The Knowledge Mobility of Renewable Energy Technology

Knowledge bases are described to consist of three types of knowledge: analytic, synthetic and symbolic knowledge [3, 33]. In this context, analytic knowledge is understood to be science-based, created in deductive processes based on formal models. Synthetic knowledge is understood as engineering-based, created through the application of existing knowledge or through inductively combining existing knowledge. Finally, symbolic knowledge is characterized as cultural or artistic knowledge.¹¹1In this research we will mostly focus on the distinction between analytic and synthetic knowledge. As the knowledge base of technologies often contains multiple types of knowledge, it is more instructive to think about the extent to which it is analytic as a spectrum or a scale. In this line of thinking, we define the analyticity of a knowledge base as the extent to which it consists of analytic knowledge.

The analyticity of knowledge has been associated with several other theoretical dimensions of knowledge. First, where analytical knowledge is associated naturally with basic research, i.e. research aimed at truth-finding, synthetic knowledge is associated with applied research, i.e research aimed at solving practical problems [7, 38]. Technologies that strongly depend on analytic knowledge are therefore understood to have stronger ties with the natural sciences. While closely related, basic and analytic (or applied and synthetic) cannot be considered synonyms: basic research may occasionally produce synthetic knowledge, and vice versa. Second, and closely related, where analytic knowledge is universal and theoretical, synthetic knowledge is context specific and practice related [33]. It is therefore expected that it is more difficult to work with synthetic knowledge outside the context in which it was developed, that is synthetic knowledge is stickier and place dependent. Third, analytic knowledge is often associated with codified knowledge and synthetic knowledge with tacit knowledge. However, here too, there are certainly exceptions. Not all published work is easy to fully understand or reproduce without the aid of those that produced the work. Authors have therefore argued that there sometimes is a tacit element to analytic knowledge as well [33].

Knowledge bases can also be characterized by their ’technological cumulativeness’, the idea that today’s technologies are developed by building on the insights from yesterday’s technologies and will themselves be used to develop the technologies of tomorrow [42, 12]. Perspectives on the exact meaning of technological cumulativeness however vary, for an overview of this discussion we refer to [39]. In this work, we understand a technological development to be cumulative when a later technological result depends on an earlier technological result. In the context of technological knowledge, we broadly interpret this dependency as the usage, modification or improvement of earlier ideas. In this line of thinking, we understand the knowledge base of a technology to be more cumulative when the developments in this technology are more cumulative. This allows us to define the cumulativeness of a technology as the extent to which developments within this technology are cumulative. In other words, the more a technology builds on its earlier developments, the greater its cumulativeness.

Technological cumulativeness is often mentioned as a defining characteristic of a technological regime, which is a description of the relevant environment or circumstances for companies and organizations to innovate [34, 12]. When a technological regime is characterized by high cumulativeness, established parties largely dominate innovative activities and it is relatively hard for new parties to enter. Highly cumulative technologies allow firms or organisations to gain absorptive capacity through learning and specialization [14]. Within a technological regime therefore, greater cumulativeness is associated with a greater appropriability of innovation and a greater geographical concentration of innovative activities [29, 30].

In an earlier contribution, where the cumulativeness was explicitly approached as the extent to which a technology builds on its earlier developments, we established that the cumulativeness of a technology increases approximately linearly with the size of its knowledge base, at a technology specific rate [39]. Especially when cumulativeness is compared across technologies, this suggests that next to considering the cumulativeness of a technology, it will be useful to consider the rate at which the cumulativeness increases, i.e., the cumulativeness relative to the size of the knowledge base.

When cumulative developments stretch over longer periods of time, the products associated with a technology tend to become ’more complex’, meaning that the number of interrelated (functional) parts of a product architecture increase. Technological complexity is therefore often associated with greater cumulativeness. The complexity of technologies is in the literature however mostly approached anecdotally or on a case to case basis, as there is no general agreement on a single objective measure for complexity [43].

Where some types of knowledge travel easily from one place to another, other types are bound to a certain location. In order to investigate this dimension of knowledge, we define the knowledge mobility as the extent to which knowledge travels geographically. By geographical traveling, we mean that knowledge developed in one location is subsequently used or applied in another location, where the two locations are separated by a geographical distance. High knowledge mobility then corresponds to knowledge that travels with ease to more distant locations, i.e., ’footloose knowledge’. Low knowledge mobility corresponds to Knowledge that travels less easily, i.e. ’sticky knowledge’. A highly mobile body of knowledge is thus expected to travel farther, in other words, we expect mobile knowledge to be more widespread (or less concentrated) than sticky knowledge.

Knowledge bases characterized by greater analyticity are expected to be more mobile (or ’footloose’) [2, 18]. A motivation for this first expectation is the universality and theoretical nature of analytic knowledge, which almost per definition implies time, location and application independence. The context specificity and practical nature of synthetic knowledge on the contrary makes it more time, location and application bound. Another motivation is the supposed association with codified knowledge: what is written down travels easier than know-how fixed in the minds of experts [27, 17]. As mentioned earlier though, this association is also criticized. These motivations also count when the causality is reversed: when innovative activities are fixed and concentrated geographically, there may be less need to formalize or rationalize findings because knowledge is communicated orally, developed during collaboration and hence may remain largely tacit and fragmented. A gradual shift towards knowledge more synthetic in nature is thus expected when engineers work close together. Likewise, when collaborators are forced to communicate their results at a distance, it may stimulate them to formalize or rationalize their implicit ideas or intuitions.

Knowledge bases characterized by higher cumulativeness are expected to be stickier[18]. A motivation for this second expectation is the expected greater geographical concentration of innovative activities in technological regimes characterized by high cumulativeness. With greater geographical concentration, we expect the development to be less widespread and hence to travel shorter distances. Note that this relation too can be reversed, namely that the knowledge is concentrated because it is sticky. Another motivation for this second expectation comes from the association between cumulativeness and technological complexity: technologically complex knowledge does not travel well [5]. Working with or improving a complex system from a distance is challenging, because it becomes more difficult to experiment or interact with the system.

In this research we aim to investigate how the knowledge dimensions vary for different Renewable Energy Technologies (RETs). While a ’technology’ can be approached or characterized from many different angles, we will in this contribution largely focus on the knowledge properties of technologies, hence approaching the different RETs as distinct bodies of knowledge. The knowledge properties may cover various aspects of the technology, for example, how the technology operates or how it is constructed. While the purpose of the various RETs largely coincide (enable the generation of renewable energy), the renewable energy sources that the various RETs exploit (and thus their working principles) fundamentally differ. Following the International Renewable Energy Agency (IRENA), we distinguish between geothermal, hydropower, ocean, wind, solar thermal, solar photovoltaic, and bio-energy [23]. In addition, we include a number of enabling technologies allowing for the storage of energy such as hydrogen technology, and three energy related technologies that are not entirely renewable yet may help reduce CO2 emissions: nuclear energy, carbon capture & storage (ccs) and clean combustion. We will provide a more precise list of the individual RETs in the next section.

Earlier contributions have indicated that RETs generally build strongly on scientific knowledge, suggesting a highly analytic knowledge base [37]. In agreement with this finding, innovative activities related to RETs are observed to take place on ever larger geographic scales [36, 16]. At same time the knowledge bases are known to vary greatly across different RETs [6] and across energy technology in general [35]. More specifically, we know there is a large variation across RETs in the extent to which the knowledge base is science based [40, 21]. Where photovoltaics, non-fossil fuels and to some extent fuel-cells and hydrogen technology were found to be more science based, wind turbines, hydroelectric and geothermal energy were found to be less science based. The more a RET depends on science, the more analytic its knowledge base, the greater a knowledge mobility we expect for these technologies.

While the development of different RETs has been studied in numerous contributions, it appears that the current literature lacks a systematic comparison of the cumulativeness across different RETs. Even though the size of the knowledge base varies across RETs, this does not automatically translate to a similar variation in cumulativeness [39]. The closely related technological complexity however does appear to vary largely across RETs. Interpreting a larger technological complexity for systems with many interdependent parts, RETs such as wind turbines, geothermal energy, nuclear fission and energy from sea are identified as rather complex [19], more complex than photovoltaics and non-fossil fuels.²²2In some cases the technological complexity varies with different applications of a technology. For example for solar thermal energy, the systems in domestic use are limited to elements that efficiently capture and store heat, and are therefore relatively simple, whereas the systems used in power plants are typically larger, contain more different elements and have the additional features of concentrating the heat and transforming it to electric power, making these systems far more complex. The variation in technological complexity suggest there may be large variation across RETs in cumulativeness too (though this needs empirical validation). As the knowledge bases characterized by high cumulativeness tend to be stickier, we expect the higher cumulativeness RETs to show a lower knowledge mobility. Taking a slightly different perspective, Binz, Tang and Huenteler distinguishes between ’complex engineered systems for specialized users’ and ’standardized mass-manufactured goods’, wind-turbines again being an example of the former and household energy storage systems, stationary fuel-cells and photovoltaics an example of the latter [8]. Based on their findings about photovoltaics, they expect life-cycle dynamics of the latter group to be more ’spatially fluid’ than the former.

Summarizing, we expect to observe a greater knowledge mobility for RETs with a stronger dependence on science and RETs characterized by lower cumulativeness.

Earlier approaches to measuring the analytic-synthetic knowledge distinction were often based on data from questionnaires or professional occupations [33, 41, 31]. While useful, these data are largely an indirect measure of knowledge characteristics, because they are based on the characteristics of the people that use or produce the knowledge, instead of the knowledge itself. In this contribution we aim to directly measure the knowledge characteristics by studying codified forms of knowledge, more specifically, patent data.

Patent data directly represent technological knowledge, containing a wealth of detailed information about both the technological content as well as the inventor or applicant. Furthermore, the citations in patents, both to other patents and scientific literature, to some extent allow us to proxy knowledge connections and flow. While patent data offer a unique opportunity to quantitatively study novel and relevant technological knowledge development, there are also some limitations. Not all technology is patented and not all patents represent relevant technological developments. While acknowledging these disadvantages, we believe that for the purpose of understanding RET development there is a great potential for patent data.

A possible criticism of the usage of patent data to proxy the analytic-synthetic distinction is the supposed association with the codified-tacit distinction: as patents are codified knowledge, we risk observing analytic knowledge only. However, as mentioned earlier, the association with codified-tacit distinction is also criticized, and we strongly believe that patents, a key element of engineering practices, may equally well contain a large degree of synthetic knowledge. Our approach is therefore, that within codified knowledge, there may be different degrees of analytic knowledge. More specifically in the context of technological knowledge, the more a body of codified knowledge can be associated with scientific activity, the greater we will interpret its degree of analytic knowledge.

Finally, we shortly comment on the geography of patents. In this research we will do a separate analysis for patents from the EPO (European Patent Office) and the USPTO (United States Patent and Trademark Office), henceforth ’EP patents’ and ’US patents’ respectively. There are two reasons for this choice. First, different patent offices, but in particular EPO and USPTO, have institutionalized different rules for citation, hence limiting the analysis of knowledge connections to one patent office may give biased results. Second, an applicant files a patent with an office if there is market potential in the geographical jurisdiction of that office. As we are interested in the worldwide geography of innovation, we do not want to limit the analysis to a single geographical jurisdiction.

For the analysis of analyticity we will mostly use the scientific character of this type of knowledge. To proxy for a given technology the dependence on science and the scientific content of the knowledge base we define the following indicators:

• •

  The science dependence(sd) of a technology is defined as the average number of references to scientific literature per patent. A reference in a patent to a scientific source can be interpreted as a dependency link, suggesting that scientific knowledge was somehow relevant in the content of the patent. The more scientific sources a patent therefore refers to, the more we expect it to be science based. We therefore take the science dependence as an indicator of analytic knowledge.

• •

  The science dependence fraction(sdf) of a patent is defined as its number of references to scientific literature divided by its total number of references. To obtain the sdf of a technology, we take the sdf of each patent in that technology and take the average. Hence where the sd is based on the absolute number of references, the sdf is based on the relative number of references, thus taking into account variation across patents and technologies in the number of references. A similar indicator was earlier used in [20, 21].

• •

  The university fraction(uf) of a technology is defined as the number patents in that technology for which the inventor or applicant is university³³3As we will see later it more correct to speak of university-related organisations affiliated divided by the total number of patents in that technology. When the inventor is affiliated with a university, we expect the patent to be based more on scientific knowledge than the average patent from non-scientific organisations. We therefore take the university fraction to be an indicator of analytic knowledge.

To proxy the cumulativeness we will use

• •

  The internal dependence(id) of technology is defined as the average number of internal references per patent. An internal reference is a reference in a patent to a patent within the same technology, which can be interpreted as a dependency link from the technology to itself. Cumulativeness can be interpreted as the extent to which a technology builds on itself. This indicator was earlier used in [39]. For an approach based on general references, we refer to [1].

• •

  The internal dependence fraction(idf) of a patent is defined as its number of internal references divided by its total number of patent references⁴⁴4Alternatively, we can also include the references to scientific and/or other sources in this total. However, in this contribution we choose to define it as a fraction of patent references only, so that we can consider it to be independent from the sdf. To obtain the idf of a technology, we take the idf of each patent in that technology and take the average. Hence where the id is based on the absolute number of references, the idf is based on the relative number of references, thus taking into account variation across patents and technologies in the number of references.

• •

  The relative internal dependence(rid) of a technology is defined as the internal dependence of that technology relative to its total number of patents, or equivalently, the number of internal references per patent squared. As explained earlier, the internal dependence tends to increase linearly with the number of patents. When we compare technologies with different number of patents or when we are interested in the rate at which the cumulativeness increases, it is therefore useful to additionally consider the cumulativeness per patent.

For the knowledge mobility we define the following indicators:

• •

  The inter-patent distance(ipd) of a technology is defined as the average geographic distance between each pair of patents within that technology. From the inventor or applicant addresses in patents we can create an overview of the approximate⁵⁵5That is approximately, as there is no guarantee the actual process of inventing took place at the mentioned address locations of inventing. The mutual distances between patents can thus be used to proxy the geographical spread of inventing in a certain technology.

• •

  The reference distance(rd) of a patent is defined as the average geographic distance between that patent and the (set of) patent(s) it refers to⁶⁶6We take the reference distance of a patent which does not refer to any other patent to be undefined. The reference distance of a technology is defined as the average reference distance per patent. Where the inter-patent distance proxies the geographical spread, it does not directly proxy the possible knowledge flow between distant places. With the reference distance we therefore additionally consider the kilometers covered by references to obtain a better estimate of the actual movement of knowledge. Note however that the reference distance also includes references to other technologies, thus to some extent also measuring the knowledge flow of other technologies.⁷⁷7Excluding the references to other technologies can be demonstrated to result in an indicator very closely related to the inter-patent distance

Note that all of these indicators can be determined for technologies (i.e. groups of patents) and a selection of these indicators can also be determined on the level of individual patents. In the first part of our analysis, we will use the indicators acting on the level of individual patents to establish a baseline and demonstrate more general relations between analyticity, cumulativeness and knowledge mobility (where the patents are not necessarily confined to the considered technologies).

This analysis is mainly based on data from Patstat (spring 2020 edition) focusing on European and US patents. As a consequence, there are number of subtleties involved with the actual measurement of the indicators:

1. 1.

   We count as a ’patent’ each unique DOCDB patent family, where an ’EP patent’ represents each unique family with an EPO patent application and likewise for ’US patent’ but then for USPTO applications⁸⁸8The Patstat records of USPTO applications are biased to granted patents before the year 2000. As our focus is not on the time development we expect this to be a minor issue for our purpose.

2. 2.

   To identify the references to scientific literature we use the type ’s’ classification of the cited non-patent-literature (NPL), which signals articles in journals and periodicals. Where in Patstat the NPL appears to be classified rather well for EP patents, for the US patents the large majority of NPL, probably due to a lacking of rich structure in references, is classified in the general category ’a’ (abstract of no specific kind). To obtain a better indication which fraction of the cited NPL is actually scientific, we use the database by Marx and Fuegi [32] which links the references in patent applications to scientific publications, and is accurate for US patents.

3. 3.

   To identify the inventors or applicants affiliated with a university we use the automatized sector allocation in Patstat of persons [28, 44]. This classification however allows an applicant to be allocated to multiple sectors. For the university fraction we include each patent where at least of one the allocations is the ’UNIVERSITY’ sector. We therefore also include organisations closely related to the university, making it more correct to speak of ’university-related organisations’.

4. 4.

   To link the patents to geographical coordinates we use the ’Geocoding of worldwide patent data’ database (shortly ’Geocoding’) constructed by Rassenfosse, Kozak and Seliger [15] based on the applicant or inventor addresses. The Geocoding database is limited to first filed patent applications, which we linked back to patent families using Patstat. This research is based on the Geocoding table with inventor addresses. Yet, as the makers of the database acknowledge, disambiguation of inventors and applicants is generally challenging and a research task on its own. Indeed a quick comparison with the table bases on applicant addresses does not seem to amount to substantially different results.

5. 5.

   The addresses of inventors of EP patents are not necessarily confined to Europe, and likewise for US patents and the US. The typical reference distance of a EP patent with an inventor from the US however structurally differs from that with an inventor from Europe: the reference distance is location specific. While these variations are expected to average out when the number of patents in a technology is large, this effect may be disproportional for technologies with a smaller number of patents. To demonstrate this effect, we determine the reference distance from EP patents with US inventors and vice versa and compare these to the reference distances of EP (US) patents with European (US) inventors in Appendix B. To account for this effect, when we determine the reference distance of EP patents we sub-select the patents with an inventor in Europe. Likewise when we determine the reference distance of US patents we sub-select the patents with and inventor from the US. These sub-selections contain for most of the technologies considered the majority of patents. Note that, while we sub-select patents based on the location of the inventor, the references in these may still be to patents from inventors located anywhere in the world.

We base our selection of energy generating technologies on the set of renewable energy sources identified by the International Renewable Energy Agency IRENA [23]), including geothermal, hydropower, ocean, wind, solar and bioenergy. As mentioned earlier, these energy generating technologies are complemented with set of technologies relating to energy storage and a set of technologies which may not be considered fully renewable but nonetheless help reducing greenhouse gas emissions, such as nuclear energy, clean combustion and carbon capture and storage (ccs). For an overview see Table 1. To identify the patents associated with these (partial) RETs we use the Cooperative Patent Classification (CPC) used by both EPO and USPTO, or more specifically the CPC tagging scheme ’Y02’ which identifies technologies with the potential to mitigate climate change [45]. Each of these RETs correspond then to a collection of patents classified on the group or subgroup level in CPC. The various technologies and corresponding CPC descriptions are shown in Table 1, including the symbols which represent them in later figures. Note that a substantial number of EP and US patents are members of the same patent family, hence there is a substantial overlap between both data-sets.

In Table 2 we include the descriptive statistics for a number of indicators discussed in the previous section. All of these indicators are only positive and characterized by distributions skewed towards the value zero, which is in line with the observation that the standard deviations are of the same order as the averages. The variation across technologies is substantial especially across the analyticity and cumulativeness indicators. The science dependence of non-fossil fuels is much higher than that of the other RETs. This is in line with earlier findings [40, 21] and may be related to the strong link of non-fossil fuels to fields such as (Applied) Microbiology, Biochemistry and Molecular Biology. While we will measure and plot the indicator values for non-fossil fuels, we will not include it in data fits and statistical analysis.

To explore the geographical distributions of inventive activity in RETs worldwide, we use the geographical coordinates to plot the number of US patents (using the inventor or applicant address in the patents) in a grid defined for each longitudinal and latitudinal half degree. We do this for photovoltaics and wind-turbines respectively in Figures 1 and 2. Because the patenting activity is distributed highly unevenly (a small number of areas producing the majority of patents), we chose a coloring following a logarithmic scale. We observe some variation between the figures, Germany and France innovating strongly in photovoltaics, while Denmark focusing more on wind-turbines. The main observation however, at least on a global scale, is that the geographical distributions of innovative activities are fairly similar, even for rather different technologies such as photovoltaics and wind turbines. In fact in a ranking of countries by total number of US patents, see appendix A, the US, Japan and Germany are consistently in the top 5 for each RET considered in this research (and France for all but 3 RETs). For EP patents, these countries likewise dominate each top 5. Together these four countries account for 76 and 58 respective percentages of the US and EP patents (for RETs). This is line with the findings of earlier literature considering energy technology in general [10]. The uneven distribution is not due to our choice for counting at the country level. When instead consider spatial the level below countries (corresponding to the ’name_1’ level in the Geocoding database), we again see the same regions or locations recurring: California, New York, Tokyo, Bayern and Baden-Württemberg rather consistently dominate in the top 10 locations with most patents for each considered RET. An important part of the knowledge base development of RETs therefore appears to take place in a small number of dominant areas. Together with the similarity of the worldwide geographical distributions, these are relevant descriptive statistics: it indicates that despite the obvious location-boundness of the application of specific RETs (hydro energy near rivers, photovoltaics in sunny locations, wind turbines near windy locations, etc.), the development of the knowledge base of these RETs still largely occurs in dominant areas which work on the development of all RETs at the same time.

We will first explore some general relations between on the one hand the knowledge mobility and on the other hand analyticity or cumulativeness of knowledge. We explore these relations using the indicators that are defined on the level of individual patents: the science dependence fraction (sdf), the internal dependence fraction (idf) and the reference distance (rd). In the following analysis we include all EP and US patents for which a reference distance could be determined. One exception is the analysis of the US sdf: there we include, due to calculation challenges, a random selection of 20 percent of all such patents. As explained in Section 3.2, we sub-select those EP patents for which the inventors are from Europe and those US patents for which the inventor is from the US. To calculate the idf, the internal references are determined using within CPC-group references.

In Figure 3 we divide the sdf in exponential bins and plot the average rd (left panel) and number patents (right panel) for each bin. We observe in the left panel that the rd increases with increasing sdf for both EP and US patents (though more strongly for EP patents). Not included in this Figures are the many patents for which the sdf is zero ($7.0\cdot 10^{5}$ EP patents and $2.8\cdot 10^{5}$ US patents, respectively 6.4 and 2.0 times the total number of EP and US patents in Figure 3). The average rd of these zero sdf patents are 4114 km for EP patents and 3380 km for US patents, which are similar values to those in the lowest sdf bins in Figure 3 and therefore in accordance with the observed relation. Even though the reference distance appears to go down for large sdf for both the EP and US patents, we note from the right panel that there relatively few patents with an sdf$>0.5$ (to be precise respectively 4 and 8 percent of the total EP and US patents). For the majority of the patents it therefore counts, in line with expectation, that the greater the sdf, the greater the rd. In other words, greater analyticity can be associated with greater knowledge mobility.

In Figure 4 we divide the idf in bins of constant size and plot the average rd (left panel) and cumulative number of patents (right panel) for each bin. We clearly observe that the rd decreases when the idf decreases (illustrated also by the linear fits). This is the case almost over the entire range of the idf. A minor exception are the US idf values $<0.15$. As is clear from the right panel however, there are relatively little patents in this range. As the right panel in Figure 4 illustrates, most of the patents have mid-range idf values, although there are relatively many patents with idf equal to one (counted in the bin with the largest idf value). As the left panel illustrates, the average rd of the patents in this bin are however in line with the observed pattern. We therefore conclude, in line with expectation, that the greater the idf, the smaller the rd. In other words, greater technological cumulativeness can be associated with lesser knowledge mobility

Where in the previous section we discussed the general relations between knowledge dimensions based on a general data set of patents, we will in the following analyze these relations specifically considering the RETs. We will first qualitatively discuss the relation between on the one hand a knowledge mobility indicator and on the other hand either an analyticity or cumulativeness indicator. Subsequently, we will consider these relations more quantitatively, where we determine the correlations and estimate some models.

In Figure 5 we plot the rd for the sdf for both the EP patents (left) and the US patents (right). The main observation for both graphs is a positive relation between both quantities which is well fitted by a linear relation. We refer to Table 1 for a legend of the icons and the short-names of the technologies. The sdf of non-fossil fuels can be observed to exceptionally large, which is, as discussed earlier, not included in these and later fits. It is therefore also challenging to compare the rd of this technology to the rest. It appears the values of the other technologies do allow for comparison however, and in line with expectation, technologies such as wind turbines, geothermal, hydro, solar thermal and energy from sea show relatively low rd, whereas photovoltaics, fuel-cells, energy storage and hydrogen technology show relatively large rd. Nuclear fission, ccs, clean combustion and electric grid technology are somewhat in between these two groups. Using Table 1, we note that technologies with a large number of patents (wind turbines, solar thermal, photovoltaics, fuel-cells) occur on both ends of the spectrum. It seems therefore that sheer numbers of patents, often a proxy for the size of the knowledge base, are not sufficient to explain the observed relation.

In Figure 6 we instead plot the inter-patent distance (ipd) for the university fraction (uf). The positive relation from Figure 5 remains largely unchanged, the technologies we find upper right (down left) in Figure 5 also tend to be in the upper right (down left) of Figure 6. This indicates that the variation across RETs in the considered knowledge dimensions is consistent for the different indicators for these dimensions. A closer look reveals some minor variations. The differences between the EP and US patents in Figure 5 are relatively large in particular for wind turbines and fuel cells. In Figure 6, these differences are relatively less. This suggest that the ipd indicator may be more uniform between EP and US patents. We discuss the rd variations (and in particular those of wind turbines and fuel cells) in more detail in a part of Appendix B. Especially for the US patents, the uf of nuclear fission and clean combustion is relatively low in Figure 6 as compared to their sdf in from Figure 5. This suggests that the knowledge base of these technologies, while retaining a scientific component, is to a lesser extent developed in universities.

While there are these minor differences, for most technologies the overall pattern is in agreement with Figure 5, again confirming that the technologies that build stronger on science also tend to show greater knowledge mobility.

Next we plot the ipd for the internal dependence (id) in Figure 7. The main observation is a negative relation between both quantities which is rather well fitted by a negative logarithmic relation (note the horizontal axis is logarithmic).⁹⁹9We may also take the log of the ipd and instead fit a power relation, the results will be largely comparable. This is in line with the expected negative relation between knowledge mobility and technological cumulativeness. The only technology defying this pattern, both for EP and US patents but especially US patents, appears to be photovoltaics, which despite a relatively id, shows great ipd. In earlier contribution however we already demonstrated that the internal dependence tends to increase linearly with the number of patents [39]. Photovoltaics consists of far more patents than the other RETs (especially for US patents), which possibly explains the exceptional value for the internal dependence in this context.

Alternatively, we may therefore consider the cumulativeness relative to the size of the knowledge base, which we measure by the relative internal dependence (rid) in Figure 8. In that figure the value of photovoltaics indeed shifts both for the EP and US patents to the left, in better agreement with its large value for the ipd. We observe a similar shift for wind turbines, though to a lesser extent, which is in line with expectation given its shorter ipd. Other than these changes the pattern is largely similar to the one in Figure 7.

Finally, note in both Figure 7 and 8 that the values for non-fossil fuels are more or less in line with the rest of the technologies, where earlier for the science dependence its values were rather exceptional. This therefore presents an extra reason for considering both the science dependence and internal dependence: an exceptional value for the former need not automatically imply an exceptional value for the latter.

We will not plot all possible combinations between the indicators we consider, yet for completeness we include in Figure 9 the Pearson correlation coefficients of each combinations and whether or not this combination is statistically significant. We conclude from Figure 9 that all correlation coefficients, most of which are substantial, have the expected sign: all analyticity indicators have positive signs with knowledge mobility indicators and all cumulativeness indicators have a negative sign with all knowledge mobility indicators. Especially the analyticity indicators show strong correlations with the knowledge mobility indicators. As expected the correlations between indicators of the same knowledge dimension are generally strong. One exception is the relative internal dependence (rid), which despite strong correlations with knowledge mobility indicators does not correlate strongly with other cumulativeness indicators. Interestingly, the rid does not (anti)correlate strongly with analyticity indicators either, which suggests its relation to the knowledge mobility is to some extent independent of the other indicators. We also observe this for internal dependence (id) of the European patents. To follow up on this suggestion, we will finally consider the possibility to model the knowledge mobility as a linear combination of an analyticity indicator and a cumulativeness indicator.

Again we will not present here all such possible linear combinations here in detail, there are simply too many, but instead share our general conclusions and include two examples (Table 3). As we only consider 13 technologies, i.e. 13 data points, it does not make much sense go much further than combinations of 2 variables. We will first discuss this for the EP patents and than for the US patents.

When we model for the EP patents the internal patent dependence (ipd) as a linear combination of any given analyticity and any given cumulativeness indicator, the performance of the model in terms of minimizing the residual standard error and maximizing the Pearson correlation squared ($R^{2}$) is much better than for the case where all this indicators are individually considered as predictors. One specific example is given in Table 3(left panel), where the EP ipd is modeled as a linear combination of the sdf and rid. The residual standard error (548.6) is much lower than that in a model with only the sdf (662) or the rid (724). The found $R^{2}=0.72$, corresponding to a Pearson coefficient of $R=0.85$, is also greater than the $R$ values in Figure 9 for ipd-sdf and ipd-rid. When we take linear combinations of only analyticity or only cumulativeness indicators to model the ipd, this only results in a better model in half of the cases. This therefore indicates it makes sense to consider the analyticity and cumulativeness as independent factors relating to the knowledge mobility. As Figure 9 already indicates, the EP patent reference distance very strongly correlates with most of the analyticity indicators, which is difficult to improve considering extra indicators. For the EP rd, we therefore only find very few combinations which present better models than the indicators considered individually.

When we model the knowledge mobility indicators for the US patents as a linear combination of indicators we reach similar conclusions. We find for both knowledge mobility indicators that any combination between the rid and any analyticity indicator result in a better model than when the indicators are considered individually (again judged on the basis of the residual standard error and $R^{2}$). We present one example in Table 3 (right panel), where we model the US rd as a linear combination of the US sdf and US rid. The found residual standard error (207.4) is much smaller than that in a model with only the sdf (251) or only the rid (244). Also the found $R^{2}=0.67$, corresponding to $R=0.82$, is greater than the $R$ values in Figure 9 for rd-sdf and rd-rid. We note that this is largely due to the success of the rid. It is not directly clear why this indicator, as compared to the other cumulativeness indicators, performs much better for the US patents. At least it underlines the need to consider multiple indicators to describe these knowledge dimensions. Only one combination (sd & sdf) of either considering only analyticity indicators or only cumulativeness indicators can be evaluated as a better model than considering the indicators individually. This again indicates that especially the combination of a cumulativeness indicator and an analyticity indicator results in a better model, thus confirming the earlier assertion that the science and internal dependence are complementary indicators, both relating to the knowledge mobility.

In sum, while there is considerable variation across different RETs in terms of knowledge mobility, this variation is to some extent explained by their variation in analyticity and cumulativeness, thus in line with the expectations of Section 2. We can distinguish rather consistently a collection of footloose RETs (photovoltaics, energy storage and fuel cells) characterized by relatively high analyticity and low cumulativeness, from a collection of sticky RETs (energy from sea, wind-turbines, geothermal, hydro, and solar thermal energy) characterized by relatively low analyticity and high cumulativeness.