Digital technologies, technological improvement rates, and innovations “Made in Switzerland”

Abstract

Technologies evolve at different paces and their rate of improvement varies considerably. We demonstrate that the fastest technological progress currently occurs in the digital domain and empirically investigate the relationship between technologies’ improvement rates and breakthrough innovations as measured by forward citations of patents. Our empirical estimates suggest that patents from the digital sphere, as well as those related to fast-improving technologies, are associated with a higher probability to produce breakthrough innovations. We then investigate Swiss core industries’ specialization patterns toward these potential high-impact technologies and compare the state of cutting-edge innovation in Switzerland to other countries. Our findings imply that the Swiss innovation system is among the laggards regarding innovations in today’s fastest improving digital technologies.

1 Introduction

Today's rapid technological progress primarily concerns digital technologies, be it artificial intelligence (AI), cloud computing or customer relationship management. But it is by no means restricted to the computer and software industry. Rather, digital innovations are also widespread in the manufacturing sector, which primarily reflects that digital technologies can have general-purpose characteristics.¹ Such technologies are a crucial ingredient of economic growth (e.g., Helpman, 1998; Bresnahan & Trajtenberg, 1995), and their early adoption can yield long-lasting advantages for first-movers in their respective fields (e.g., Brynjolfsson et al., 2021; Tambe et al., 2020; Triulzi et al., 2020). Unsurprisingly, software-related patenting has surged dramatically over the last decades, whereas the bulk of the increase was heavily concentrated in a few tech-clusters (Chattergoon & Kerr, 2022).² With this respect, Bloom et al. (2021) find that clusters which were pioneers in inventing disruptive technologies over the last decades have higher wages and more high-skilled jobs many years after the technology first emerged, suggesting that early involvement in novel disruptive technologies may have long-lasting economic benefits.

Which set of technologies are potentially disruptive today and in the near future? And how are different countries—particularly Switzerland—positioned with respect to innovations in these technologies? These are the questions to which our paper contributes. Naturally, technologies from the digital domain are primary candidates to focus on, since digitization is transforming all aspects of economic activity (e.g., Brynjolfsson & McAfee, 2014). However, many other technologies also evolve at high speed and might become disruptive as well (e.g., battery technology). Furthermore, since some digital technologies have already emerged more than 40 years ago, they differ considerably from each other with respect to their rate of technological improvement. For example, digital control systems for loudspeakers is a rather mature digital technology with mostly incremental improvements. In contrast, improvements occur very rapidly in cloud computing (Singh et al., 2021). Accordingly, not every digital technology is necessarily related to disruptive changes today and it is challenging to distinguish disruptive technologies from others. As a workaround, researchers have often focused on particular technologies that have already been found to be disruptive. The most prominent example is the subject of artificial intelligence and its potential labor market implications.³ A recent study by Singh et al. (2021) takes a different and more holistic approach: Instead of focusing on one or a few selected technologies, these authors introduce a framework which allows to estimate different technologies’ improvement rates.⁴ This enables us to distinguish very dynamic (and potentially disruptive) technologies from slower evolving ones. Our paper thus builds heavily on this framework to approach our above-stated research questions.

To do so, we first create a new dataset from different sources of information. More specifically, we combine patent data from the United States Patent and Trademark Office (USPTO) with information on whether a patent contains a digital technology from Inaba and Squicciarini (2017) and a novel indicator for technological improvement rates of 1757 distinct technologies that we obtain from Singh et al. (2021).⁵ To the best of our knowledge, our paper is the first to connect these different sources of information. This allows us to accurately analyze the state of cutting-edge innovation in Switzerland and abroad.

A main advantage of our constructed dataset is that it enables us not only to evaluate the quantity of digital and non-digital innovations across countries and industries (i.e., their stock or share of digital and non-digital patents). It also allows us to approximate their technological quality (i.e., the technological improvement rate of a technology a patent is associated with). We show that this is relevant for two main reasons: First, the variation regarding the rate of technological improvement across digital technologies is rather large. Second, patents from the digital domain and such related to technologies with high improvement rates are associated with a higher probability to contain breakthrough innovations as measured by forward citations of patents.

To demonstrate the latter, we follow Kerr and Kerr (2018) and estimate a linear probability model in which the left-hand side contains a dummy variable indicating whether a patent contains a breakthrough innovation, as measured by forward citations. We provide empirical estimates and robustness tests showing that this pattern is also robust for different industries. This suggests that being innovative in digital and fast-improving technologies is important in various industries of the economy, including, for example, the pharmaceutical or machinery industry, toward which Switzerland’s innovation system is relatively heavily specialized.

Yet, we show that Swiss innovations in most of the country’s core industries are not particularly directed toward fast-improving digital technologies when compared to other countries. This is because the Swiss innovation system is generally only weakly engaged in digital technologies, and digital innovations in Switzerland are less likely to occur in the fastest improving digital technologies. In non-digital domains, Switzerland’s position is somewhat better, but it is also not among the leaders in rapidly evolving non-digital fields (except for innovations from the medical and pharmaceutical industries). Overall, Switzerland can thus be considered as a laggard in terms of innovations in today’s fastest improving technologies. We argue that this could be a cause for concern, especially if adaption and catch-up become more difficult in the future, and if new technologies represent substitutes for more traditional ones.

Our paper is related to different strands of the literature that study technological changes and their interplay with competitiveness. From a technical point of view, our paper builds heavily on prior work regarding the emergence and speed of technological innovations (see, e.g., Singh et al., 2021; Triulzi et al., 2020; Magee et al., 2016).⁶ Singh et al. (2021) provide us with our empirical measure for technologies’ improvement rates, which is the basis for all empirical analyses in this paper. Our paper extends prior work in this area in two ways: First, we demonstrate a robust association between patented inventions’ corresponding technological improvement rates and their probability to contain a breakthrough innovation as measured by forward citations. Second, we assess the extent to which countries’ innovation systems are specialized with respect to fast-improving technologies, with a particular focus on Switzerland.

With this latter regard, our paper has a connection to several studies that focus on the state of innovation across industries in different countries. For example, Kelly et al. (2021) use patent texts to investigate long-run trends in innovation activities across different industries considering data back to 1840. Their results imply that innovation activities have been mainly dominated by the information technology industry in recent years. Another example is Confraria et al. (2021), who have a similar focus and investigate emerging technology patterns. One of their main findings is that European firms are not particularly well positioned in digital innovations such as software engineering and semiconductor devices. Furthermore, reports by the OECD (2019) or the European Commission (2017) provide extensive descriptive overviews of digital trends across countries, illustrating that firms from EU countries are typically lagging behind their peers from the USA and Japan in digital innovations.

With this respect, our paper also has a loose connection to several contributions that are focusing on the impact of early involvement in disruptive technologies on competitiveness. A major example is Bloom et al. (2021), who identify a set of 29 disruptive technologies from the last decades and show for the USA that regions who were pioneers in inventing these technologies have obtained long-lasting benefits in terms of wages and high-skilled employment. Tambe et al. (2020) focus on the firm level and demonstrate that digital capital accumulation predicts the productivity of firms in the USA in the near future.

Finally, our paper’s main focus is on Switzerland, whereas existing studies focus mainly on counting the stock of digital patents in selected technological areas (Gramke & Glauser, 2017, in German language) industries (Rutzer & Weder, 2021, also in German language) or on the general scope of patent activities of the Swiss innovation system (Grampp et al., 2018, also in German language). These studies use patent data and compare the innovativeness of Switzerland in digital domains with other countries. Besides overall trends, the work of Gramke and Glauser (2017) also investigates in more detail the positioning of Switzerland in some important fields such as AI, the Internet of things, and robotics. The general conclusion of these three studies is that Switzerland is not among the top innovators in terms of the number of digital patents. Finally, also OECD (2019) focuses on Switzerland and highlights that the country’s recent patent activities in ICT-related fields are below the OECD average. What we add to this literature is an analysis that additionally takes into account the specialization patterns of the Swiss innovation system with respect to its orientation toward faster or slower improving technologies.

The remainder of this paper is organized as follows. Section 2 focuses on the concept of technological improvement rates and describes data sources that allow us to investigate it. It then shows that digital technologies are among the most dynamic technologies and provide empirical estimates suggesting that patents from the digital domain and those related to fast-improving technologies are associated with a higher probability to produce breakthrough innovations. Section 3 examines patterns of the Swiss innovation system with respect to digital and fast-improving technologies, compares them with other countries, and discusses the findings. Section 4 concludes the paper.

2 Technological improvements and digital technologies

New and improved technologies are crucial ingredients for economic growth. After they first appear, inventors constantly add new functions, develop new methods and find new implementations that make a technology more valuable, efficient, and effective. As a result, technologies constantly evolve and improve. One well-known example for this is the famous Moore’s law (named after Intel co-founder Gordon Moore), which states that computer processing power doubles approximately every 18–24 months (Gustafson, 2011). Similar patterns can be observed for many other technological domains but their rate of improvement typically varies considerably: Some technologies evolve at a very fast pace, while others progress slowly (Magee et al., 2016). A natural question arising from this is which technologies are the fastest-improving ones. Previous research has mainly relied on case studies to evaluate progress across different technologies which makes comparisons rather difficult.⁷ In turn, they offer some insight with regard to the technologies that evolve particularly fast. Herrmann et al. (2018) for health care, Ferràs-Hernández et al. (2017) for automotives, and Midttun and Piccini (2017) for the energy sector all argue that especially digital technologies are improving at remarkably fast pace across these very different sectors of the economy. But beyond such case studies, it remains challenging to investigate technical improvement rates for a wide range of detailed technologies in a standardized way. To approach this, Singh et al. (2021) provide a framework that allows to capture annual improvement rates of an extensive set of 1757 granular technologies. These technologies range from “Network management specifically client-server applications” to “IT based prepayment for services,” “Automatic vehicle washing,” or “Hitching assemblies for towing vehicles.” Since these are very distinct technologies, their improvement rates also vary considerably.⁸ Singh et al. (2021) build on an extensive previous literature to arrive at these improvement rate estimates. A key contribution in this regard is Magee et al. (2016) who calculate technical improvement rates for 28 fields based on different “real-world” metrics (e.g., based on the cost of watts per hour for batteries, of sequencing a genome, or of printing one mm3 per second). In a follow-up contribution, Triulzi et al. (2020) identify patents that belong to the 28 technologies whose annual improvement rates have been determined by Magee et al. (2016). They then use information from these patents to train an empirical model that is able to accurately predict the improvement rates of the technologies these patents are associated with. Eventually, Singh et al. (2021) use this trained model to extend and predict improvement rates for 1757 technologies. “Appendix A.1” provides methodological details regarding this framework.

The 1757 technologies Singh et al. (2021) focus on were constructed endogenously using the classification overlap method introduced by Benson and Magee (2013, 2015) and are assigned unique identifiers that can be associated with patents.⁹ Hence, we can combine information from patent data (e.g., on the location where a patented invention was developed) with the improvement rate of the technologies a patent is associated with. This allows us to investigate the rate of technology improvement across countries and industries. Naturally, however, the focus on patents also means that we only capture patented inventions in our analysis. This is an important yet common limitation in the corresponding literature. For example, it is well established that not every invention is patentable (e.g., Griliches, 1998) and some important innovations may never be patented (e.g., Fontana et al., 2013). Furthermore, the propensity to patent and to cite other patents varies across industries (e.g., Lerner & Seru, 2022; Kuhn et al., 2020) and differences in patenting over time can be affected by legal changes—especially for ICT (Graham & Vishnubhakat, 2013). This  limitation  could be mitigated by utilizing alternative data sources that proxy innovative activity more reliably. However, finding such data has been extremely difficult, which is why patent data are generally thought of as an imperfect but relatively good measure of inventive activity (e.g., Acs et al., 2002). Other challenges of using patent data, such as differing propensities to patent across technology fields, can be more directly approached with appropriate techniques, which we describe in the following. In doing so, we also present the patent dataset we use for our study and explain how we combine different sources of information for out final dataset.

2.1 Dataset construction

We consider all granted USPTO patents for 9 important inventor countries obtained from the official USPTO patentsview database and leverage information from Patstat on DOCDB patent families to avoid double counting of patents containing the same invention.¹⁰, ¹¹ In particular, we only consider the first patent filed at the USPTO from all patents belonging to the same DOCDB patent family. We then attribute technology improvement rates from Singh et al. (2021) to these patents. To do so, we gather the patents’ International Patent Classification (IPC) number(s) and their US Patent Classification System (UPC) number(s) which allow us to merge technology improvement rates to patents.¹² For USPTO patents UPC codes are only available until early 2015. Thus, the time span of our analysis is limited to patents filed till the year 2015, as we cannot add improvement rates to patents filed later. It is important to keep in mind that we thus assign the same rate of technological improvement to every patent belonging to a certain technology from Singh et al. (2021). Hence, a patent’s improvement rate refers to its corresponding technology and not to a hypothetical improvement the patent makes to its corresponding technology.

Next, we use the 4-digit IPC number(s) to differentiate whether a patent is a digital patent or not. We build on Inaba and Squicciarini (2017) who determine for each 4-digit IPC number whether the class is a digital technology or not. Each patent is assigned to one or more IPC numbers. We define a patent as digital if it belongs to at least one 4-digit IPC number that has been classified as digital by Inaba and Squicciarini (2017).¹³ This information enables us to distinguish whether a patent or a technology is a digital one. Further, we also map patents to NACE industries. To do so, we use the correspondence table from Patstat between 4-digit IPC numbers and NACE industries (see Looy et al., 2014). Each patent is assigned a probability of belonging to a certain NACE industry based on its four-digit IPC number(s), and we assign a patent to the industry with the highest probability.¹⁴

In a next step, we gather metadata stated on patents from our USPTO sample. We consider information on the year of a patent’s filing, the year of its publication, and the country address(es) of its inventor(s). The latter are used to map patents to countries. If a patent has inventors from several countries, we assign the patent to each country for which an inventor address exists.¹⁵ Furthermore, we extract the number of inventors, the number of claims of a patent, and the number of different countries involved in the research that led to the patent. Finally, we also approximate the importance of patents. To do so, we use information on patent citations and calculate the number of citations a patent receives from subsequent patents (so-called forward citations). Forward citations are a well-established measure in the literature following a simple underlying idea: Patents that protect very valuable innovations are receiving more citations from subsequent patents (see, e.g., Kogan et al., 2017; Hall et al., 2005). Thus, forward citations can be used as an approximation for an innovation’s importance and patents can be ranked according to their number of forward citations. We consider for each patent the number of received forward citations within five years after publication. Following Kelly et al. (2021), Grampp et al. (2018) or Gramke and Glauser (2017), we define a patent as containing a breakthrough (or significant) innovation if it is among the 10% most cited patents within its corresponding World Intellectual Property Organization (WIPO) technology field and publication year.¹⁶ The combined information from all these sources allows us to perform analyses across technologies, countries, and industries in the remainder of this paper.

2.2 Digital technologies, improvement rates, and breakthrough innovations

We first want to investigate improvement rate differences across technologies. Since case study evidence points to significant differences between the digital and non-digital domain, we start by focusing on improvement rate differentials between digital and non-digital technologies. To do so, we check for each of the 1757 technologies we obtained from Singh et al. (2021) if their corresponding IPC 4-digit number is labeled as digital by Inaba and Squicciarini (2017) and classify it accordingly. We can then visualize improvement rates for the two groups in Fig. 1.¹⁷

Fig. 1

Technological improvement rates of digital and non-digital technologies. Notes: The boxplot shows the distribution of improvement rates of 1753 different technologies from Singh et al. (2021). The split into the digital or non-digital group is based on the approach proposed by Inaba and Squicciarini (2017).  The horizontal line shows the median, the big dot the mean, the upper limit of the box the  25th, and the lower limit the 75th percentile. The length of the whisker shows the data that are within 1.5 times the interquartile range. Outliers are marked by small dots

The average and median rate of technological improvement is clearly higher for digital technologies (45.6 and 29 vs. 11.7 and 9, respectively), and the fastest improving technologies are all to be found in the digital group. This clearly highlights how digital technologies are progressing at remarkable pace. At the same time, the variation is large within both groups—and substantially more pronounced for digital technologies. This indicates that there are substantial differences within the digital domain and some digital technologies are evolving much more dynamically than others. However, even though several digital technologies have modest improvement rates, the current frontier of technological improvement seems clearly directed toward digital technologies.

But does faster technological progress also mean that these technologies produce more breakthrough innovations compared to slower evolving ones? We can investigate this crucial question by analyzing whether patents from the digital domain and related to technologies with high improvement rates are likelier to contain a breakthrough innovation as measured with forward citations of patents. To do so, we follow a similar approach as Kerr and Kerr (2018) and estimate a linear probability model of the following functional form:

$$\begin{aligned} & {\text{TP}}_{i} = \beta _{1} D_{i} + \beta _{2} k_{i} + \beta _{3} D_{i} :k_{i} + \beta _{4} {\text{inv}}_{i} + \beta _{5} {\text{num}}\_{\text{ctry}}_{i} \\ & \quad + \beta _{6} {\text{claims}}_{i} + \beta _{7} {\text{bwd}}\_{\text{cits}}_{i} + {\text{FE}}_{{j,t}} + \varepsilon _{i} . \\ \end{aligned}$$

(1)

${\rm TP}_{i}$ is a dummy variable indicating whether patent i belongs to the breakthrough-patent group proxied by our previously explained measure that is based on the top 10% forward citations (FWD90). We estimate three specifications: In the first one, the right-hand side contains a dummy variable $D_i$ stating whether patent i belongs to a digital technology or not. In the second, we consider the improvement rate of the technology of patent i, $k_{i}$. In the third one, we include the digital dummy and also add an interaction term between the digital dummy and the improvement rate, $D_{i}:k_i$. This allows us to analyze whether an association exists between the improvement rate and breakthroughs for the group of digital and non-digital technologies alike. Thus, $\beta _{1}$, $\beta _{2},$ and $\beta _{3}$ are our parameters of interest. Moreover, we include in all specifications several variables to control for different types of research and development (R&D) input that might impact the importance of the innovation. We use the number of inventors ${\rm inv}_i$ and the number of distinct inventor countries ${\rm num}\_{\rm ctry}_i$ as proxies for the employed human capital. The variable ${\rm claims}_i$ contains the number of claims of a patent. Patent claims represent the intellectual property protection provided by a patent. They can thus be seen as an indicator for a patent’s technological scope, which might affect the number of its received forward citations (Kerr & Kerr, 2018). In addition, we use the number of backward citations ${\rm bwd}\_{\rm cits}_i$ to capture the amount of external knowledge which has been embodied in the patent. Each patent belongs to one industry and year. In order to take into account unobserved heterogeneity across industries and years, we also consider industry (j), year (t), and industry-year fixed effects summarized by the vector ${\rm FE}_{j,t}$.¹⁸ Finally, $\epsilon _{i}$ is the error term of the model and we cluster standard errors by industry j.

Table 1 Technological improvement rates and breakthrough innovations

Table 1 presents the estimation results for the time window 1990–2015. In column (1), we take only the digital dummy, control variables, and fixed effects into account. As the positive coefficient shows, patents from digital technologies are associated with more breakthrough innovations as measured with forward citations of patents: All else equal, our estimates imply that a digital patent has a 1.86 percentage points increased likelihood of being a breakthrough innovation.¹⁹ Next, we focus on the technology improvement rate. Column (2) shows a positive association for the improvement rate k with our breakthrough indicator, implying that patents from faster-improving technologies have an increased likelihood of containing a breakthrough innovation. In particular, according to our estimate, a patent belonging to a technology with a ten percentage points higher improvement rate has, ceteris paribus, a 0.3 percentage points higher likelihood of containing a breakthrough innovation.²⁰ In column (3), we analyze whether this positive association from column (2) can be observed for both the digital and non-digital group. The results show a positive association for both groups, but it is much stronger for the non-digital domain. While this might come as a surprise at first sight, it can be well explained. First, improvement rates of digital technologies are much more widely dispersed. Second, they have a higher average improvement rate. This implies a high multicollinearity between the digital dummy and the interaction term digital : k, which is also visible by the increased coefficient of the digital dummy in column (3) compared to its counterpart in column (1). In Tables 7, 8, and 9 of “Appendix,” we show that the pattern from Table 1 remains very robust when considering different subgroups of years, different time thresholds for forward citations to indicate breakthrough innovations, and some alternative measures for breakthrough innovations, respectively.²¹

Taken together, these results show that patents belonging to the digital domain or a technology with faster progress are associated with a higher likelihood of containing a breakthrough invention as measured by forward citations. This supports our initial hypothesis that the current frontier of technological improvement seems clearly directed toward fast-improving digital technologies. But does this pattern also hold for different industries? To evaluate this, we now focus on six different industries, which are of particular importance for the Swiss innovation system.²²

Fig. 2

Technological improvement rates of digital and non-digital technologies across industries. Notes: 1757  different improvement rates from Singh et al. (2021) are assigned to USPTO patents of the filing years 2010–2015. This results in a total of 283’431 USPTO patents. Patents are then split into the digital or non-digital group based on the approach proposed by Inaba and Squicciarini (2017) and assigned to industries according to De Rassenfosse et al. (2014). The horizontal line shows the median, the big dot the mean, the upper limit of the box the 25th, and the lower limit the 75th percentile. The length of the whisker shows the data that are within 1.5 times the interquartile range. Compared to Fig. 1, we do not show outliers to increase clarity

As a starting point, Fig. 2 depicts descriptive statistics for the technological improvement rate across industries based on patents from 2010 to 2015.²³ The same overarching pattern as shown before in Fig. 1 for technologies also holds for these six industries: The digital group’s average rate of technological improvement is higher in all industries. Apart from that, there are interesting patterns across industries. First of all, the average technological improvement rate is relatively similar across industries for the non-digital group, ranging from 7.8 in the pharmaceutical industry to 19.0 in the computer/ICT industry. Substantial differences only emerge when focusing on the digital group, whose level differs considerably. For example, digital technologies in the machinery industry have a substantially higher average improvement rate of 39.7 compared to the pharmaceutical or chemical industry, with 13.5 and 23.9, respectively. In other words, companies in machinery are much more intensively incorporating fast-improving digital technologies into their R&D activities. Could this mean that digital technologies are simply less important in the pharmaceutical or chemical industry, for example? If this were the case, fast-improving digital innovations should not be more valuable than non-digital ones in these industries. Again, this can be evaluated using patent data. As before, we estimate the following simple linear model to investigate this question empirically:

$$\begin{aligned} & {\text{TP}}_{i} = \beta _{{1j}} D_{i} :{\text{IND}}_{j} + \beta _{{2j}} k_{i} :{\text{IND}}_{j} + \beta _{{3j}} D_{i} :k_{i} :{\text{IND}}_{j} \\ & \quad + \cdots \quad + \beta _{4} {\text{inv}}_{i} + \beta _{5} {\text{num}}\_{\text{ctry}}_{i} + \beta _{6} {\text{claims}}_{i} \\ & \quad + \beta _{7} {\text{bwd}}\_{\text{cits}}_{i} + {\text{FE}}_{{j,t}} + \varepsilon _{i} . \\ \end{aligned}$$

(2)

In comparison with model (1), we now additionally consider industry-interaction terms denoted by $...:{\rm IND}_{j}$, where j marks the industry to which patent i belongs to. Again, we estimate three specifications. In the first one, we include the interaction term $D_{i}:{\rm IND}_{j}$, which allows us to analyze whether digital domains are associated with more breakthrough innovations as measured with forward citations of patents than non-digital ones at the industry level. In the second specification, we use the second interaction term $k_{i}:{\rm IND}_{j}$. This gives indications on whether the positive association between improvement rates and breakthroughs also hold for different industries. In the last specification, we consider the interaction terms $D_{i}:{\rm IND}_{j}$ and $D_i:k_{i}:{\rm IND}_{j}$. This enables us to investigate for different industries whether the associations are evident for digital and non-digital technologies alike. Hence, the parameter vectors $\beta _{1j}$, $\beta _{2j}$, and $\beta _{3j}$ are of interest to us. The control variables and fixed effects are similar to model (1) and used in each specification. Again, we cluster standard errors at the industry level.

Table 2 Technological improvement rates and breakthrough innovations across industries

Table 2 shows the results. As one can see from column (1), the positive association between digital technologies and our indicator for breakthrough innovations holds for all investigated industries. The same is true for faster-improving technologies (column 2). Thus, the previous results across all industries were not solely driven by some industries but show up for all considered industries. Moreover, there exist substantial differences between the industries. In particular, the positive associations linked to a higher improvement rate are particularly strong in the electrical and medical industry, and rather low in the machinery and, especially, in the computer/ICT industry. It is now interesting to analyze whether the associations are more driven by innovations in the digital or non-digital domain. First of all, the first rows of column (3) show that patents from the digital domain are associated with an increased likelihood of containing a breakthrough innovation as measured with forward citations of patents in all six industries. At the same time, this digital level effect is accompanied by a reduced association between improvement rates and breakthrough innovations when compared to non-digital domains: All else equal, faster-improving technologies are more strongly associated with breakthroughs in the non-digital domain compared to the digital one. This even goes so far that there is no longer an association between the improvement rate and our breakthrough indicator for the digital domain in the chemical and medical industry.²⁴ Still, in these industries, the digital domain as such is associated with more breakthroughs as measured with forward citations of patents, albeit for these industries it seems not to matter whether these are faster or slower progressing digital technologies. At the same time, however, a positive association between technology improvement rates and our indicator of breakthrough innovations shows up for the non-digital domain for all investigated industries. In addition, in Tables 10, 11, 13, and 14 of “Appendix,” we show that the pattern from Table 2 remains robust when different subsets of years, different time thresholds for forward citations to indicate breakthrough innovations, and some alternative measures of breakthrough innovation are considered, respectively. This heterogeneity in the association between digital and non-digital domains at the industry level shows that it is important to consider both dimensions (i.e., distinction between digital and non-digital domains and differences in the improvement rates of technologies).²⁵

The results of these regressions can thus be summarized as follows: Patents of the digital domain are associated with a higher probability of containing a breakthrough innovation as measured with forward citations. At the same time, this is true for technologies with higher improvement rates. When differentiating between digital and non-digital technologies at the industry level, the latter association is still evident for the non-digital domain. For the digital domain, in turn, it only remains valid for some industries. However, for all industries, digital innovations per se are associated with a higher incidence of breakthrough innovations. These results suggest that companies which are relatively strongly specialized in digital and rapidly improving technologies should also see a higher number of breakthrough innovations. Consequently, this finding should also translate to the level of industries and countries: If a country’s innovation system produces more inventions in digital and rapidly improving technologies, it should benefit from a higher number of breakthroughs. And since early involvement in innovations in disruptive fields has been found to strongly affect long-term prosperity (e.g., Bloom et al., 2021), our empirical results suggest that innovation systems that are involved in bringing forward the fastest improving technologies may benefit from substantial benefits in the future.

3 The state of digital innovation in Switzerland and abroad

Against the background of our empirical results, we next analyze the specialization patterns of Swiss industries toward digital and fast-improving technologies in comparison with other important countries. We start by examining the shares of Swiss industries’ digital patents and compare them to those of other countries.²⁶ Figure 3 shows that Switzerland’s share of digital patents in an industry in relation to all patents of that industry is rather low across all industries, whereas the distance to the first ranked country is particularly large for the chemical and pharmaceutical industries.²⁷

Fig. 3

Share of digital patents of different industries and countries. Notes: Calculations based on the definition for digital IPC classes from Inaba and Squicciarini (2017) that were matched to USPTO patents between 2010 and 2015. The figure shows the number of digital patents of industry j of country c relative to the total number of patents of industry j of country c, normalized by the value of the respective Swiss industry:  $\frac{({\rm num}\_{\rm digital}\_{\rm pat}_{j,c}/{\rm num}\_{\rm pat}_{j,c})}{({\rm num}\_{\rm digital}\_{\rm pat}_{j,{\rm c}={\rm CH}}/{\rm num}\_pat_{j,{\rm c}={\rm CH}})}$

It is noteworthy that Switzerland’s innovation system is relatively heavily specialized in exactly these two industries compared to most other countries (a further one being the medical industry, see Table 6 in “Appendix”): Over the time window of our study, the pharmaceutical industry represented 22% of Swiss patenting, and the chemical industry accounted for another 10%. Yet, the amount of digital patenting in these two core Swiss industries is about three to six times lower compared to the leading countries, Japan and South Korea. Another industry with substantial weight for Switzerland is the machinery industry (14% of Swiss patents). But again, digital patenting is much lower compared to the leading countries. Similar and consistent to the findings of, e.g., Gramke and Glauser (2017) and Grampp et al. (2018), Fig. 3 thus clearly demonstrates that Switzerland’s innovation system is not particularly directed toward the digital domain—and that this holds for all investigated industries. This could be a problem since, as we have previously shown, such innovations are associated with a higher probability of breakthrough innovations.

Fig. 4

Average technological improvement rates for digital patents of different industries and countries. Notes: Calculations based on improvement rates of 1757 technologies taken from Singh et al. (2021) and the definition for digital IPC classes from Inaba and Squicciarini (2017) that were both matched to USPTO patents between 2010 and 2015. The average technological improvement rate is normalized according to the value of Switzerland

However, in addition to simply examining digital patenting shares, we can now also focus on the improvement rates of the technologies Swiss digital patents are associated with. This provides an indication about whether the relatively small number of Swiss digital patents is nevertheless specialized toward fast evolving technologies. Figure 4 provides the respective graphical evidence. Similar to before, the figure again suggests that Switzerland lags behind the leading countries. Swiss digital innovations generally occur in digital technologies with rather low improvement rates, and Switzerland’s backlog against other countries is most pronounced for the medical industry. For this industry, the average improvement rate is only about half of that of the UK. Furthermore, Switzerland lags the top-ranked country by around 60% in the pharmaceutical industry, by around 30% in the electrical industry, and by around 15% in the machinery and computer/ICT industries.²⁸ For these latter four industries, our regression estimates have shown significant relationships of digital patents’ improvement rates with their breakthrough potential. Thus, Switzerland’s lack of specialization toward the fastest improving digital technologies might indicate a further threat to its future potential to produce breakthroughs in these industries.

That said, fast-improving technologies naturally exist outside the digital sphere as well, and the Swiss innovation system might be better positioned in the non-digital domain. Figure 9 in “Appendix” illustrates that Swiss innovations related to non-digital technologies have similar improvement rates in the medical and pharmaceutical industry compared to other countries. But for the chemical, computer/ICT, electrical, and machinery industries, Switzerland is again positioned among the laggards, whereas the backlog is particularly substantial in the electrical and machinery industries. Hence, there is also a backlog for Switzerland compared to other countries in non-digital technologies. But the Swiss innovation system seems to be much closer to the forefront of cutting-edge innovation outside the digital domain. Nevertheless, overall, the relatively weak performance of the Swiss innovation system in digital technologies dominates. Figure 10 in “Appendix” illustrates this by showing average technological improvement rates for all patents no matter if they are digital or not. Switzerland again lags the leading countries’ average improvement rates substantially in almost all industries. In the machinery industry, Swiss innovations are associated with an around 80% lower improvement rate compared to South Korea, which leads the ranking. In the electrical industry, Switzerland is around 25% behind the highest improvement rate of Japan, and in the pharmaceutical industry it is lagging South Korea by close to 20%.²⁹

Taken together, the descriptive evidence thus highlights a relatively weak engagement of Switzerland’s innovation system with digital technologies. Furthermore, digital innovations in Switzerland are less likely to occur in the fastest improving digital technologies compared to the leading countries. Together, these two patterns are the drivers for Switzerland’s rather low overall specialization toward technologies with high improvement rates, which suggests that the country’s innovation system tends to be a laggard regarding the most dynamically evolving technologies.

3.1 Discussion of results

The question is whether Switzerland should be concerned about these observed patterns. Since theoretical models typically suggest that technology diffusion is associated with the existence of first-moving innovators, early adopters, and laggards that catch up later, there is an argument that Swiss companies may simply focus on adoption instead of innovation in digital technologies.³⁰ However, since digital technologies may have special characteristics, being an adopter rather than an innovator can have various consequences.³¹ To consider potential effects on longer-term economic competitiveness, it is therefore crucial to assess whether Switzerland’s current backlog is a cause for concern.

On the one hand, R&D activities in digital and fast-improving technologies are typically associated with local spillovers, higher wages, and substantial value creation in the future.³² Local R&D activities might also foster the technology adoption by local firms, which has been shown to depend on the existing overall knowledge stock regarding a new technology (e.g., Battisti et al., 2009). Moreover, in the majority of cases, digital and non-digital innovations are likely to be increasingly mingled together to create new products and services. If digital components become increasingly important in a wide range of products an ever greater share of the generated surplus might go to digital innovations.³³

Another negative implication could arise if innovations compete (directly) with each other, i.e., are substitutes. In this case, faster-improving technologies might replace or lower the demand for products that are based on slower improving ones, since the former have usually new (and superior) features or perform much better (Hoisl et al., 2015). As a result, countries and their core industries might be at risk of being disrupted and leapfrogged if they focus on less rapidly advancing technologies.³⁴ With this regard, Switzerland’s particularly pronounced digital backlog in some of its core industries (pharmaceuticals, chemicals, as well as the medical and machinery industry) could be critical.³⁵

Hence, there are several factors that may lead to a situation where Switzerland might be confronted with challenges and miss out on long-term benefits if its innovation system is relatively weakly embracing novel digital technologies. Our empirical results support this view suggesting that fast-improving digital technologies are associated with a higher likelihood of breakthrough innovations as measured with forward citations of patents. It might therefore be beneficial to try to shift the Swiss innovation system toward technologies that could be associated with higher value creation in the future (see, e.g., Redding, 1999 for a theoretical rationale).

On the other hand, researchers have shown that laggards may catch-up to first-movers by exploiting positive spillovers, skipping some stages of the development process, or by following completely different, yet more efficient, technological paths (see, e.g., Au & Kauffman, 2001; Lee & Lim, 2001; Hoppe, 2000). In principle, economic theory even provides an argument that it may be beneficial for a country to refrain from changing its specialization at all, because countries are likely to generate the highest welfare when they specialize on the basis of their comparative advantages. Following this logic, our results would then simply imply that the Swiss innovation system has (at least until recently) its comparative advantage in more traditional, not-so-fast-improving fields. And an ongoing orientation toward these technological areas may well have advantages. For example, it might be easier to maintain a high competitiveness (e.g., by protecting some selected products with patents), because these areas do not require innovations that go beyond relatively slow and steady improvements.

In addition, due to specific characteristics of digital technologies (see Footnote 31), only a few so-called tech-clusters and superstar companies are likely to benefit greatly, while everyone else tends not to (Chattergoon & Kerr, 2022; Tambe et al., 2020; Triulzi et al., 2020). Since Switzerland is currently not one of the leading innovators in these areas, it could be advantageous to continue to stay out of such a tech-race and instead source ICT from the respective technology leaders. By doing so, Switzerland’s lacking orientation toward digital innovations might be less serious as Swiss companies could simply relocate selected R&D activities to other countries or entirely source the required digital components from foreign firms (see, e.g., Harhoff et al., 2014; Griffith et al., 2006). Doing so might mitigate Swiss companies’ risk of being leapfrogged and could thus sustain their international competitiveness.³⁶

Overall, potential implications of Switzerland’s backlog in digital innovations are thus ambiguous. However, we would consider it more concerning if the following conditions are met: First, we would expect more negative implications if the fraction of Swiss companies’ products that is or will be competing with digital alternatives is large. Second, if it becomes apparent that digital parts of products will increasingly receive a larger share of the value creation. And third, if technological catch-up becomes more difficult over time, for example, due to a particular “technological regime” (Lee & Lim, 2001) that is associated with digital technologies (e.g., network effects).

4 Conclusion

Technologies evolve heterogeneously and differ substantially with regard to their rate of technological improvement. In this paper, we have combined different sources of information to study these differences in detail. Our empirical findings suggest that primarily digital technologies improve at very fast pace, and patents from the digital domain and those related to the fastest improving technologies are more strongly associated with breakthrough innovations as measured with forward citations across industries. We then compare countries’ specialization patterns with regard to the digital domain and investigate their orientation toward fast-improving technologies. We find that Swiss innovations are neither particularly focused on the digital domain, nor toward the fastest improving digital technologies. In the non-digital domain, the Swiss innovation system’s backlog to the leading countries is (much) less pronounced, but it is also not among the forerunners in rapidly evolving fields except for the medical and pharmaceutical industries. However, overall, the relatively weak engagement in the digital domain dominates and Switzerland seems to be among the laggards with respect to innovations in today’s fastest improving technologies.

Against this background, the question arises whether this could be of concern for Switzerland. As we have discussed, this might be especially the case if catch-up becomes more difficult, and if new technologies compete with older ones and thus represent substitutes. However, instead of being pure substitutes, it is likely that digital and non-digital innovations are increasingly merged together to create new products, services, and even entirely new ecosystems of connected smart products. A corresponding strategy for Switzerland in this scenario could be to focus on its core innovative strengths in the more tangible areas and to increasingly adapt digital innovations from abroad. However, this is not without risk, since digital innovations in particular are likely to be accompanied by high value creation, which Switzerland and its core manufacturing industries would then be missing out.

Overall, a crucial, yet open, question for the Swiss innovation system is thus how rapidly and smoothly it can adapt itself to fast-improving technologies. If catch-up is rather fast, the above-mentioned concerns would become less threatening for Switzerland as a research location. Therefore, we consider it a very interesting avenue for future research to evaluate the Swiss innovation system’s rate of adaption toward differently evolving technologies. Another very interesting and challenging analysis would be to reveal underlying determinants that lead to the observed differences in countries’ innovation systems.

5 Computational details

Most computations were performed at sciCORE scientific computing center at the University of Basel (http://scicore.unibas.ch). Data processing and visualizations were conducted in R (Version 4.1.3). We have mainly relied on the package collection tidyverse (Wickham et al., 2019) and estimated regressions using the package fixest (Bergé, 2018).

A Appendix

1.1 A.1 Technical appendix: estimating technological improvement rates

The paper builds on prior work by Singh et al. (2021) who estimate technological improvement rates based on information encoded in patents. Their approach is motivated by an observation from Triulzi (2015), who notes that companies with more “central” patents in the semiconductor industry were able to catch up faster to technological leaders. Triulzi et al. (2020) show that this observation does not only apply to companies in the field of semiconductors, but that the “centrality” of a whole technology field within the patent universe is indicative of its improvement dynamics. Building on these insights, Singh et al. (2021) estimate improvement rates for 1757 different technologies. In the following, we briefly outline how Singh et al. (2021) define and calculate the “centrality of patents” and how they use it to estimate technology improvement rates. This requires several steps. In a first step, Singh et al. (2021) calculated for each patent i the total number of so-called incoming paths of its backward citations:

$$\begin{aligned} {\rm incoming}~{\rm paths}_i = L_{{\rm BWD}_i} + \sum _{b \in {\rm reachable}_{{\rm BWD}_i}} L_{{\rm BWD}_b}, \end{aligned}$$

(3)

where $L_{{\rm BWD}_i}$ is the number of direct backward citations patent i has made (i.e., all patents that are cited by patent i) and the second term on the right-hand side the number of backward citations of all patents that can be reached from patent i by traveling backward within the patent citation network (see Fig. 5 for an illustration). In addition, Singh et al. (2021) also calculated the total number of so-called outgoing paths of patent i along its forward citations up to three years after filing:

$$\begin{aligned} {\rm outgoing}~{\rm paths}_{i, t + 3} = L_{{\rm FWD}_{i, t + 3}} + \sum _{ b \in {\rm reachable}_{{\rm FWD}_{i, t + 3}}} L_{{\rm FWD}_b}, \end{aligned}$$

(4)

where $L_{{\rm FWD}_{i, t + 3}}$ is the direct number of forward citations patent i has received until three years after the patent has been granted. And the second term on the right is the number of forward citations of all patents that can be reached from patent i by traveling the patent citation network forward to three years after the patent has been granted (see again Fig. 5 for an illustration). In a next step, they use these two measures to calculate a patent’s “Search Path Node Pair” (SPNP) index. The SPNP index is calculated by multiplying Eqs. (3) and (4) with each other:

$$\begin{aligned} {\rm SPNP}_{i,t + 3} = ({\rm incoming}~{\rm paths}_i + 1)*({\rm outgoing}~{\rm paths}_{i, t + 3} + 1). \end{aligned}$$

In order to avoid multiplications with zero, a constant of value one is added to each term.³⁷ The SPNP index depends on the filing year of patent i, its technology, and the number of citations it mentioned and received. Thus, in order to separate the centrality of a patent from all of these factors, Singh et al. (2021) calculate for each patent i the expected SPNP that includes all dependencies except the one they are interested in—namely, whether the patents that patent i cites and is cited by represent key nodes in the patent citation network. To achieve this, they calculate for each patent i 1000 different hypothetical ${\rm SPNP}_{i,t + 3}$ values by randomly swapping the patents along the incoming and outgoing paths while taking into account various constraints. First, they randomly swap patents from the same USPC class as patent i with patents from the same class and filing year as the ones swapped. Second, they randomly swap patents from a different USPC class than patent i with patents from the pool of all other patents having the same filing year as the swapped ones. Due to this randomization, “each patent preserve the same number of citations made and received, the same age profile of its citations made and received and the same share of citations made that go to patents classified in the same class” (Singh et al., 2021, p. 11). The only difference between the 1000 hypothetical worlds is that the cited and citing patents of patent i have different numbers of forward and backward citations.

To give an example, consider Fig. 5, where $p_i$ is the actual observed patent in the citation network. Assume that it has received one direct backward citation and two indirect backward citations along the incoming paths. In addition, it received two direct forward citations and one indirect forward citation along the outgoing paths. In contrast, the backward and forward paths of patent $p_i*$ have been artificially generated. By assumption of the randomization process, it has the same number of backward and forward citations as patent $p_i$. However, its randomly assigned backward and forward cited patents have fewer citations, resulting in a lower SPNP score of nine instead of sixteen.

Fig. 5

Illustration of the SPNP index and randomization process. Notes: Assume patent $p_i$ is the actual observed one in the citation network. It has received one direct backward citation, two indirect backward citations along the incoming paths and two direct forward citations and one indirect forward citation along the outgoing paths. Together with the added constants of one, this results in a SPNP of sixteen. In contrast, patent $p_{i*}$ has randomly created backward and forward paths. By construction, it has the same number of backward and forward citations as patent $p_i$.  But in the example the randomly assigned backward cited patent only cites one patent and the randomly assigned forward cited patents were not cited at all. This results in a lower SPNP of nine

In order to obtain the expected SPNP value of patent i, Singh et al. (2021) take the average over the 1000 hypothetical worlds. Using the resulting expected value and the corresponding standard deviation, they calculate the z-value of the SPNP for patent i as

$$\begin{aligned} z_i = \frac{{\rm SPNP}_{i,t + 3} - E({\rm SPNP}_{i,t + 3})}{\sigma _{{\rm SPNP}_{i,t + 3}}}. \end{aligned}$$

Since the number of possible input paths increase over time, the z-values increase also as an artifact of the randomization process. To account for this, they normalize the z-values by using the rank quantile to which the z-value of patent i belongs according to its filing year and use this as the patent’s centrality value. In the next step, Singh et al. (2021) take the average among the centrality values of all patents assigned to a technology and use it in an OLS-regression to estimate a relationship between the observed technology improvement rates (based on “real-world” metrics) for 30 technologies (which are the same as in Triulzi et al. 2020) and the average of the centrality of the associated patents. Finally, Singh et al. (2021) use this estimated relationship to predict the technology improvement rates for 1757 endogenously determined technologies, for which patent data exist but no “real-world” metrics on technology progress are available. In doing so, they take the mean of the centrality values of all patents belonging to a technology, put it into the estimated relationship, and eventually obtain an estimate for each of the 1757 endogenously determined technologies.

1.2 A.2 Additional graphs

See Figs. 6, 7, 8, 9, 10, 11.

Fig. 6

Cumulative density of the patent-industry mapping probabilities. Notes: The graph shows the distribution of probabilities used to map patents to the Chemical, Computer/ICT, Electrical, Machinery, Medical, and Pharma industry. The data contain all patents used for our descriptive analysis. Specifically, it contains the filing years 2010–2015, the countries Canada, China, France, Germany, Japan, South Korea, Switzerland, the UK, and the USA

Fig. 7

Digital patents per employee across industries and countries. Notes: The y-axis shows digital patents of the years 2010–2015 relative to the average number of employees between 2010 and 2015 per industry and country normalized by the value of Switzerland. For the number of employees, we used data from the OECD-STAN database. Unfortunately, we could not calculate the number of employees for Medical Technology and Computer/ICT, as these are composed of different NOGA sub-industries. Moreover, values for China are not included in the STAN database

Fig. 8

Average technological improvement rates for digital patents across industries and countries for different percentile subsets. Notes: Calculations based on improvement rates of 1757 technologies taken from Singh et al. (2021) and the definition for digital IPC classes from Inaba and Squicciarini (2017) that were both matched to USPTO patents between 2010 and 2015. The average technological improvement rate is normalized according to the value of Switzerland. The plot shows average improvement rates for patents whose improvement rate is above the xth percentile of a given country. For comparison, the dots labelled as all show the averages across all patents as used in the main text

Fig. 9

Average technological improvement rates for non-digital patents across industries and countries. Notes: Calculations based on improvement rates of 1757 technologies taken from Singh et al. (2021) and the definition for digital IPC classes from Inaba and Squicciarini (2017) that were both matched to USPTO patents between 2010 and 2015. The average technological improvement rate is normalized according to the value of Switzerland

Fig. 10

Average technological improvement rates of all patents of different industries and countries. Notes: Calculations based on improvement rates of 1757 technologies taken from  Singh et al. (2021) that were matched to USPTO patents between 2010 and 2015. The average technological improvement rate is normalized according to the value of Switzerland

Fig. 11

Average technological improvement rates of all patents of different industries for different percentile subsets. Notes: Calculations based on improvement rates of 1757 technologies taken from  Singh et al. (2021) that were matched to USPTO patents between 2010 and 2015. The average technological improvement rate is normalized according to the value of Switzerland. The plot shows average improvement rates for patents whose improvement rate is above the xth percentile of a given country. For comparison, the dots labeled as all show the averages across all patents as used in the main text

1.3 A.3 Additional tables

See Tables 3, 4, 5, 6 and 7.

Table 3 Improvement rates of the 10 top and bottom ranked technologies

Table 4 Industry names and NACE codes

Table 5 Number of patent UPC-IPC code combinations per country and industry

Table 6 Distribution of countries’ patents across industries

Table 7 Technological improvement rates and breakthrough innovations: time period estimates

Table 8 Technological improvement rates and breakthrough innovations: different time spans of forward citations

In Table 8, we use different time thresholds for forward citations to indicate breakthrough innovations. While we take into account different citation practices between different technology areas by classifying breakthroughs per WIPO technology field and publication year, our threshold of five years could imply a systematic bias toward digital patents. As our results show, digital innovations have higher technology improvement rates and are therefore likely to spread and be adapted more quickly. This could imply that within a WIPO technology field digital patents are more often cited than other patents in the first years after publication. Using a time horizon of five years, breakthroughs in the non-digital area in particular could therefore be missed. To check this, we also consider seven- and ten-year thresholds of forward citations as criteria for breakthrough innovations. As the results of Table 8 show, digital patents are still associated with a higher probability of containing a breakthrough innovation when using seven- and ten-year forward citation thresholds. Also, the size of the coefficient remains very robust. This suggests that the results are not driven by the possibility that non-digital patents require a longer time horizon to be cited.

Table 9 Technological improvement rates and breakthrough innovations: different breakthrough measures

In Table 9, we use an alternative measure to indicate breakthrough innovations based on the similarity and dissimilarity of patent texts as popularized by Kelly et al. (2021) and Arts et al. (2021).³⁸ In particular, Kelly et al. (2021) calculate the importance of a patent by dividing the five-year forward by the five-year backward similarity of patent texts and propose that a higher value is a good indicator of breakthrough innovations. This is because a higher value can either emerge because of a lower backward similarity, which is the case if, ceteris paribus, the patent text differs stronger from past patents, indicating that the invention is somehow of a completely new type. Or it can be due to a higher forward similarity, which means the patent text is, ceteris paribus, more similar to future patents. As argued by Kelly et al. (2021), this should be the case for a patent with a strong influence on future inventions. They use a list of significant inventions such as stem cells, Google’s PageRank algorithm, and gene transfer in order to substantiate their claim. As they show, patents codifying significant inventions also have a high importance score. Following Kelly et al. (2021), Grampp et al. (2018), Gramke and Glauser (2017), we thus define a patent as containing a breakthrough or significant innovation if it is among the 10% having the highest importance score within its WIPO technology field and publication year. This indicator then provides an alternative measure for identifying breakthrough patents and allows us to examine the robustness of our regression results. In addition, we also use different thresholds (75th percentile and 99th percentile) to identify breakthrough innovations. As Table 9 shows, the results remain robust (Table 10).

Table 10 Technological improvement rates and breakthrough innovations: time period estimates across industries

Table 11 Technological improvement rates and breakthrough innovations across industries: different time spans of forward citations

In Table 11, we use different time thresholds for forward citations to indicate breakthrough innovations across different industries. See text in Table 8 of Appendix for a brief rationale for this table. As the results of the table show, digital patents are still associated with a higher probability of containing a breakthrough innovation for seven- and ten-year forward citation thresholds across all considered industries. Interestingly, the strength of the association is actually increasing for the two important Swiss industries: Pharmaceuticals and Medical-Tech (Tables 12, 13, 14, 15, 16).

Table 12 The digital domain and technological improvement rates: time period estimates across industries

Table 13 Technological improvement rates and breakthrough innovations: breakthrough measures across industries (part I)

Table 14 Technological improvement rates and breakthrough innovations: breakthrough measures across industries (part II)

Table 15 Technological improvement rates and breakthrough innovations: heterogeneity between the digital and non-digital domain

Table 16 Breakdown of the average technology improvement rate by digital, non-digital, and all patents for different countries and industries