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Modeling the growth of patent value using patent citation networks
Daniël E. Smeding a
Supervisor: dr. B. Los a
a Rijksuniversiteit Groningen, Faculty of Business and Economics, Nettelbosje 2, 9747 AE Groningen, The Netherlands
Abstract:
2 1. Introduction
It is a widely held belief that technological development is vital to the competitiveness of a developed economy. However, technological development is not a risk free venture. Companies and universities alike have to invest considerable amounts of resources when undertaking research projects, without any guaranteed returns. In most modern states the existence of patent rights make it possible to get a temporary (usually 20 years) legal monopoly on the exploitation of invention. However, a patent right does not have any value per se. In fact, we observe that many patents have very little value, and just a few have very high value. In almost all industries,
technological development obtained by means of research and development (R&D) is considered a risky endeavor.
When an R&D project is successful the results are often captured in patents so that a temporarily set of exclusive rights on the innovation can be claimed. Patents, also referred to as intellectual property, are considered to be an asset class with economic value. Typically patent rights are legally equivalent to any other property and can be sold, mortgaged, transferred, or abandoned. The economic value of patents is the potential economic profit that can be obtained from the legal monopoly right on a patented innovation.
Imagine yourself for a moment in the position of a manager being tasked to maximize the return on a portfolio of intellectual property. In any typical strategic decision (e.g. transfer, abandoning or mortgaging patents) you need to make, (current) value of a patent is paramount. Although it is legal to buy and sell patents, there is as of yet no broadly accessible open market for intellectual property. Therefore, potential economic value of a patent cannot be derived from the resulting forces of supply and demand of similar patents on the marketplace. The manager or investor thus has the following problem: how can you determine the value of a patent?
To address this problem we must first define what the economic value of a patent is in the absence of market prices. We do this by comparing patents on their technological importance. When
comparing patents on their technological relevance or importance in it is helpful to look at patent citations. The rational to do so hinges on the fact that a patent's location in 'technology space' can be defined by patent citations from and to other patents.
Every patent applicant is by law required to clearly define the boundaries of its claims to a
technology. Consequently, if a patent is based on previously patented technology, so called ‘prior art’, it has to provide a reference to that patent. This practice can be compared with the more familiar citation requirements in formal academic publications. We need to emphasize that citations are common but not a given. A certain patent may or may not be required to cite other patents and/or receive citations from other patents. This happens when the subject matter of the claims on a novel invention is not based on any known prior art.
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combined with the legal dependence of other patents. Hence, the number of citations a patent receives during its legal lifetime serves as an indication of its economic value. Note that we estimate the economic value of a patent, not the market value. The economic value of a patent is the value that would be required to replace the patent, which is not its per se the value a patent would have on a hypothetical open market. This economic definition of value is better suited to describe the combination of technological relevance and legal dependence of other patents than a market value because we do not consider the direct result from supply and demand forces. The number of citations a patent receives during its legal lifetime will be the measure we use to analyze economic value of patents.
In this thesis we try to find a solution to the problem of the valuation of patents. Before we can construct a model however, we first have to understand how economic value among patents is distributed. There are statistical methods one can use to identify differences in economic value between patents on which we will expand in the next two sections. However, these methods have a major drawback: they require data of the entire legal lifetime of a patent. After the legal lifetime of a patent, the economic value of the patent drops to zero. This statistical approach can thus only tell us what the economic value of a patent was in retrospect. For the manager who has to maximize the value of a portfolio of patents, such an analysis is insufficient. He or she needs to be able to estimate the economic value at the beginning of a patents legal lifetime in order to be able to make strategic decision at an optimal moment. In this thesis we propose a model that can be used to estimate the economic value at the moment a patent is granted.
By now it will be no surprise that the information that we will use to predict the economic value of patents is obtained from the patent documents themselves. Among the information that is available on all patent documents are the following relevant pieces of information: claims to a novel
technology, the patent holder, the date of granting, technology classification codes, and finally the citations. Bear in mind that there will always exist information about technologies that is not documented in the form of patents. However, it has been estimated that about 80% of all
information of modern technology can be found in patent publications (Blackman, 1995). Although this claim is hard to verify, patents are generally regarded as the most complete source of
technological and commercial knowledge (Park et al., 2005).
When a group of patents have citations referring to each other, they form networks. The network character of patent data is important for the model we will propose later on. The problem of the manager is an implicit research question for a more formal hypothesis.
The working hypothesis of this thesis is:
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In order to search if there is any empirical support for this hypothesis and simultaneously answer the problem of the investor or manager, we formulate the following central research question:
What can patent citation networks tell us about the growth of economic value of a patent?
So as to formulate an answer to this question, we split the research problem into three smaller sub problems and formulated appropriate guiding questions. We will now shortly discuss these
questions, which will serve as a framework throughout this thesis.
The value (growth) identification problem:
Recall that we want to understand the distribution of value among patents. To explain why this is important I will use a short analogy. Imagine you plant a few plant seeds of which you cannot identify the species. When you plant the seeds there is no way of knowing what the differences in height of the different plants will be after some time. However, if you have information on the growth characteristics of each seed, you actually can estimate the differences in height of the plants in a future period. The problem and solution to estimating the patent value is very similar. We need to know what kind of growth characteristics there are among patents in order to estimate the differences in value among patents in a future period.
When we collect information on the accumulated number of citations at the end of the lifetime of a group of patents, we can draw a frequency distribution. From previous research on patents we know that those patent citation frequency distributions are heavily skewed and have medium sized tails that can best be described by a power-law distribution. (Silverberg and Verspagen, 2007) Moreover, from the distribution we are able to identify two distinct groups following different growth regimes.
In the first group the patents follow a citations growth path, which are best, described by a
Gaussian random stochastic process. This means that the patents of this group have the chance of receiving a positive number of citations is every single point in time is constant and independent from the past. In continuous time, a large enough sample of patents with Gaussian random growth process, observed at the end of the legal lifetime, form a normal distribution.
The second group is characterized by following different growth paths than the first group. Here the patents follow growth paths described by a power-law regime. In the power-law growth regime the chance of receiving a positive number of citations at every point in time depends on the number of citations received in the past. This type of growth regime is sometimes in the literature referred to as ‘preferential attachment’.
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the amount of citations a patent receives during its legal life, can be captured with a normal distribution. In contrast, the second group is expected to have received citations at a faster pace than the first group. This results in relatively higher values within the distribution of patents. The expected value for these patents can best be captured with a power law distribution. In terms of our patent citation network; we expect a given patent in the citation network to grow in the number of connections (i.e. citations received) in the manner described by characteristics of its respective group.
The first guiding question we will attempt to answer addresses the identification problem of value and value growth of a patent:
1. Which patents can be identified to exhibit power-law distributions in their citation frequency distribution?
Using extreme value statistics we will identify which distributions can be can be identified among patents. Being able to identify the power-law patents at the end of their lifetime will give us the information we need to formulate a growth model.
The value estimation problem:
For the manager, a model that can only explain economic value in retrospect is inadequate. Therefore, we need to construct a model that is able to predict the economic value of a patent and deal with differences in value growth speeds. At the same time the model should only require information, which is available at the date a patent is granted. In order to build such a model, we use of graph theory. Graph theory is the mathematics designed to formally analyze networks. We will explain how the proposed model works in more detail in the ‘review of methods’ section. For now it is sufficient to get an intuitive idea of how the model provides a prediction on the economic value of a patent. Additionally, we explain what kind of information we need for the inputs of the model. An important aspect of the proposed model is that every patent is assumed to have a single parameter that indicates the ability to attract citations. We will call this ability the ‘fitness’ of a patent. Patents with a high fitness parameter have a greater chance to attract citations from other patents. This parameter is very important for the model because it will largely determine the estimated speed at which a patent value grows.
In order to make sure that the model is useful to satisfy the problem of the manager, the fitness parameter needs to be observable at the date a patent is granted. The model we propose
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2.
Can we find specific topological patterns, which are instrumental to a citation growth model?We propose to use the so-called Katz centrality index to proxy the fitness of every patent. For this purpose, it is necessary to look at patents as individual parts (which are called nodes) that form a network through the citations that connect them. The Katz centrality index measures the relative importance of each individual node within a network. There are many different ways to look at the patent citation network. One way of constructing a network only requires us to use data that is available at the date a patent is granted. We will discuss the construction of such a network in more detail later. Using graph theory we are able to calculate the centrality index for every patent of such a network.
The problem of empirical verification:
Finally, we want to explain how the model we proposed can be applied using real data. In other words, we explain how the manager or investor could use this model. We will discuss the need for statistical analysis of historical data as we have used to answer the first question to test and calibrate the model. Historical data should be used as well to validate and benchmark the performance of the growth model. We formulated the question in the following:
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How can we verify the value growth model?7 2. Literature Review
The previous decades have seen a diligent effort among economists and researchers from other disciplines to explain the role of innovation and technological change in economic growth.
Economists from Adam Smith on have recognized the role of technology as a shaping process of economic growth. However, for a long time the ability of studying this difficult to conceptualize and complex phenomenon of technological change has been limited.
The most tangible measure of technological impact is its use and offshoots into other technologies. These are best captured in the citation trail patents create. Just as in research on the impact of scientific discoveries (Radicchi et al., 2008), patent citations have been used to proxy technological impact (Trajenberg, 1990; Hall et al., 2002).
The research based on citations expanded into several topics, and is addressed by different fields of research. Here we will discuss the relevant research that has been previously done. The relevant literature can be grouped into two general categories. The first category concerns itself mainly on the subject of valuation of patents based on citation frequencies. The second group attempts to model the dynamics within networks. The research in the last group is predominantly from outside the field of economics, mainly in physics and computer science. This paper tries to bridge the two fields, with an attempt to show how the theory of network dynamics can be applied to the field of valuation of patents.
Much of the underlying theory on patent value that we use in this paper is based on the research that we categorized in the first group. Initial research on patent value focused on quantitative research searching for evidence of patents as explanatory variables on value measures of firms. These studies have had mixed results (Harhoff et al., 1997). The failure to get solid indicators of patent value was explained by the noisy characteristics of both the patent- and financial data of firms. Although these attempts might not have been satisfactory in terms of explaining patent value, they did bring new insights in the distribution of patent data. A pioneering approach of
Silverberg en Verspagen (2007) showed that patent citation data as well as patent value estimation based on surveys of inventors shared a similar characteristic. The frequency citation could only partially explained by normal distribution characteristics. The data revealed signs of so called ‘medium tails’ which means that the right tail of the frequency distribution could better be explained by a power-law distribution than the assumed normal or Gaussian distribution. We use these findings as the theoretical foundation of our growth model. To test for the sizes of the two
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was observable at the grant date of a patent (so called backward-looking measures). The study makes a cross-correlation between backward looking measures and equivalent variables based on data that comes available after the patent has lived out its legal life (forward looking measures). Trajtenberg concluded from this study that the predictive strength of backward looking measures is strongly correlated with the predictive strength of similar defined forward measures.
The literature that concerns itself with value of patents provides great insight and ideas about what drives patent value. However, the nature of the literature above (with the exception of Trajtenbergs paper) is to use exclusively historical data. This means that most of the insight cannot be applied to estimate patent value when it matters most to managers and investors: in the first few years the legal lifetime.
In the other group of relevant literature the focus is on networks. The network-centric perspective on patent data prompted new possibilities for the visualization of patents using social network analysis tools (Sternitzke et al., 2008). Patent citation networks can be combined with other characteristics of patents. Examples of such characteristics found in patent documents are technological classification and data on the country of application. Different topological patterns were discovered using such network analysis. On the topic of network growth the early break through was the discovery of so called ‘scale-free’ networks. Scale-free networks are networks where the number of connections per node in the network follows a power-law. In the literature the growth process in a network where the distribution of citations follow a power-law is often referred to as preferential attachment. Adamic and Huberman (2000) show in their paper that a growth process of a network governed by preferential attachment leads to a scale-free network. The citation growth model we propose in this paper is based on a model developed by Bianconi and Barabási (2001). The paper combines the effect of growth described by a power-law (i.e.
preferential attachment) with a node specific ‘fitness’ value. The author shows how the distribution of the ‘fitness’ value will affect the distribution of citations within the network. The paper by
Bianconi and Barabási (2001) uses numerical simulation to prove the validity of the proposed model, which challenges the researcher who wants to use it for practical application.
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distribution. In the supplementary material of the paper Wang, Song and Barabási describe how in their model only a small amount of data is needed. By the data of the first few years of growth path of citations received they extract paper specific parameters by using statistics, and combining them with network specific parameters extracted from past data. Using these parameters, the growth path is predicted for individual scientific papers based on just a few years of growth path. The work is an impressive accomplishment, showing the predictive strength of network-based parameters. However, the scientific citation process had several advantageous characteristics that are not found in patent data. First of all, in networks defined by scientific journals there are a relatively small number of inter-journal (i.e. connections between different journals) connections compared to connections between technology groups in patent citation networks. This is an advantage, because smaller complexity in the structure of the network requires less computation to extract parameters dependent on the network structure. Secondly, the citation ‘culture’ between journals contrasted compared to the citation ‘culture’ between technology groups, is less divers. Citation culture is used as a term to describe the behavioral norms shared among different groups of people with a common characteristic (e.g. country, expertise) that influence the situations or criteria for which citations are made. In the data section of this paper we will go into more detail about the
consequences of citation ‘culture’. The more homogeneous cultures you have between different groups in your citation analysis, the better-generalized parameters will operate in predictive models. These small but significant differences between the citation network of scientific papers and that of patents lead me to suspect difficulty of applying the ‘Wang-Song-Barabási model’ on
patents. Future research may prove if this is possible.
This thesis will attempt to (further) bridge the gap between the literature on patent valuation and the network dynamics. Although occasionally patent citation networks are mentioned in the network dynamics literature, and the existence formation of networks is sometimes brought up in the literature concerning patent valuation, this paper will be of the one of the first to combine tools based on graph theory and patent data to with the objective to further our understanding of patent valuation. The relevance of this thesis to the field of economics should be obvious. By proposing a model of the economic value of patents, an asset class for which there are no known open
markets, this paper provides economists with a new valuation tool regarding these assets.
10 3. Review of methods
This section is split up into three subsections. In the first subsection we discuss the method that we use to provide an answer to our first guiding question. We proceed after this by describing how the value growth model works in the second subsection. Finally, in the last section we explain how we can calculate the Katz centrality index using data that is available at the moment a patent is granted. These two sections provide the necessary tools in order to answer the second and third research question.
3.1 The statistical approach: The Hill estimator
We will start off with the introduction of tool that will help us answer our first research question: which patents can be identified to fit a power-law distribution in the citation frequency distribution? As we explained in the introduction, this method focuses on the citation frequency distribution (that is: the cumulative amount of citations a patent receives over its legal lifetime) using extreme value statistics. The statistical approach is inherently backward looking. This means that the information we obtain from this method requires data only observed at the end of the lifetime of a patent. From a value perspective, at the end of the (legal) lifetime of patent the patent has received all the citations that matter. Patents often receive more citations after their legal lifetime but we will consider this as irrelevant as the economic value drops to zero at this point.
Assume that we can identify two groups of patents: one group that has a normally distributed citation frequency, and the other group that has a power-law distributed citation frequency. When we observe a citation frequency distribution of a random sample of patents, the two different groups could be identified using a method that estimates 'cut-off point' in a frequency distribution plot. We know that the normally distributed will be found in the ‘body’ of the citation frequency distribution and power-law distributed in the ‘tail’ of the same distribution. The reason for that is that the majority of the patents receive citations that can be best characterized by a Gaussian (normal) random process. For a few patents however, the attraction of new citations for a patent will be determined in a different manner. They follow a power-law distributed random process. The border between the normal and power-law distributed patents can be marked by an imaginary ‘cut-off point’. Patents on the both sides of this point have a different mechanic governing their citation growth. The power-law process is governed by a dynamic where the chance of receiving citations increases exponentially and depends on the citations they have already received in the past (see for example formula 2). In the literature on the topic ‘citations between scientific papers’ this process is often referred to as ‘preferential attachment’. There is preferential attachment if one can observe that new patents that come into the world will cite a patent that already has a high number of citations accumulated with a higher probability then a patent with only a few citations
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The question that remains unanswered so far is how to determine the location of such a cut-off point. Let us first examine a method of choosing a fixed cut-off point. Using an arbitrary cut-off point within a citation frequency distribution like a fixed upper quantile of the citation distribution (see for example: Akkermans et al., 2009) has several drawbacks. First of all, we know that inventions are not always patented. Inventors might instead opt for to keep their innovation secret and get economical rent from the invention through first mover advantage or by forcing competitors into negotiations of cross-licensing contracts. Obviously, the opportunities for keeping a
technological advantage secret differ between industries depending on a range of factors like market size, production complexity, etc. Consequently the incentive to patent will automatically differ as well. As we observe different patenting cultures that vary in patenting frequency and motives for patenting, a category-level perspective is required. Furthermore, patents are linked with stages of industries and technological life cycle. In early stages of the life cycle of a new
technological field most generated innovations are likely to be product improvements and varieties of such products. In later stages of the technological life cycle, innovations are more likely to center on cost reducing and quality improvements. Dosi (1982) termed the concept of technological trajectories for pointing out in how we have to differentiate between innovations in different stages of the technological life cycle. Recognizing the existence of these trajectories we have drawn the sample per annual cohorts. The observed power-law distribution can be explained by the argument that important patents create a 'technological paradigm' which spawns follow up inventions (see Dosi, 1982) that would all cite the preceding patent. The degree of success of such a patent is of course influenced over time and by the behavior of the technological environment. An important result is that the proportion of important patents will be different per time unit and per technological area, different from the fixed quotient approach. In summary, to avoid generalization errors we require a technology category specific and time specific measure. Moreover, the method has to differentiate between patents that received their citations by random events and patents that received citations by their success (the power-law patents).
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In this paper we will follow the procedural steps made by Castaldi and Los (2008) in their working paper. We will however use a different dataset as described in the section above. This is the major reason to use a revised choice of categories. The statistical procedure that is required to estimate the category-specific and cohort-specific proportion of the frequency distribution stems from extreme value statistics. For the cohort-specific and category-specific citation frequency
distributions we look for the existence and size and the cut-off point for the medium tails. Medium tails of generalized Pareto distributions follow the Pareto law: F(x) = 1-x-α. By using the Hill estimator a maximum likelihood parameter (α) can be estimated (Hill, 1975). For a sample of patents in which the frequency of observations (Xn) for a given number of citations (n) is ordered in
the following way: X(1)≥X(2)≥ ...≥X(n), the Hill estimator has the simple expression:
(1) 𝛾̂ = (𝛼̂)−1= 1 𝑘⁄ ∑𝑘𝑖=1[ln 𝑋𝑖− ln 𝑋(𝑘+1)]
Where α parameter is an estimation of the exponent of the power law and k is the number of observations included in the tail. Note that α can be observed as the negative slope in a Pareto plot.
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With a large number of observations (k), the underlying distribution can be identified as Paretian (i.e. distribution with a power-law) if the Hill estimator (𝑦̂) becomes a constant. However in our samples the distribution is only partial Paretian (in the tail) and will become normally distributed in the ‘body’ of the distribution (see the curvature on the left of figure 1). To estimate where the normal distribution (body) stops and the power-law distribution (tail) starts we approximate a cut-off point, where k is optimal, considering the stability of the Hill estimator. For this estimation we will follow a modified version of the Drees and Kaufman (1998) estimation method. This method works as follows: while the number of observations to the tail (k) is inflated the Hill estimator is monitored. This means that the Hill estimator is calculated successively over an increasing interval of X
starting at the right side of the distribution as shown in figure 1. When fluctuations in the
successively calculated Hill estimator exceed a predetermined threshold value, the optimal value k is found. By setting a higher threshold the cut-off point is more sensitive and will shift to the right, the tail then includes fewer observations.
The Drees-Kaufman-Lux method described above will provide a single estimation of a cut-off point per cohort and category of citation distribution. In order to get an idea of the strength of these estimations we used the bootstrapping method proposed by Castaldi and Los (2008) as a way to get a 90% confidence interval of the cut-off estimate. The Drees-Kaufman-Lux method is repeated a large number of times using pseudo-samples equal to the real sample by drawing from the observations with replacement (Efron and Tibshirani 1986, 1993). Now the value of the estimators of 5th - and 95th percentiles are representative of the confidence intervals around the cut-off estimate.
One of the drawbacks using the Hill estimator is that you need well-shaped distributions. For this you need large sample sizes. The amount of data available in a patent citation distribution depends on the size of the technology categories. When defining large categories, differences within the category are not captured amounting to loss of information. For the same reason the observation time of one cohort has to be long. Concluding, when enough data is available the statistical method offers useful insight in a backward looking model. One should be aware however that the results will always depend on the defined patent categories (see Data for a more extensive discussion on the categorization of patents).
3.2 Building a value growth model with preferential attachment and competition among patents. Now we have described a tool to identify which patents belong to the power-law tail of the
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By answering our first research question, we know that the model must explain two types of growth regimes. Let us consider a patent as a node in a network of other patents. The connections (links) between the nodes that form the network represent the citations of the patents in the network. The patent citation network is a so-called directed network, because the links between the nodes have a direction (i.e. citation from patent ‘A’ points to patent ‘B’). When time goes by, more patents are published and connect to different nodes into the network by means of their citations. This way the network grows (see for a visual example of a real patent in the figures in Appendix A4). The figure below is a schematic overview of the structure of a citation network. In this network we can
differentiate between forward- and backward citations. The forward citations consist of the citations that directly or indirectly cite the patent in focus. Backward citations are those patents that are cited directly and indirectly by the patent in focus. The terms forward or backward citations are used because citations can only be observed when looking forward or backward in time relative to the patent in focus.
Fig 2: A schematic overview of a patent citation network structure
We will show in the data section that the model has to take three important characteristics of a citation network into account to explain the dynamics at work. First, the most obvious but
nevertheless important observation is that the network grows over time. A second property of the network is that the new nodes will attach with a higher probability to nodes that have themselves already received many connections (i.e. there is preferential attachment). And third, there is a difference between nodes in the growth regime when receiving citations, as observed at the ex-post citations received frequency distribution.
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(2)
𝑘
𝑖(𝑡) = (
𝑡𝑡𝑖
)
𝜏
, 𝑤𝑖𝑡ℎ 𝜏 =
12Where ki(t) represents the connectivity (in some literature referred to as the degree of a node) of
node i, ti is the time in which this node is added to the network and t is the current time period. As
you can see, this model amounts to a power-law growth regime. It is important to point out that in this model the concept of time is different from the ordinary time units that we are used to. Here the passing of time unit occurs when a new node is added to the network. The prediction of this model is that the oldest nodes will have attained the most links within the network since they have had the most time to attain them. This type of growth regime differs from our observations in the end of life citation frequency distribution (see figure 1) of the patents belonging to the same cohort. The data suggest that patents seem to grow in the amount of citations they receive at a different speeds. The growth speeds of patent citations obtained from the data seem to be governed by a Gaussian random growth regime and the growth speeds governed by power-law growth regimes. Of which growth speeds given by the the former are smaller than those given by the latter.
To incorporate different growth speeds between patents confirmed by our third observation, we adopt the so called ‘fitness model’ which was proposed by Bianconi and Barabási (2001). We will discuss below how this fitness model is constructed, and how we can use it for the patent citation network.
In the Bianconi and Barabási’s model the nodes each have a property, called ‘fitness’. The fitness is the ability of a node to compete for citations from other nodes, which are added to the network in a later period. In terms of our patent citation model, the fitness of a patent would be captured in some explicit or inexplicit characteristics of the patent.In the data section we find that the model best fits our data when using an exponential fitness distribution. We can observe the fitness value of an observed patent by the ability of spawning other patents which incorporate some of the technology of the observed patent. The spawned patents are obliged by law to cite the observed patent.
In order to mathematically ‘build’ the fitness model, we want to assign a fitness parameter μi to
each node, which is drawn from a distribution θ(µ). In this alternative scenario of the generalized preferential attachment model in (2) the probability (πi) that a new node will connect to an existing
node in the network depends on the connectivity (ki) and the fitness parameter (μi) of that node.
Both parameters are non-negative with no upper bound. The probability of a new node connecting to an existing node (πi) is proportional to its fitness in the following way:
(3)
𝜋
𝑖=
𝑘𝑖 𝜇𝑖∑ 𝑘𝑗 𝜇𝑗 , 𝑤𝑖𝑡ℎ 𝑘𝑖 𝑎𝑛𝑑 𝜇𝑖 ∊ [0, ∞)
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citations a new patent makes to other patents as the parameter m. Notice that low values of the fitness parameter will cause the model to have almost no preferential attachment. In this case the probability of a new node connecting to the existing node equalizes for all nodes. Starting from equation (3) we can state that the connectivity of each node increases as follows (in continuous time):
(4)
𝛿𝑘𝑖𝛿𝑡
= 𝑚 (
𝑘𝑖 𝜇𝑖∑𝑘𝑗 𝜇𝑗
)
It can be shown that the evolution of ki follows a power law:(5)
𝑘
𝑖(𝑡, 𝑡
0) = 𝑚 (
𝑡𝑡𝑜
)
𝜇𝑖𝐴 ⁄
where t0 is the time node i is added to the network and A given by the singular integral:
(6)
1 = ∫
𝑑𝑥𝜃(𝑥)
𝐴1𝑥−1
𝜇𝑚𝑎𝑥
0
Here, µmax is the maximum fitness that any individual node in the network can get upon entering
the network. The derivations and proof can be found in the paper of Bianconi and Barabási (2001). From (5) we can see that the connectivity of a node grows faster if its fitness high. It is possible to prove that if we have a distribution in which every node has the same fitness (i.e.: μ1= μ2=…= μi),
equation (5) will take the form of the scale-free model as described in (2).
To make the model applicable for the patent citation network we assume that the distribution of θ(µ) is exponential of the form
𝑒
−𝜇1.
With this distribution,t
he average time required for a large µto be drawn from the distribution scales with time as τ(µ) ∼ 1/p(µ) ∼ eµ. We can then state that the
largest fitness parameter of any node (µmax) scales with time as µmax ∼ ln(t). Given these properties
hold for the fitness distribution, we have that the fitness weighted sum of connectivity of all the nodes in the network is smaller than some function D: ∑𝑡𝑗=1𝑘𝑗 𝜇𝑗 ≤ D ln(t)t. Using some mathematical steps 2 we can show that the model can be rewritten as:
(7)
𝑘
𝑖(𝑡, 𝑡
0) = 𝑘
𝑖(𝑡
0) (
ln (𝑡) ln(𝑡0))
𝐷(𝑡) 𝜇𝑖 ⁄1 Moreover, we assume in our fitness distribution θ (µ
max)≠ 0 and µmax is reached in a short timeframe. Translating these assumptions
into our patent citation model, this means that the fitness parameter patents must be observable in the early stages of its life.
2 Assuming that lim 𝑡→∞
∑ 𝑘𝑗 𝜇𝑗 𝐷 ln(𝑡)𝑡
𝑦𝑖𝑒𝑙𝑑𝑠
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When we compare the fitness model equation (7) with the preferential attachment model described by equation (2) there are two important differences. For one, the base of the exponentiation
changed to the ratio of two logarithms. Another difference is that the constant exponential term (
𝜏)
is now a complex ratio of
a function. The ratio describes the (fitness) weighted sum of the connectivity of the network 𝐷(𝑡) and the fitness of the given patent 𝜇𝑖 . Function D described in mathematical terms is:(8) 𝐷(𝑡) =(∑ 𝑘𝑗 𝜇𝑗
𝑡
𝑗=1 )
𝑚𝑡 ∙ ln (𝑡)
The model projects the growth path of the connectivity of patent i over time (t) given the time it was added to the network (t0), its fitness (μi) and average links a new node adds to the network (m).
The connectivity, which is the number of citations received for patent i, at time t = t0, takes by
definition the value of one in the model of the patent citations network. After all, we have defined the time steps as the addition of one new patent to the network, and a given patent can only make one citation to another given patent. The term connectivity term on the right hand side of equation (7) drops out as
𝑘
𝑖(𝑡
0) = 1.
A node (patent) is added to the network at t = t0 when another patentcites patent i for the first time. This is different from the publication date of a patent, at which time it did not receive any citation and is not considered part of any network. Consequently nodes that will never receive any citation are assumed to experience no growth in this model. This also means that this model cannot explain the forces that determine when the first citation is received. We can now rewrite equation (7) in the following way.
(9)
𝑘
𝑖(𝑡, 𝑡
0) = (
ln(𝑡ln (𝑡) 0))
𝐷(𝑡)
𝜇𝑖
⁄
In order to apply this model to the data we are going to collect some data for the parameters. We only use the data we are able to observe at t = t0. First of all we can calculate the (average)
number of citations patents give (m) and we find that m ≈ 6. For simplicity it is assumed that m is constant over time. Remember that time is measured in the adding a single node to the network, so t0 can be interpreted as the size of the network at the moment patent i receives its first citation.
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3.3 Measuring fitness: the Katz-centrality of a patent at the date of publication.
Now we have constructed our model we need to find the fitness parameter. In order to create a proxy for the fitness of any patent, we choose an observable characteristic (pattern) of the network structure. This observable characteristic will be the Katz centrality index of the patents at the publication date (tp < t0 < t). A centrality index, as the name reveals, determines the relative
importance of a node within a network. There are several kinds of centrality indices. We want to use a centrality index that extends the information value you get from a simple citation count. A per patent citation count in graph theory is in fact the simplest form of a centrality index, called the degree centrality. There are three alternative centrality indices to the degree centrality: Eigenvalue centrality, Page rank and Katz centrality index. These three centrality indices measure the
influence of a node in the network, taking into account not just the number of connections a given node has but also the relative position of nodes that a given node is connected to. We will not go into much detail about the differences between these three measures, except to say that the Katz centrality index a generalization is of the degree centrality index, and is most suitable to use and interpret in this thesis. In deciding which centrality index to use, we also have to be sure that the structural characteristics of the network allow for its calculation. The network citation network is acyclic, which is a specific characteristic that says that there are by construction no loop’s in the network. In other words, when you would be traveling from node to node over the connections in the direction of the citation, you will never end up in a node which you have previously visited. This is another reason why we will use the Katz centrality index, as it is a suitable index to use in directed acyclic graphs like a patent citation network is.
The Katz centrality index should be interpreted in the following way. The relative height of the index number of a patent signifies the relative influence of the node X on other nodes. The higher the centrality index, the more central the position of a node is in the network relatively to other nodes. Katz developed this centrality index as early as 1953. He used it to measure the relative influence and status of agents in social networks (Katz, 1953). The Katz index works as follows. We start of by constructing an adjacency matrix A of a network. In this matrix element (aij) takes the value 1 if
node 'j' is connected with node 'i', and takes the value 0 if not. The power 'k' of matrix Ak represents
links between vertices between intermediate connections. The Katz centrality index for node ‘i’ can be mathematically described as follows:
(9) 𝐶𝐾𝑎𝑡𝑧(𝑖) = ∑∞𝑘=1∑𝑛𝑗=1∝𝑘(𝐴𝑘)𝑖𝑗
Where α is the attenuation factor that weights the connections (edges). If α =0.5, direct
connections (k=0) are weighted α0 = 0.50=1. For the connections that have k-1 intermediaries, the
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centrality index for a small network giving each node the intrinsic value 1 and using α =0.5 as an attenuation factor.
Figure 3: Example of the Katz centrality index of a small network. The numbers, color and size of the nodes denote the Katz centrality index.
In this thesis we will use the Katz centrality index to measure the fitness of a patent. The network we are going to use to calculate the Katz centrality is directed, which means that the citations point in a certain way. Using the citation network, we can calculate a Katz centrality index for every node at time t = t0 only using the backward citations. Remember from figure 2 that the backward looking
citations go in the opposite direction of the forward-looking citations. The backward citations only point to ‘j’ other nodes for which t0 > tj. The Katz centrality index calculated in a large network will
contain the relative position of the node in the network as well as information on the number of citations it makes.
Constructing a backward citation network can be compared with ‘telling the story backwards’. From a given node (patent) i, we look back in time, following the citations node (patent) i makes to
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Fig. 4: Citation network centered on the patent: US4185465 A, “Multi-step regenerated organic fluid helical screw expander hermetic induction generator system”. From top-left to bottom-right, 2nd to 7th generations of citations into the past.
Having calculated the ‘backward’ Katz centrality index for all the nodes in the network, we can define the fitness of the patent to be equal to the Katz centrality of those nodes in the following way. The attenuation factor (α) we use in the calculation of the centrality index for every node is 0.25 (~1/median of citations given in the complete population). The network size we used for the calculation of the Katz centrality index is up to 5 generations back, in order to limit the time (and memory) it takes to calculate the centrality index for each node. Giving citations from nodes at the edge of the network only a marginal increase of the index of about 0.001 to the central node. From figure 4 you can see that a high centrality index is obtained when patents attach themselves to nodes in the network which have high values of the centrality index. Note however that figure 4 is just an example of the sampling for the network around one given node. For consistency, such networks have to be sampled for every node individually before calculating the Katz centrality index. This way we will not create any bias due to the truncation at the 5th generation in a given
sample.
We define the Katz centrality index as the patent’s fitness parameter.
(10)
𝜇
𝑖≡ 𝐶
𝐾𝑎𝑡𝑧(𝑖)
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negligible. This means that the for patents with a low fitness parameter, the end of life distribution of citations received will look like a normal distribution, as observed on the left of the frequency distribution in figure 1. For patents with fitness parameter values, the growth process can be described as a power-law process where the preferential attachment mechanism amplified by the fitness parameter influence the growth speed.
22 4. Data description
We will now look at the data we have used for the two different analyses. Not surprisingly we need different methods of gathering data for the two approaches. We will discuss the method for data mining for both approaches and the relevant statistics. We will start off with data gathering method for the Hill estimator, which is rather straightforward. Then we will turn to the more involved
process required to mine data for the network theory process. Finally we discuss some statistics of the dataset that are relevant for the interpretation of the outcomes.
For patent research there are several datasets available. Hall, Jaffe and Trajtenberg for the NBER (Hall et al., 2002) created a database that is commonly used in recent literature. For example the work of Castaldi and Los (2012) harvested their data from the NBER dataset. The NBER dataset is based on the database of the US patent office (USPTO) and refined for academic use. This thesis uses exchange of patent information as produced by the European patent office (EPO) from their master documentation database (DOCDB). The DOCDB database is a collection of the combined information of all patent offices linked to the World Intellectual Property Organization (WIPO) of the United Nations. Some 185 United Nations members have patent offices that share their collected digital patent data that is stored in the DOCDB dataset. Unfortunately the dataset is set up mainly as a tool for reference and technical category oriented search for legal and technical examination. Building a usable data set from a raw information database like the DOCDB implies numerous challenges. Patent offices have shifting procedures. For example the technology categorization has changed several times over the past decennia. These irregularities are compounded with some human made errors ranging from incompleteness to typos creating a small jungle of systemic inconsistencies.
When working with the worldwide data set, one should remember that every country has its own laws and procedures (many of them designed before the digital age). The dataset we use in this paper consists of all the patents and applications from 1900 on to 2010. Of all these patents we have 20 year of patents (1970-1990) granted by the USPTO including their complete aggregate legal lifetime of 20 years on which we focus. The analysis includes however citations from patents of all countries.
4.1 Creating data for the Hill-estimator
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To categorize the patents in our data set we use the IPC classification. The IPC is a tree-like classification scheme that starts off with 8 different stems. Each stem branches out three more times, each time increasing the detail of description of the sub-category. The nature of
technological development is to venture into new unclassified areas. Classification of technologies is therefore often subjective and consistency in the classification process is a complicated matter. It is therefore necessary for the WIPO to review the IPC classification periodically. Sometimes new category branches are created and/or existing branches are split or re-ordered because of new groups of inventions that cannot satisfactory be labeled by the existing categories. This means that the classification needs to be constantly updated. Because patents are always categorized on the most detailed level (the outer branches of the IPC) the practice is to assign them all classifications that fit the technology. The result is that any patent can have up to 80 classifications, and almost no patent is categorized in a single group. For research purposes it can be problematic to have patents that hold multiple categorizations. To solve this problem it helps to consider only the less detailed branches of categorization (the branches close to the stems). However, although the multiple category characteristic of patents indeed becomes smaller this way, some patents remain having more than one category. This can happen when a patent for computer hardware has classifications in multiple stems (i.e. 'physics' and 'electronics’).
As explained in the methodology, the data for the Hill-estimator needs to be organized into singular technology categories and publication years (cohorts). In order to give a patent a unique category we have taken the following steps. The most obvious solution at hand was to use the less detailed categorization. However, choosing a low branch of the categorization tree means that the statistics cannot identify the internal category differences. Furthermore, we need a reasonable amount of patents per category in order to be able to calculate the Hill-estimator with some precision. Taking these things into account we decided to use the categorization of the first level of branches. This leaves 127 categories (see Appendix 2 for details). By a trial and error method we found that this satisfies the required population size per category to get adequate results using the Hill-estimator and less loss in specificity in the results that would be linked to a category. In order to get rid of the odd patent that would still have multiple classifications we need to do more aggregating. First, all the categories of the patents were binned in the 127 IPC groups. Secondly, IPC that contained the largest group of classifications was considered the dominant classification of a particular patent. This results in a unique (dominant) IPC for every patent.
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the whole world, a necessary scope in a globalized world with ongoing development in
communication. So called patent families, which are single patents granted in multiple countries, are not considered in this thesis.
4.2 Creating data for the patent citation network
Before we go into the data collection methods we used in order to obtain data for the network analysis, we have to understand the structure of the network. In the figure below we show the structure of a patent.
Fig. 5: Schematic interpretation of citations received and citations made by a singular patent.
In the schema above shows a singular patent (represented by the square), its citations
(represented by the black circles) and the citations it receives (represented by the white circles). Notice that the citations have arrows indicating their direction. In network terms this is called a directed network, in which the nodes are connected by directed links. The size and structure of the network depends on the time you observe it. At t= t+1 the number of connections that point toward the observed patent (the degree of the observed node) is 5. At t=t+2 it has a degree of 7 and at t=t+3, a degree of 13. Furthermore it we observe at t=t that the patent has made 7 different citations, which we can observe from all t>t.
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several network sampling methods: node sampling, link sampling and snowball sampling. (Lee, et al., 2006) With node sampling random nodes are selected. If there are links between the selected nodes they are included in the sample. Link sampling is an inverse method where edges are randomly drawn from the data and the vertices at both ends of the link are included. Snowball sampling selects one particular ‘seed’ node and then a breadth-search is performed to create the sample. A breadth-search is a search strategy that first visits a particular node, then checks its direct neighbors and visits them in the next round. This search method works as a loop, repeating the steps in cycle. The results of a breadth-search can be seen in the successive steps in figure 4. The breadth-search can be stopped in two ways (Ahn et al., 2007). Either it stops automatically when the network has a finite number of connections, or a limit to the search iterations is enforced. Snowball sampling is the most suitable sampling method to crawl the patent data for three
reasons. First, in a large dataset, node and link sampling are inefficient. As revealed by the statistical citation frequency patent data includes many nodes (which resemble patents) with only very few citations. In order to get a picture of a network, the sample size needs to be very large. This is needed because the chance that the randomly selected nodes or edges belong to a
particular larger network is small. Second, by randomly selecting nodes in a very large dataset, you will automatically underestimate the mean number of connections (node degree) and cannot find the correct number and size of any clusters. Third, we want to develop measures that target a particular set of patents (the patents that show power-law distributed citation amounts) which requires that we sample the full size of the sub networks around the selected patents. One of the upsides of using the snowball sampling is that we will leave the topological
characteristics intact. An equally important benefit is that we can direct the breadth-search in two directions. We can make an iterative loop crawling the connections created by citations received by the seed node. This obviously requires that the seed node is a patent that was published in the past so that preceding documents citations are available in the data. In the same manner we can also breadth-search to crawl the citations that the seed node has given. This way we look into the network of citations that preceded the seed node. For this we only need data preceding the date of publication of the patent that is the seed node. This way allows us to look how the network of patents looked before a certain patent was published, as well as what happened afterwards. As we will see this comes in handy when creating forward looking measures.
4.3 Some descriptive statistics on the data.
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per patent per year in the US.
Fig. 6: US patent and average citation growth per year.
Figure 7 shows that the trend over all US patents is similar to the trend in growth of average citations per patent in the classification of ‘Basic Electric Elements’ (IPC 122).
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Two of the assumptions we have made about patent citations earlier will create biases. From the table below we can see why. Firstly, the total number of patents grow at different rates between countries.
Country Patents granted 1970-1990 m
US 1503329 6.12
DE 24873 2.11
JP 1662876 0.27
Table 1: Patent counts and average citations per patent (m) over period 1970-1990 for the US, Germany and Japan.
From the data we found that over all the citations received by US patents, only 13.5% are made by non-US patents, meaning that there is a 86.5% chance that the citation a patent will receive will be also from the US. Furthermore, we found that when considering all countries, on average only 2 out of 10 citations received will be from a patent from a different country. It is easy to include the patents of the rest of the world in the statistical analysis. In the network model it is also possible to work with country aggregated data. We have made the decision to exclude citations received from ‘foreign’ in our network model for the following reasons. The most important reason is that our model is endogenous (k(t) depend on the past growth of k, due to the preferential attachment). Therefore we can solve this model only by an iterative process, which is very computational heavy when we include large numbers of nodes (patents) in the model. Secondly, we will compromise the data integrity by aggregating the data over countries. This might happen when institutional
differences cause the changes in patent growth and the patent network size (e.g. the reunion of East- and West Germany).
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probability of receiving a citation in t=y over the amount of citations received previously (t<y) accumulated.
Fig. 7: Preferential attachment in US patents with publication date 1990.
In the example picture above (see full analysis in Appendix A1) we observe a positive linear
29 5. Results
Let us go back to the problem of the manager/investor. In order to be able to make strategic decisions on its intellectual property portfolio, the manager needed a method to estimate the (current) value of a patent at the moment it was granted.To solve this problem we proposed a model based on patent citation networks. This model is on the hypothesis that patent citation networks contain information on the future value growth of a patent. We could test the validity of such a model on the premises that we cannot reject (with some certainty) this hypothesis. So as to find empirical support of the hypothesis above, we formulated the main question of this thesis: What can patent citation networks tell us about the growth of economic value of a patent? In this section we will attempt to answer the three sub questions we formulated in the introduction so as to answer the sub-problems that address key elements of the main question.
The value (growth) identification problem:
Which patents can be identified to exhibit power-law distributions in their citation frequency distribution?
An estimation of which patents belong to the power-law distribution kind can be identified to as the patents left of the cut-off point as estimated by the Hill-estimator. In the figure below the estimated cut-off points and the 95% confidence interval for the category ‘Basic Electric Elements’ (IPC 122) are depicted. The Hill-estimator method can also be applied to different IPC groups or cohorts. Yet in order to successfully estimate a cut-off point using the Hill-estimator method the amount of patents available per cohort and category has to be sufficiently large. This method is therefore limited to the analysis on broadly defined technology groups. In figure 8 below we show the predicted cut-off points as predicted by the Hill-estimator. The increase in the cut-off point can be explained by the growth of the network as shown in the data section.
The cut-off values will tell you the minimum of citations a patent must have received at the end of a patents’ lifetime to be in the power-law tail of the citation frequency distribution (see figure 1 for the example of cohort 1975). The red and green lines are the lower and upper bound of a 95%
confidence interval created by the results from bootstrapping. You see that the cut-off point
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Fig 8. Hill-estimator cut-off values IPC 122, US patents
We can conclude from these observations that normal distributions as well as power-law tails can be identified in the ‘end of life’ citation frequency distribution category 122 of US patents of multiple cohorts in a row. This underlines the importance of allowing for different value growth speeds among patents when estimating their future value.
The value estimation problem:
In the proposed model we assumed differences between patents in their ability to accumulate citations. For that purpose we constructed a growth model that depends on network specific parameters that can be observed at the beginning of a lifetime of a patent. The second guiding question related to the identification of these network specific parameters:
Can we find specific topological patterns that are instrumental to a citation growth model?
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Fig. 10: Scatter plot of the Katz centrality index and citations received at end of legal life time per patent. The insert plot is a histogram of the observation density in the scatter plot. Sample is taken from US patents, filtering on publication year 1970
Figure 10 illustrates that there is a required positive relationship between the Katz centrality index and the citations received. However, this relationship is clearly not as strong as we expected. It should be noted that most of the observed patents resided in the lower left corner (see histogram insert in the top right of figure 10). This picture contains 72500 observations.
A linear regression of a simple regression model on the data comprised of US patents in 1970 gave the following results:
Regression Model
: 𝐶𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 = 𝛽 ∙ 𝐶
𝐾𝑎𝑡𝑧+ 𝜀
Coefficient [𝛽] (Std. Err.) t-statistic (P>t)
Katz centrality index [𝐶𝐾𝑎𝑡𝑧] 0.712 (0.004) 187.35 (0.000)
Table 2: OLS regression results. Dependent var.: Citations received after 20 years, Independent var.: Katz centrality index (backward looking). [R2-value: 0.33]
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the null hypothesis that there is homoscedasticity versus the alternative of unrestricted heteroskedasticity. The test statistics are shown in table 3.
Chi2 (df) P > Chi2
1285.73 (2) 0.0000
Table 3: Test statistic results from White test
As the test results show we cannot reject the null hypothesis of homoscedasticity with a high degree of certainty. In other words residual variance from the regression is constant.
We must warn that analysis is not a substitute for the model. In the model we assume a nonlinear relation between the ‘fitness’ of a patent and citation frequency at the end of the legal lifetime of a patent. Nevertheless, we can carefully conclude that for the observed year the backward looking Katz centrality index is captures a patent specific characteristic which can be instrumental in the success rate of a patent attracting citations.
Fig. 11: Histogram of Katz centrality index. Sample is taken from US patents, filtering on publication year 1970.
Finally, we need to check the distribution of the Katz centrality index, to make sure it is distributed exponentially as we assumed. In figure 11 we show a histogram of the Katz centrality index over the same sample as we will use in the model.
The Katz centrality index distribution in our sample, θ(µ), scales exponentially (θ = 𝑒−𝜇
)
as we had33
Concluding, we have found a suitable topological pattern that is instrumental to our proposed growth model. The backward looking Katz centrality index capturing the relative importance of a new patent in the network of existing patent citations is a good instrument for predicting future patent value growth. It should be noted however that there could different topological patterns that suit our model, which have yet to be discovered. We will discuss in the conclusion some ideas on improving the fitness parameter using the Katz centrality index in alternative ways.
The problem of empirical verification:
How can we apply the value growth model?
To apply this model and estimate the economic value of a patent it is necessary to acquire three important parameters. First, you need to calculate the Katz centrality index for every single node (i.e. for every patent) in the network. Second, you need to estimate the yearly growth in patents in the twenty years that follow. And third, you need to estimate the average citations each patents will have in the same period of twenty years after the date a patent is granted. Combining the Hill-estimator as a benchmark for the minimum number required citations received after 20 years it is possible to use the model to find a minimum required fitness parameter.
From the numerical tests in the paper of Bianconi and Barabási (2001) we know that for large networks function (7) describes a stable exponential growth path. However, using the patent citation network data in order to calculate the growth path of any single patent requires calculating function (7) over the time period of 20 years. To do this we encountered two major obstacles. The first difficulty lies in that patent citation networks are very large in nature. In the data section we show that average yearly growth should be estimated well above 50.000 for patents that are published in 1970, and over to 200.000 for patents that are published today. The larger network3 in
1970 has a size of roughly 90 million connections (citations) linking the different nodes (patents and applications). The second obstacle is the calculation of the iterative summation over all (fitness weighted) patents in the network up to the end of life date and you will have a function that takes even the faster computers today a very long period to calculate.
Bianconi and Barabási (2001) show that the embedded function (8) is an iterative process that stabilizes around a number. When the long term value of (8) is computed (D*) the growth process as described by function (7) can be calculated with less effort.
In order to compute D* the Katz centrality index value of every node (patent) has to be calculated first. Then the sum of all the nodes weighted with their respected ‘fitness’ (which is the Katz centrality index) can be calculated for every successive year. After these two steps D* can be calculated, which is to be expected to be more or less constant over time.
34
35 6. Conclusion
We started this academic endeavor with the intention to create a model for the manager, which he or she could use to calculate the economic value of a patent. In order to be able to build such a model, the following question needed to be answered: What can patent citation networks tell us about the growth of economic value of a patent?
We choose to split this problem into three sub problems. The first two sub problems centered on the characteristics of the value distribution of patents and the existence of value indicators in the network of patent citations. From our attempts to provide an answer to the first two sub problems we can conclude the following. The value distribution among patents implies two types of growth regimes among patents. A Gaussian random growth regime and power-law regime, patents with the first type of growth regime gain less value over their lifetime then patents with the latter growth regime. Furthermore, we found that some of the characteristics observed in the citation networks can explain the growth mechanics observations made at the ex-post value distribution. We focused on two characteristics: preferential attachment and a so-called ‘fitness’ parameter. We reasoned that the existence of preferential attachment among patents could only explain the existence of power-law growth regimes. Preferential attachment does not explain the Gaussian random growth regime of the patents observed in the lognormal body of the citation frequency distribution in a cohort (where patents have the same publication date). Our proposed model is able to explain both observed distribution characteristics, using a patent specific fitness parameter as a supplementary measure to preferential attachment. The fitness parameter represents the power to attract citations from others while the patent citation network is growing. We argue that the Katz centrality index could be used as a proxy for the fitness parameter. Unfortunately the model we proposed is rather computationally heavy. For this reason, we were not able to simulate the value growth of patents within the patent citation network. If the model could be tested, then the Katz centrality would be a good proxy for fitness, if the model predicts a differentiation of the speed of value growth among patents in a similar way as it is observed by the Hill estimator using ex-post citation data.
From the model we would have expected to see the patents that had high centrality indices and which receive their first citations in early stages of their life, to be more successful. However, there is likely much to improve on the performance ‘fitness’ proxy (see figure 10), that would in turn improve the performance of the model. One-way to improve the information value of the ‘backward looking’ Katz centrality index that we have used is to provide weights to the nodes within the network. Weights could for example be constructed for patents of different countries or technology groups. We leave this for future researchers.
