPTO and EPO. Scientometrics, 66 (1), Foland, P & Shelton R.D. (2010) Why is Europe so Efficient at Producing Scientific Papers, and Does this Explain the European Paradox? 11 th International Conference on S&T Indicators, Leiden, Sept Posted at Accessed Feb. 12, Godin, B. (2001). The Emergence of Science and Technology Indicators: Why Did Governments Supplement Statistics with Indicators. Montreal: OST Project on the History and Sociology of S&T Statistics, Paper No. 8, Accessed Feb. 12, Holton, G. (1978) Can Science Be Measured? In Y. Ekana, & al. (Eds.), Towards a Metric of Science: The Advent of Science Indicators. New York: John Wiley. Jin, B. & Rousseau, R. (2005) China s Quantitative Expansion Phase: Exponential Growth, But Low Impact. Proceedings of the 10 th International Conference on Scientometrics and Informetrics, Stockholm, July, Leydesdorff, L. (1990). The Prediction of Science Indicators Using Information Theory. Scientometrics 19 (3-4), Leydesdorff, L. (2006). The Knowledge-Based Economy: Modeled, Measured, Simulated. Boca Raton: Universal Publishers. Leydesdorff, L., & Wagner, C.S. (2009a). Macro-level Indicators of the Relations between Research Funding and Research Output. Journal of Informetrics, 3 (4), Leydesdorff, L. & Wagner, C.S. (2009b). Is the United States Losing Ground in Science? A Global Perspective on the World Science System, Scientometrics, 78 (1), Moed, H.F. (2002). Measuring China s Research Performance Using the Science Citation Index. Scientometrics 53 (3), Narin, F., Hamilton, K.S. & Olivastro, D. (1997). The Increasing Link between U.S. Technology and Public Science. Research Policy, 26 (3), NSB (2012), Science and Engineering Indicators Arlington: National Science Foundation. NSB OECD (2010), Main Science and Technology Indicators. Paris: OECD. Volume 2010/1. USPTO (2012). Accessed Feb. 12, Price, D de Solla (1978). Toward a Model for Science Indicators. In Y. Ekana & al. (Eds.), Towards a Metric of Science: The Advent of Science Indicators. New York: John Wiley. Shelton, R.D. & Leydesdorff, L. (2012). Publish or Patent: Bibliometric Evidence for Empirical Trade-offs in National Funding Strategies. Journal of the American Society for Information Science and Technology, 63 (3),

12 Shelton, R.D., (2008), Relations between National Research Investment and Publication Output: Application to an American paradox. Scientometrics, 74 (2), Shelton, R.D. & Foland, P. (2010). The Race for World Leadership of Science and Technology: Status and Forecasts. Science Focus, 5, p. 1-9 (Feb. 2010) in Chinese. Also, Proceedings of the 12 th International Conference on Scientometrics and Informetrics (pp ). Rio de Janeiro, July, Soete, L. (1987), The Impact of Technological Innovations on International Trade Patterns: The Evidence Reconsidered. Research Policy, 16 (2-4), Thomson Reuters (2011). Thomson Reuters Research Confirms China Leads the World in Patent Applications, Trademark Filings, Press Release December 20, Accessed March 6, UNESCO (2010). UNESCO Science Report 2010: The Current Status of Science Around the World. Paris: The United Nations Educational, Scientific, and Cultural Organization. UNESCO (2012). Institute for Statistics Accessed Feb. 22, Zhou, E.Y. & Stembridge, B. (2010). Patented in China The Present and Future State of Innovation in China. Thomson Reuters: World IP Today. 767