Fueling the Fire? How Government Support Drives
Technological Progress and Complexity

Carolin Nast, Tom Broekel and Doris Entner

Papers in Evolutionary Economic Geography# 24.07

http://peeg.wordpress.com

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Fueling the Fire? How Government Support Drives
Technological Progress and Complexity
Carolin Nast
University of Stavanger Business School, Stavanger, Norway
ORCID: 0000-0003-1067-2946
carolin.nast@uis.no (corresponding author)

Tom Broekel
University of Stavanger Business School, Stavanger, Norway
ORCID: 0000-0003-4516-4626
tom.brokel@uis.no

Doris Entner
V-Research GmbH, Industrial Research and Development, Campus V, Stadtstraße 33, A 6850
Dornbirn, Austria
ORCID: 0000-0002-7133-9517
doris.entner@v-research.at

Acknowledgements
We express our gratitude to Lars Mewes, whose initiation of this project and subsequent fruitful
discussions were invaluable. Our thanks also extend to Ron Boschma for his insightful comments
and suggestions on an earlier version of this paper. Special appreciation goes to the editor, Alex
Coad, and three anonymous reviewers whose constructive comments and suggestions played asignificant role in enhancing the quality of our paper.
Funding: This project has received funding from the European Union's Horizon 2020 research andinnovation programme under the Marie Skłodowska-Curie grant agreement No 860887.
Declaration of interest: The authors declare that they have no conflict of interest that could haveinfluenced this work.

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Abstract
This study investigated two major trends shaping contemporary technological progress: thegrowing complexity of innovation and the increasing reliance on government support for private
research and development (R&D). We analyzed United States patent data from 1981 to 2016 using
structural vector autoregressions and uncovered an indirect interplay between these trends. Ourfindings showed that government incentives and support played a crucial role in spurring privatesector innovation. This government-fueled innovation, in turn, paved the way for advancements inmore intricate and sophisticated technological areas.
Our study sheds light on the dual role of the United States' innovation policy over the past four
decades; the policy has not only accelerated technological advancement but also steered it toward
increasingly complex domains. While this trend presents opportunities for economic growth andtechnological breakthroughs, it also poses challenges, including the potential for further escalating
R&D costs. This research has significant implications for policymakers and industry leaders,suggesting a need for a balanced approach to fostering innovation while considering the long-term
economic and technological landscape.
Keywords: Innovation, patents, technological complexity, government R&D
JEL: O31, O33, O38

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1 Introduction
Today’s technological progress is characterized by two major trends. The first is the increasing
complexity of technologies and their research and development (R&D) activities. Many of today’s
technologies can do more things, have more elements and connections, and need more R&D
resources and development time than before (Broekel, 2019; Hidalgo, 2015; Prencipe, 2000;
Strumsky et al., 2010). For example, keeping up with Moore’s law—according to which computer
chips get twice as dense every two years, implying massively growing computational power and agreater diversity of applications—requires eighteen times more R&D staff now than in the 1970s(Bloom et al., 2020). The second is the growing role of government intervention and support ininnovation processes. The government can support innovation in different ways, for example byfunding basic research that creates new opportunities for firms or by directly helping thedevelopment of specific technologies or solutions. After the Second World War, a small percentage
of all US patents were associated with some form of government backing. Today, this share is
between 25 and 30 percent (Fleming et al., 2019).
We argue that these two trends are likely to be related to each other due to two mechanisms. On
the one hand, the rising complexity of technologies makes it harder and costlier for private actors
to innovate on their own. Therefore, government resources and assistance are needed to keep up
with technological progress. On the other hand, the government may encourage innovations thatpush complexity in order to generate economic and social benefits associated with suchdevelopments. For instance, Mewes and Broekel (2020) showed that regions with capabilities inmore complex technologies grow economically faster than regions without such competencies.
In the empirical part of this study, we sought to identify the dominant direction of the influence:
Does growing complexity lead to more government support, or vice versa? To answer this question,

4
we used patent data on 630 technologies from the United States Patent and Trademark Office(USPTO) for the period 1981–2016. These data were matched with information on government
support (Fleming et al., 2019) and technological complexity (Broekel, 2019). We used the VARLiNGAM (Vector Autoregressive Linear Non-Gaussian Acyclic Model) method, which can,arguably, detect causal relationships in non-normal data (Hyvärinen et al., 2010).
We found that government support was not uniformly distributed across technologies. On thecontrary, it increasingly concentrated on complex technologies. In agreement with the literature,
our study confirms that government support stimulates private innovation activities. In addition,
we contribute to this literature by providing evidence for government support being indirectly
responsible for the growth of technological complexity. That is, greater government support(government ownership and funding) tends to increase private investments that subsequently
contribute to the growth of technological complexity. Similarly, innovations referring to previous
government R&D may also facilitate the growth of complexity. In summary, we show thatgovernment support is not a reaction to increasing complexity. Rather, it acts as a driver of thegrowth of complexity and, given the positive effect of complexity on economic growth (Hidalgo& Hausmann, 2009; Mewes & Broekel, 2020), it may (indirectly) contribute to today’s economic
growth. However, by pushing the levels of technological complexity, government support is likely
to increase the future resource requirements of R&D and thereby lower its productivity andcontribution to economic growth.
The paper is structured as follows. Section 2 discusses the relationship between complexity andgovernment support from a theoretical perspective. Section 3 presents the data and empiricalapproach of this study. The results are presented and discussed in Section 4. Section 5 concludes
the paper by putting the findings into perspective and outlining their future research potential.

5

2 Is government support the answer to increasing complexity or its
cause?
2.1 Government-supported research fuels innovation
Recent research suggests that private R&D activities are increasingly relying on government
support. For example, Fleming et al. (2019) classified US patents that rely on some types of(federal) government support. According to these authors, the share of government-supported
patents in overall patenting has constantly increased from 1926 onward. While it was 5% shortly
after the end of the Second World War, it grew to over 30% in 2011. Hence, already by 2011, every
third US patent relied on government R&D support, and there are few reasons to believe that thisshare has decreased over the last decade.
In general, such government interventions are justified by the belief that R&D activities are subject
to market failure (Arrow, 1962; Nelson, 1959). Knowledge is frequently assumed to be a nonrivalrous and non-excludable good (although this is debatable; see, for example, Witt et al., 2012),
as the use of knowledge by one actor does not prevent its use by others and it is impossible toexclude others from using the knowledge. Consequently, actors investing in knowledge cannot
fully appropriate all its benefits and, therefore, underinvest in it. Another reason for market failuresis argued to be the high uncertainty inherent in knowledge production (Nelson, 1959). Uncertainty
describes a condition under which actors in an economy must decide on inputs when the output isdifficult to predict or even completely unknown. In the case of technological innovations, theuncertainly inherent in basic research is related to the question of when and where the innovation
is applied (Pavitt, 1991). In response to these market failures, private actors may invest in R&D
investments below the socially desired optimum (Klette et al., 2000; Mazzucato, 2012; Weber &Rohracher, 2012). Basic research, often supported by the government, increases the stock of useful6knowledge, thus expanding technological opportunities available to society by providing new ideas
and technological knowledge (Klevorick et al., 1995; Narin et al., 1997; Salter & Martin, 2001).
There are multiple approaches to raising R&D investments to a socially desired optimum. One ofthe primary approaches is the patent system, which grants innovators a temporary monopoly on thecommercialization of their inventions in exchange for publishing the corresponding knowledge anda small fee. In addition, the government provides public research capacity. Such government R&D
activities are most visible in basic research activities, where uncertainty is highest and the goals
are less tied to specific practical problems. This is evident in the US, where government spending
on R&D for basic research accounts for 57% of the total spending on basic research. In comparison,
government spending accounts for only 26% of the total R&D spending in the US (Mazzucato,2012). In 2017, universities and colleges conducted the majority of basic research in the US (48%),
while the business sector accounted for 27% and the federal government (being the main source offunding for basic research) for only 11%. However, even in applied research, where uncertainty isless pronounced and the research goals are more visible than in basic research, government
agencies, non-profit organizations, universities, and colleges carried out 43% of the activities, withthe business sector engaging in the remaining 57%.1 Deficiencies in private R&D activities areproblematic for many reasons, one of them being that the application of basic research, potentiallyenabled by government support, depends on investment in downstream activities by private firms(Pavitt, 1991).
The different approaches to R&D support are frequently interrelated. The original patent system
has been amended multiple times to strengthen its supporting role and to better integrate other1

The numbers are drawn from the National Science Foundation (NSF) at https://ncses.nsf.gov/pubs/nsb20201/u-s-rd-performance-and-funding, accessed on September 11, 2022.

7
government support measures. For instance, the Bayh–Dole Act (BDA) of 1980 encouraged US
universities to patent their research outcomes by granting them full property rights, includingcommercial licensing. Although the BDA has stimulated university patenting, its overall effect isarguably overstated (Mowery et al., 2001; So et al., 2008). Consequently, and considering the rather
monotonically growing shares of government-supported patents, the BDA is not enough to explain
the strong increase in government-supported patenting, as shown by Fleming et al. (2019). The
same is true for the second substantial change to the intellectual property rights system: the Federal
Technology Transfer Act of 1986, which allowed federal research laboratories to enter into
Cooperative Research and Development Agreements with private organizations (Mowery, 1998).
These changes stimulated public actors’ greater involvement in patented R&D activities as well as
collaboration with private actors. Further measures involve programs that explicitly target researchcollaborations and grant R&D subsidies to private as well as public organizations (Hall & Lerner,
2010). One such program is the Advanced Technology Program, which aims to stimulate high-risk
R&D conducted by private organizations (Mowery, 1998). These programs frequently require
private–public cooperation, further expanding government involvement in and support for R&D.
There is an ongoing debate about the consequences of government investments in R&D withrespect to the crowding-in or -out effects of private investments. However, there is increasing
evidence substantiating the positive impact of government subsidies on commercial R&D activities(i.e., the economic return) at the micro-level (Becker, 2015; Carboni, 2011, 2017; Clausen, 2009;David et al., 2000; Trajtenberg, 2002) and in relation to military R&D crowding-in privately funded
R&D (Pallante et al., 2023). However, the market failure–based justification of government
intervention is not without criticism. Some argue that government support is unlikely to be
successful on average and even less likely in the case of projects with a high social return that the

8private sector does not realize on its own (Klette et al., 2000). The reasons are that government
officials lack ownership competence (in reference to “which resources to own, […], how to create
value by owning these resources […], and when to own them,” Murtinu et al., 2022, p. 60). R&D
projects become successful because of entrepreneurship and not because of government action(Murtinu et al., 2022). These authors argue that it is “merely” the law of large numbers that leads
to economically and socially successful R&D projects, as the state simply supports many projects.
Based on these arguments, the first contribution of this paper is to investigate the relationshipbetween government support and the extent of innovation activities, with the number of private
patents as a proxy of the latter. We propose the following as our first hypothesis:
H1: Government support increases the number of innovations.
Our rationale for this positive relationship is mainly based on the assumption that government
support enables private actors to develop innovations that would otherwise be too uncertain or
risky.

2.2 Government support and complexity
Government support can lead to increased innovation, but this does not always translate to sheer
quantity. While the innovations or new products might be fewer in number, they might explore
more complex and advanced technologies. Therefore, an apparent decrease in innovative activities
could merely be a result of measuring quantity without considering quality. To account for this, we
introduce the concept of “complexity” as a measure to gauge the quality and depth of technologicaladvancements.
Technological complexity grows over time because technology and knowledge are cumulative.
Each technological advancement builds on the knowledge of previous innovations (Aunger, 2010;

9
Hidalgo, 2015; Jones, 2009). Moreover, technologies begin to deepen in complexity when theyembark on serving more functions (like Microsoft’s Windows) and need to be compatible withother innovations (Broekel, 2019; Fai & von Tunzelmann, 2001). Recent studies by Broekel (2019)and van der Wouden (2020) empirically confirm this increase in technological complexity overtime. They show that the average complexity across all technologies is growing and that younger
technologies tend to be characterized by higher levels of complexity. The creation of these newtechnological combinations involves the meticulous task of piecing together different knowledge
fragments, often through guided trial-and-error methods (Dosi, 1988). The more complex atechnology is, the more diverse its knowledge base. This means that its creation involves rarer
knowledge components and demands more trial-and-error efforts (Carbonell & Rodriguez, 2006;
Fleming & Sorenson, 2001; Broekel, 2019).
Such complexity drives increased R&D efforts since developers need stronger absorptive
capacities (Cohen & Levinthal, 1989). This can result in longer development periods (Griffin,1997) and a heightened risk of setbacks (Singh, 1997). In this case, market failures may arise,
which justify government support to provide the necessary security net for innovators. Given theincreasing average complexity, such situations may become more frequent, implying continual
extension of government support. Another observation supports this idea. Research teams havenotably expanded in size over recent decades (Jones, 2009; 2010). This expansion is intrinsicallytied to the escalating complexity of innovative endeavors (Broekel, 2019; van der Wouden, 2019).
The quantum of global knowledge has surged exponentially. Unlike the Renaissance, marked bypolymaths with proficiency across myriad disciplines, the present landscape is dominated by highly
specialized experts (Jones, 2009). Balland et al. (2022, p. 2) articulated the view that augmentationof societal knowledge operates on an extensive margin: “The collective knowledge reservoir

10
deepens not because individuals know more, but because they know differently. The proliferationof know-how is essentially a product of specialization.”
At its core, innovation is the art of ingeniously reconfiguring pre-existing ideas (Fleming &Sorenson, 2001; Weitzman, 1998). The propagation of novel technologies necessitates theamalgamation of insights from these hyper-specialized individuals. Yet, the resultant
fragmentation and stratification of knowledge amplify coordination exigencies (Becker & Murphy,1992). To actualize multifaceted technological innovations, these individuals need to function
within harmonized, cohesive teams (Neffke, 2019). However, the orchestration of such synergistic
assemblies not only escalates resource demands, due to an increased workforce, but also poses thechallenge of multiple iterative attempts to curate a team that perfectly coalesces.
State-sponsored interventions can foster and amplify social interconnectivity, knitting a denser webof relationships within technological communities. This, in turn, augments the reservoir of
specialized talents accessible to enterprises (Callon, 1994; Lundvall, 1992; Salter & Martin, 2001).
The empirically observed enlargement in R&D team dimensions provides tangible corroborationof the narrative of burgeoning complexity.
In sum, advancements across the (ever more) complex technological landscape have become more
complicated and resource-intense (Bloom et al., 2020). Jones (2009) famously summarized thisdevelopment as “the burden of knowledge,” which triggers increasing government support.
However, there are also arguments for the opposite to hold true. Government support may also bea driving force behind the growth of technological complexity.
Complex technologies provide a better basis for further technological advancement anddiversification (Hidalgo & Hausmann, 2009). They often require a deep understanding of various

11scientific principles and engineering concepts and specialized skills. The engagement with suchtechnologies necessitates a workforce with high levels of education and expertise. Thisaccumulation of knowledge and skills creates a foundation for further technological advancement,
amplified by spillover effects and the creation of opportunities for diversification. Consequently,
the investment in complex technologies promises greater economic returns (Broekel, 2019; Kogut& Zander, 1992; Sorenson et al., 2006; Winter, 1987; Zander & Kogut, 1995), which attract support
from the government seeking to benefit from these gains.
Another rationale behind the increased government support attracted by complex technologies is
the recognition that certain highly desirable technologies, notably green technologies, areinherently complex (Barbieri et al., 2020). Despite the scarcity of empirical research on the linkages
between ownership structures and sustainable technological change, recent findings by Steffen etal. (2022) reveal a conspicuous trend: state-owned utilities within the electricity industry outpace
their private counterparts in investing significantly more in renewable energy, signaling
responsiveness to climate policy objectives. This phenomenon also encompasses instances such as
military technologies in the US, characterized by not only social benefits for specific groups but
also substantial catalysis of technological progress, exemplified by the internet’s development, as
discussed by Abbate (2000).2
Typically, such societal advantages are not pivotal considerations in the investment calculus ofprivate entities, although noteworthy exceptions exist (Mazzucato, 2012). However, from a
political standpoint, they hold immense allure. Consequently, government backing is likely to bechanneled toward technologies that are socially and economically desirable and often coincide with2

We acknowledge that military technologies are primarily developed and used for warfare, which brings harm topeople in many ways.

12
technologies with heightened complexity. Given the challenge inherent in precisely quantifying therequisite resources or, conversely, a certain political impetus to showcase (over)investments inthese domains, the scenario arises where government support may occasionally exceed optimallevels. This implies that the R&D ecosystem could be inundated with resources surpassing thebalance for sustaining advancement in less and more complex technologies. In the case of militarytechnologies, for example, international competition and the pursuit of security compel
governments to endorse projects that are otherwise too complex and costly for private enterprises.
In such scenarios, government support could inadvertently push the frontiers of technology beyond
pragmatic economic utility, resulting in involvement with exceedingly complex technologies
whose progress is less efficient, for instance, because supportive technologies in related but simpler
fields receive less support and do not keep up with their advancement. In this case, government
support is an enabling force that actively pushes technological complexity.
An additional explanation supporting this direction of impact starts from the previously discussed
idea that the greater resource requirements, higher potential for failure, and longer development
times make market-failure situations more likely and (more) complex technologies relatively lessattractive to private R&D. Consequently, assuming a constant distribution of R&D acrosstechnologies, growing complexity should lead to lower private investments and, if a constant rateof innovation is desired, an increased need for government intervention.
In this context, it becomes apparent that technological complexity adds another dimension to the
traditional crowding-out debate (Guellec & Van Pottelsberghe De La Potterie, 2003; Marino et al.,2016). While higher levels of technological complexity imply the need for greater R&D
investments, these technologies also promise greater economic returns (Broekel, 2019; Kogut &Zander, 1992; Sorenson et al., 2006; Winter, 1987; Zander & Kogut, 1995). If these returns

13
sufficiently compensate for the necessary investments, complexity can be unrelated or evennegatively related to the degree of market failure. However, as indicated above, this is unlikely
precisely because of the long-term nature of economic returns associated with complex
technologies and the expectation that private firms would struggle to mobilize R&D resources fortechnological advancements in complex domains. When the potential social and ecological benefitsof (many) complex technologies that attract policy interest are also considered, crowding out is aless likely scenario for complex technologies. While clarifying the exact relationship between
crowding out and complexity is beyond the scope of the current paper, we nevertheless seek tounderstand the link between government support and technological complexity, which is reflectedin the following hypothesis:
H2: Government support increases technological complexity.
To conclude, the presence of compelling counterarguments to our hypothesis underscores thenecessity of the empirical investigation detailed in the subsequent sections of this paper.

3 Methods and data
3.1 Overview of the methodological approach
In this study, we investigated the intricate relationship between government support and thecomplexity of technological innovations. Our analysis used a comprehensive dataset of patent
records from the USPTO that reflected a wide range of technological innovations. These patents,
categorized into various technology groups, allowed us to examine how complexity in technology
evolves and the role government support plays in this process.
Complexity in this context is understood as the degree to which various components and ideas areinterwoven within a technology. More complex technologies exhibit a denser, more intricate web

14
of interconnected ideas and components. We assessed this complexity using the structural diversity
measure designed for patent data, which reflects the varied and multifaceted nature of technologicalinnovations. In addition, our dataset included information on whether patents were supported by
the government and whether such support was through direct ownership, funding, or building on
government R&D.
The application of VAR-LiNGAM, a structural vector autoregression (SVAR) model, in our study
was particularly important for decoding the multifaceted ways government support influences
technological complexity. By distinguishing between immediate and delayed effects, our analysis
shed light on how various forms of government support—ranging from direct funding andownership to indirect mechanisms such as building upon government R&D—exerted theirinfluence on the evolution of technological complexity. This methodological approach enabled us
to unravel not only the direct, apparent influences but also the subtler, indirect modalities throughwhich government actions shaped the technological innovation landscape. The VAR-LiNGAM
method stands out for its ability to completely identify linear relationships from data with nonGaussian error terms and acyclic contemporaneous effects, which made it an invaluable tool in ourinvestigation of the complex interplay between government support and technological complexity.
The rest of this chapter provides more detailed information on our methodological approach,including how we captured technological innovations, measured their complexity, identified
government support, and applied the empirical model.

15

3.2 Measuring technological innovations and their complexity
We used patent data from the PatentsView Database, which covers all patent applications to the
USPTO, to approximate technological activities (Cohen et al., 2000)3. The Cooperative PatentClassification (CPC) classifies patents into different technologies. The CPC is hierarchicallyorganized into nine sections at the highest level and approximately 250,000 sub-groups at thelowest level. Each patent was assigned to one main technology class and multiple secondaryclasses. We focused on the four-digit CPC level, which allowed us to differentiate between 655
technologies. The four-digit level represents an appropriate trade-off between a good degree ofdifferentiation between technologies and sufficiently large patent counts in each technology class(Balland & Boschma, 2021; Leydesdorff et al., 2017). Crucially, previous research has successfully
estimated and analyzed technological complexity at this level (Broekel, 2019).
We calculated the measure of technological complexity (“structural diversity”), which has beenshown to reflect commonly accepted characteristics of technological complexity (complexity
increasing over time and requiring more R&D efforts and collaboration, as well as concentratingin space) more accurately than alternative measures (Broekel, 2019; Pintar & Essletzbichler, 2022).
In addition, it has been used to empirically identify the positive impact of technological complexity
on economic growth (Mewes & Broekel 2020). The measure quantifies the complexity of atechnology by analyzing its structural diversity through network analysis. The foundational
premise is that technologies are composites of various knowledge elements. These elements, akinto nodes in a network, are interconnected in multiple configurations, such as star-like or lattice
structures. The assumption is that the complexity of a technology is correlated with the diversity

3

The use of patent data has several well-discussed drawbacks (Cohen et al., 2000; Griliches, 1990). However, patent
data provided essential information for our empirical analysis of technological innovations, their characteristics, andinventors.

16of these configurations. Essentially, more intricate and varied network structures indicate a higher
degree of technological complexity.
The network diversity score (NDS) was calculated for each technology (four-digit CPC code) usinga binary co-occurrence network. This network included as nodes all CPC codes listed in patents
that featured at least one CPC code belonging to the focal technology. Edges between nodes
indicated the existence of co-occurrence. A technology-specific complexity metric, which reflected
higher complexity as its value increased, was derived by applying the NDS to this network andmaking some transformations (for details, see the appendix under “Details on the empiricalmodel”).
To account for the inherent variability in patent data, particularly for niche technologies, theanalysis incorporated a three-year moving window. This approach expanded the dataset for eachyear’s analysis by including patents from the target year and the preceding two years. By doing so,
the measure was stabilized, resulting in one individual complexity score for each of the 655
technologies per year, corresponding to the four-digit CPC classes.

3.3 Measuring government support for technological innovation
The information on the link between technological activities (patents) and government support was
retrieved from a publicly available data set provided by Fleming et al. (2019).4 They collected
information on whether a patent’s creation between 1926 and 2016 relied on government support.
The reliance on support was defined in three ways. First, the government owned the patent; second,
it funded the underlying research; or, third, the patent cited government R&D5. The three categories

4

The data on government support for patents from Fleming et al. (2019) is freely downloadable fromhttps://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/DKESRC
5
The last category (government R&D cited) referred to whether the patent cited a patent or a scientific paper that met
the first two criteria (government ownership or funding) or was affiliated with a government agency.

17
were not mutually exclusive, with the sources of government support overlapping in about 39
percent of the patents (Fleming et al., 2019).6 Due to the relatively low reliability of the data before
19807, we restricted our empirical analysis to the years 1981 to 2016 (see Fleming et al., 2019, andsupplementary material). While the three types of support were distinguishable from one another,none of them seemed to be particularly related to technological complexity. Consequently, we did
not have a particular expectation concerning which type was more likely to capture thephenomenon of interest. Nevertheless, we treated them independently in the analyses for analyticalclarity.
While the dataset represents a unique information source linking (patented) innovation outcomesto government support, it is important to consider its limitations. We did not have information on
how much resources were invested or the specifics of the outcomes. Government support does notalways lead to the development of a patentable innovation. However, it is only the latter that we
observed in our data. In the case of patented innovations, we also did not have information on how
much resources a patent had received; we only knew whether or not it had received any resources.
All patents were assigned to their main four-digit CPC class, and their numbers were aggregatedat this level to obtain technology-level variables. For each technology c and time period t, we
calculated the absolute number of patents that (1) were owned by the government,
𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑂𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 , ; (2) were funded by the government, 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 , ; or(3) cited government R&D, 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑅&𝐷 𝐶𝑖𝑡𝑒𝑑 , . When aggregating patents to the level offour-digit CPC classes, their numbers tended to fluctuate strongly between years. Therefore, we
6

The dataset provided by Fleming et al. (2019) was on the patent level and stated for each patent if it was owned or
funded by the government or cited government research and development. Thus, the three original government support
variables were binary variables.
7
Data inaccuracies were due to changes in reporting, acknowledgment of behavior, requirements of references, andfunding in patent applications (for further information, see Fleming et al., 2019).

18
opted for three-year intervals as periods of observation to reduce the potential distortion of such
fluctuations.
We assessed the stationarity of our data by means of a panel unit root test (Im et al., 2003; Pesaran,
2007), log-transformed all our variables, and subsequently performed a first-differencetransformation to ensure stationarity.8 In other words, we took log-differences of the variables that
corresponded to their expression as growth rates (Törnqvist et al., 1985). Based on this, we createda final panel dataset for 561 four-digit CPC technologies and three-year periods between 1981 and2016, including information on the respective growth rates of government support (ownership,
funding, or government R&D cited), complexity, and the number of private patents9 in eachtechnology class. Crucially, for all variables, we used the mean of a period’s annual values.
In total, we obtained 6,164 individual observations that were the basis of the subsequent empiricalanalysis.10 Table 1 presents the summary statistics of all variables used in this study (Table A2 in
the appendix provides additional definitions of the variables used in the empirical model. Table A3
in the appendix provides additional descriptive statistics).

8

We report the unit root tests in the appendix (Table A7).
The number of private patents in a technology class was calculated for the final panel dataset (for 561 four-digit CPC
technologies) by subtracting patents with government support from the total number of patents.
10
Of the 655 different technology classes, 561 were present in our patent data. Thus, initially, we had 12 distinct
periods (between 1981 and 2016) and 561 distinct technology classes. We took the first differences and finallyperformed the analysis with 11 periods (between 1984 and 2016). The panel was not balanced. A balanced panel would
have needed 6171 observations (561 technologies * 11 periods); however, we had only 6,164 observations (a differenceof 7 observations). We had all 11 observations for 557 technologies; however, for 4 technologies some observations
were missing (namely 7 in total) because the technologies did not have any patents in certain periods.
919

VariableComplexity
Government
fundedGovernment
ownership
Government
R&D cited
Number ofprivate patents

Statistic
MeanMedianSD
MeanMedianSD
MeanMedianSD
MeanMedianSD
MeanMedian
SD

1986
0
0.05
0.99
0.08
0
0.54
0
0
0.53
0.15
0.15
0.53
0.05
0.05
0.33

1989
0.3
0.29
1.08
-0.03
0
0.6
-0.13
0
0.58
0.18
0.2
0.57
0.08
0.10
0.37

1992
0.46
0.44
1.07
0.09
0
0.55
0.13
0
0.6
0.11
0.09
0.55
0.09
0.08
0.32

1995
0.48
0.43
1.07
0.05
0
0.57
0
0
0.56
0.12
0.11
0.54
0.03
0.01
0.3

1998
0.48
0.48
1.11
0.04
0
0.56
-0.13
0
0.56
0.17
0.16
0.54
0.09
0.09
0.33

2001
0.45
0.40
0.99
0.12
0
0.6
0
0
0.55
0.22
0.22
0.5
0.15
0.16
0.31

2004
0.21
0.21
1.01
-0.01
0
0.57
-0.05
0
0.54
0.04
0.05
0.49
-0.11
-0.09
0.31

2007
0.08
0.09
1.08
-0.04
0
0.57
-0.11
0
0.54
-0.04
-0.01
0.49
-0.22
-0.21
0.34

2010
-0.07
-0.04
0.89
0.09
0
0.54
-0.02
0
0.49
0.1
0.1
0.47
-0.06
-0.06
0.36

2013
0.32
0.22
0.96
0.26
0.14
0.56
0.13
0
0.49
0.27
0.29
0.51
0.23
0.22
0.38

2016
0.36
0.29
1.01
0.02
0
0.57
-0.04
0
0.54
0.08
0.1
0.48
0.12
0.15
0.39

Table 1: Descriptive summary statistics.
Note: These summary statistics are based on the final variables we used in our empirical model. The variables aredescribed in Table A2 in the appendix. We provide further summary statistics using less cleaned data in the appendix(see Table A3).

3.4 Empirical model
To effectively analyze the interplay between government support and technological complexity,
we implemented the VAR-LiNGAM method, a particular form of a SVAR model (Hamilton, 1994;
Hyvärinen et al., 2010; Moneta et al., 2013). This sophisticated statistical tool was particularly
effective in disentangling the dynamic and intricate interactions present in our dataset. In contrast
to conventional models, VAR-LiNGAM is specifically tailored to address data with linear
relationships and non-Gaussian error terms, allowing full identification of the potential causal
dynamics in the data without further background knowledge.
The VAR-LiNGAM methodology operates on the fundamental premise of distinguishing between
instantaneous and time-lagged effects within the data. This approach was instrumental for
dissecting the temporal relationships in our dataset, particularly how government support andtechnological complexity interacted contemporaneously and over time. A critical assumption
underpinning this method is the acyclic nature of these contemporaneous relationships. This
assumption enabled us to delineate a directional flow of influence without the entanglement of

20
feedback loops within a single time interval. It was key to controlling for potential immediateinfluences that might otherwise have confounded our analysis.
The practical application of VAR-LiNGAM involved several distinct steps (for details see “Detailsof the empirical model” in the appendix). Initially, we estimated the coefficients of the reducedform VAR model. This step established the foundational relationships between observed variables
across different periods. We then applied the LiNGAM approach (Shimizu et al., 2006) to estimate
the instantaneous causal effects. By assuming non-Gaussian distribution of the structural residuals
and employing independent component analysis (ICA; Hyvärinen et al., 2001), we identified thematrix of instantaneous effects and statistically independent residuals. This phase was critical for
identifying the immediate causal relationships between the variables. Finally, we calculated thelagged causal effects matrices by excluding the instantaneous effects from the lagged coefficientsof the reduced-form VAR. These lagged causal effects revealed how past values of variables
influenced their current states, thereby capturing the dynamic interplay over time.
We used the code package in R from Moneta et al. (2013), adapting it slightly to suit the specificresearch needs of this study. We evaluated the model fit using different estimators (ordinary leastsquares [OLS] and least absolute deviations [LAD]) and lags. Several assumptions of the model
were assessed: (1) different information criteria for lag selection11; (2) auto-correlation of theresiduals; (3) non-Gaussianity of the residuals; and (4) acyclicity of the instantaneous effects.
Based on these characteristics, the model fit proved to be good for OLS and two lags, also
confirming the applicability of the VAR-LiNGAM approach (for details see “Details on theempirical model” in the appendix). Furthermore, we used a block-bootstrap approach with 500

11

Akaike Information Criterion, Hannan–Quinn Information Criterion, and Schwarz Information Criterion; see Tables
A7 and A8 in the appendix.

21bootstrap samples not only to evaluate the robustness of the model but also to infer statisticalsignificance of the coefficients estimated using a t-test. A further robustness analysis was
performed using different pre-processing steps of the data (see section 4.3).

4 Results and discussion
4.1 A descriptive look at government support and technological complexity
Figure 1 illustrates the increase since 1981 in patents whose inventions relied on government
support, with a certain level of stagnation observable from 2010 onward. However, this trend is notequal across all types of government support. While the number of patents citing government R&D
steadily increased, those that received funding from the government increased only minimally. The
number of patents owned by the government even stagnated. The heterogeneity in these three
indices clearly suggests their treatment as independent indicators.
Similar heterogeneities were evident in the development of individual technologies (Figure 2).
During the period of observation, the field of physics and electricity benefited the most fromgovernment support, with more than 400 patents relying on this support. Chemistry was in third
place until 2010, and after 2010, human necessities had more patents relying on government
support than chemistry. This result illustrates that there are also substantial dynamics in the rankingof technologies in terms of the support received.

22

Figure 1: The growth in different types of government support.

Figure 2: Government support across different technologies.

23

Figure 3: Differences in government support by complexity.
Note: The y-axes have different scales.

What explains these differences in government support between technologies? The first indicationthat complexity was a relevant factor in this context is apparent in the distribution of government
support across the complexity quartiles. Panel 1 in Figure 3 provides an insight into this distribution
across all types of government support, Panel 2 into patents citing government R&D, Panel 3 into
government-funded patents, and Panel 4 into government-owned patents.
The most complex technologies were characterized by the highest number of supported patents(Figure 3, panel 1). When differentiating between types of support, the most complex technologies
were also the ones that cited government R&D to the largest degree (Figure 3, panel 2) and thatgenerally had higher numbers of patents funded by the government (Figure 3, panel 3). The
dimension of government ownership showed similar patterns after 1986: the most complex
technologies had the highest number of supported patents (Figure 3, panel 4). Figure 3 clearly24shows that the ranking of “technologies” by complexity corresponds quite well to their ranking bygovernment support. A rank-correlation analysis supported this observation and revealed a positive
correlation between government R&D cited and complexity (significant rho of 0.56, p < 0.001)
and between government funding and complexity (significant rho of 0.52, p < 0.001), as well as aweakly positive correlation between government ownership and complexity (significant rho of
0.42, p < 0.001). Consequently, the bivariate correlation analysis suggested a positive relationshipbetween government support and technological complexity.1212Additional correlation analyses are provided in Tables A3, A4, and A5 in the appendix.

25

4.2 Disentangling the relationship between government support and complexity.
BO

Complexity

Complexity

Gov.
Gov.
R&D
fundingcited

No. ofGov.
privateownershippatents

Complexity

Gov.
Gov.
R&D
fundingcited

B2
No. ofGov.
privateownershippatents

Complexity

Gov.
Gov.
R&D
funding
cited

No of
Gov.
privateownershippatentscoeff

0-0.0259 0.2199-0.0308

0.4819-0.2347-0.0461

0.174-0.0301

0.5312-0.1687-0.0728 0.1434

0.00530.2255SD

00.02640.04140.02640.06160.02160.03270.04340.0297

0.05670.02230.02820.03490.0276

0.05520000.398700.005-0.4854 0.0588

0.21860.08130.0019-0.2191 0.0361

0.09610.0358

SD

0

0

0

0.016500.00630.01610.01570.018

0.02070.006

0.01620.01380.0161

0.0223coeff

00.187400.03850.41870.01530.1711 -0.4892

0.02270.29830.00670.1023 -0.2226

0.01580.1141SD

00.013400.01120.01840.00710.01340.017

0.01260.022

0.00690.01190.01630.01060.0229

coeff

0

0

0

0

0

0.00230.02950.0317-0.5133

0.072-0.0134

0.04110.0205-0.2198

0.0375

SD

0

0

0

0

0

0.00570.01520.01280.01760.01910.00620.01680.01380.01690.021700.116400.035600.01030.08290.07120.0095-0.11440.005

0.02650.01170.0087-0.0679

00.009700.010400.00660.011

0.01270.01230.02380.00670.01110.01290.01150.0242Gov. funding coeff

Gov.
cited

B1

R&D

Gov.
ownership

No. of private
Patents
coeff
SD

Table 2: Structural vector autoregression model results with ordinary least squares estimator and two lags.
Note: Coefficients in bold are statistically significant at the p < 0.01 level.

26
The results of the SVAR model for identifying the relationships between complexity andgovernment support are presented in Table 2. To improve readability and in line with the literature(Coad & Binder, 2014; Coad & Grassano, 2019; Hyvärinen et al., 2010; Lanne et al., 2017; Moneta
et al., 2013; Pearl, 2009; Spirtes et al., 2000), we present its results in a causal manner. However,since we relied on observational data without external intervention, such an interpretation can bedebated.
The table shows the estimated coefficients of the SVAR model.13 For the instantaneous effects
matrix 𝑩 (relations between variables at the same moment in time; in our case, relations within athree-year period), the following causal order was inferred: starting from government ownership,
followed by government funding, number of private patents, government R&D cited, and, lastly,complexity. The lagged effects (relations between variables across periods; in our case, relations
over periods of three years) were estimated for one and two lags and reported for the matrices 𝑩
and 𝑩 , respectively. The standard deviations of the coefficients were calculated using 500
bootstrap samples by applying a block-bootstrap approach. Figure 4 provides a graphicalrepresentation of the SVAR results listed in Table 2 (showing results for the two-lag SVAR). To
evaluate the robustness of these results, the SVAR was estimated for other lags with both OLS and
LAD analyses and always yielded the same causal order.14 Furthermore, about 65% of the 500
bootstrap samples resulted in the exact same causal order in the OLS analysis, rising to about 80%
with the LAD model. In the case of the variables’ positions in the inferred causal orders, in over13

In the case of coefficient interpretation, note that we focused on growth and interpreted the relative size of thecoefficients. Given our aggregated data structure, we refrained from interpreting the absolute magnitude of thecoefficient. However, given that we analyzed growth rates, even small coefficients could have had a relevant effect.
14
We calculated and assessed the model with one and three lags for robustness without finding significant differencesfrom the OLS model with two lags. We also compared the coefficients of the OLS model with two lags with those of
the LAD model with two lags for robustness without finding significant differences.

27
90% of the bootstrap samples, government ownership was first, and complexity was last in both
the OLS and LAD analyses. Thus, the overall order was very robustly inferred, considering that
there were, in total, 120 different possible orders with five variables (Figures A3 and A4 in the
appendix provide a further explanation).
The crucial observation is that complexity did not have any effect on any of the other variables. In
the case of instantaneous effects, complexity was placed at the end of the causal order, suggestingthat complexity was not a driver of other variables but rather an outcome of them. This held truefor effects within the same period (i.e., within a three-year period) and supported our hypothesis
H2, according to which increasing government support pushes the levels of complexity oftechnologies. Moreover, government ownership had a large effect on government funding and avery small effect on the number of private patents and government R&D cited. Government
funding had a small effect on the number of private patents and government R&D cited. The
number of private patents had a strong effect on complexity and government R&D cited, while
government R&D cited had a medium effect on complexity. This causal ordering and theinstantaneous effects suggest that government support (ownership and funding) increases private
innovations (supporting our hypothesis H1), as well as those private innovations relying on
government support driving complexity. However, complexity growth is a slow process (Broekel,2019), and from a theoretical perspective, it is difficult to achieve within three years (we aggregatedthe data into three-year periods). Consequently, the lagged effects are of greater relevance and will
be our focus.
In the case of effects lagged by one period (B1/t-1), we found that government ownership had apositive effect on subsequent growth in government funding. This means that the government
owned crucial research capacities in specific technologies of interest to it. Over time, this shifted28
toward more funding-based support schemes. However, this sequence of providing support becameless frequent over time. A possible explanation for the shift from state ownership to funding might
be linked to productivity challenges associated with state ownership of firms and innovation
processes (Steffen et al., 2022).
Government funding had a small effect on the subsequent growth in the number of private patents
and in the number citing government R&D. Thus, through its impact on government funding,government ownership also contributed to a growing number of private patents. This suggests thatthe government support for basic research provides the groundwork for further technologicaldevelopments. Alternatively, through its support, the government sends a strong signal of the future
viability of a technology.
An increase in private patenting had a medium-sized effect on the growth of patents citing
government R&D. It also strongly contributed to complexity growth. We also observed a small
effect of the number of private patents on government ownership and government funding. Thissuggests that the government does follow private investments and supports technologies after
private innovation activities have increased. It is likely that private innovation activities signal to
the government which technologies are relevant and promising or the private sector is successful
in lobbying for government support. Lastly, patents that cited government R&D had a small
positive effect on government funding, the number of private patents, and complexity growth.
With respect to lagged effects over two periods (B2/t-2), we want to highlight several interestingobservations. Government ownership still had an effect on government funding and government
funding on government R&D cited. Interestingly, government funding had a small but negative
direct effect on complexity growth over this six-year period. Government support overall did not
positively influence the number of private patents over such a long period. An increase in private

29patenting still had an effect on the growth of patents citing government R&D; however, this effectwas small. The effect of private patenting on complexity growth was weak. Patents citing
government R&D maintained a small positive effect on complexity growth.
In addition, the negative autocorrelation found for all variables (see B1 and B2) suggests a cyclicalpattern of growth rates, where a period of heightened increase was often succeeded by a period of
diminished increase. In their study of Germany, Buerger et al. (2012) observed similar patterns andsuggested that they were related to the inherently stochastic nature of human creativity underlying
the patented innovation. However, this aspect should be further investigated in future research, as
it does not directly concern our research questions. Therefore, it is not included in the graphicalrepresentation of the results in Figure 4.
In summary, our main model provided evidence for a link between government support andincreasing numbers of private patents, thereby supporting our first hypothesis (H1), which statesthat government support increases the number of innovations. Note the effect of government
support (more precisely funding and ownership) on the number of private patents, andsimultaneously, the effect of the number of private patents on government support over time.
However, the causal ordering placed the number of private patents after government ownershipand funding, which suggests that the first effect was stronger, further confirming our first
hypothesis. The results also suggested a link between government support and complexity, thereby
confirming our second hypothesis (H2). However, this link was not direct. Government support(funding and ownership) fueled complexity growth by increasing the number of patented
innovations. A direct boost to complexity comes from innovation activities that cites government

30
R&D.15 However, as in many cases, this research is not under the direct control of the governmentand represents an indirect mechanism. In addition, the relationship (the indirect link between
government support and complexity growth through the number of private patents) only existed
over a shorter period (with a lag by one period [B1/t-1]), not over a longer period (with a lag by
two periods [B2/t-2]).

Figure 4a: Graphical representation of structural vector autoregression model results from
Table 2 (one time lag).
Notes: The solid arrows indicate positive effects. The size of the arrow reflects the magnitude of each effect (thin:
0.05–0.19; medium: 0.2–0.39; thick: ≥0.4). For simplicity and to maximize visibility, this figure does not showcoefficients smaller than 0.05 and autocorrelations. We provide a graph with all effects in the appendix (Figure A2a).
Instantaneous effects are shown on the right side of the figure, lagged effects with one time lag (B1) on the left side.
The row order corresponds to the empirically inferred causal ordering: government ownership first, followed bygovernment funding, number of private patents, government citing, and, lastly, complexity.

15

We inferred the indirect link between government support and complexity from the chain of positive effects fromgovernment ownership to government funding, government funding to the number of private patents, and the numberof private patents to complexity (shown in Figure 4a). The more direct link between government support andcomplexity is shown in Figure 4b, which indicates the positive effect of government citing on complexity.

31

Figure 4b: Graphical representation of structural vector autoregression model results from
Table 2 (two time lags).
Notes: The solid arrows indicate positive effects and the dashed arrows negative effects. The size of the arrow reflects
the magnitude of each effect (thin: 0.03–0.19; medium: 0.2–0.39; thick: ≥0.4; the negative scale is equivalent[thin: -0.03 to -0.19, etc.]). For simplicity and to maximize visibility, this figure does not show coefficients smaller
than 0.05 and autocorrelations. We provide a graph with all effects in the appendix (Figure A2b). For simplicity,
instantaneous effects are not shown again on the right side of the figure, but only lagged effects with two lags (B2) are
shown on the left side. The row order corresponds to the empirically inferred causal ordering: government ownershipfirst, followed by government funding, number of private patents, government citing, and, lastly, complexity.

4.3 Robustness of the results
To test the validity and reliability of our main results, we performed several robustness checks
using different model specifications and data subsets. The details of these robustness models andtheir specifications are provided in Table A12 in the appendix.16
First, we used two- and four-year periods (models 2 and 3 in Table A12) instead of the three-year
periods in our main model (model 1 in Table A12). The main results remained consistent across16

All robustness models fulfilled the model fit characteristics of triangularity of the instantaneous effects matrix 𝑩
and lack of autocorrelation of the residuals.

32
different periods. Government support was positively associated with the number of private
patents, which in turn was positively associated with increased technological complexity. These
effects were significant both within time and over time.
Second, we accounted for potential effects specific to a technological field by including fixed
effects at the level of the technological field in model 5 (Table A12). We also followed the approachof Coad and Grassano (2018) and developed a model 6 using standardized growth rates andtechnological-field fixed effects (Table A12). The inclusion of the technological-field effects did
not alter the main results. Government support continued to have a positive effect on the numberof private patents, which was the main driver of the increase in technological complexity. The
coefficients for government support and private patents changed in size due to standardization, butthey were similar in relative magnitude to those in our main model.
Third, we tested the stationarity assumption by focusing on technologies for which this assumption
was successfully tested in model 4 (Table A12).17 The main results were robust to this restriction.
Government support remained a significant predictor of private patents, which in turn predicted
technological complexity.
In summary, all our robustness models substantiated our main results. They confirmed thatgovernment support drove the number of private patents, which was the main driver of increased
technological complexity over a rather short period. Our robustness models did not confirm thenegative effect of government funding on complexity growth over a longer period (i.e., with a lagof more than one period); rather, they indicated that there was no relationship between government

17

We applied a strict approach to stationarity testing of panel data by performing an augmented Dickey–Fuller testfor every variable of each technology. In this robustness model, we only included the technologies for which at least
one variable per technology was confirmed to be stationary. This led to the inclusion of 326 technologies.

33
funding and complexity growth over a longer period. We also found that these effects were robust
to different periods, technological field effects, and assumption of stationarity.

5 Conclusion
One of the long-standing features of technological progress is the increasing complexity oftechnologies (Aunger, 2010; Broekel, 2019; Hidalgo, 2015; Jones, 2009; Strumsky et al., 2010;
van der Wouden, 2020). This trend reflects the cumulative nature of knowledge and its growing
specialization and diversification (Hidalgo, 2015). However, it has only gained more attention fromscientists in recent times. Concurrently, a contemporary trend is spotlighting the rising reliance ofinnovation processes on government support. This shift is manifested as the expanding presence ofpatents owned by the government, those funded by government sources, and those citing
government research and development (Fleming et al., 2019).
This study proposed a relationship between the two trends. More precisely, we argued that complex
domains and higher levels of technological complexity may go hand in hand with economic andsocial benefits that the public sector seeks to harness. Thus, the public sector, in turn, pushes thelevels of complexity of technologies by providing extra resources. Alternatively, we posited that
escalating government support is crucial for maintaining a consistent pace of technologicalprogress due to growing complexity, which amplifies resource demands.
We tested these two arguments using US patent data disaggregated into 561 individual technologies
for the period between 1981 and 2016. We distinguished three categories of government support
as outlined by Fleming et al. (2019). Technological complexity was calculated using the structural
diversity index proposed by Broekel (2019) and the VAR-LiNGAM method was applied to analyze
the empirical relationships. The VAR-LiNGAM method supports a causal interpretation

34
conditional on its reliance on observational data (Coad and Grassano, 2018; Hyvärinen et al., 2010;
Moneta et al., 2010).
Our analysis identified government support as a driving force behind the advancement oftechnological complexity. Government ownership and funding of innovation activities increased
private interest in a technology (evident in the growth in the number of private patents). The
subsequent increase in innovation activities in these domains (as indicated by growing patent
numbers) contributed to the growth of a technology’s complexity. In addition, innovations citing
government R&D facilitated further complexity advancements.
While complexity is not a dimension informing the allocation of government support (Aschhoff,
2008; Yin et al., 2022), our study showed support to be skewed toward more complex technologies.
Accordingly, complexity seems to be correlated with other dimensions considered in the design ofinnovation policy. For example, many of the technologies needed for the sustainability transition
are complex (Barbieri et al., 2020). In the USA, the massive support for military technologies islikely to play a similar role, as military considerations shape significant portions of the government
resource allocation across technologies (as mentioned by Zhang et al., 2022, for the Cold War
period). In addition, our study suggests that it is because of pursuing such goals that policy(involuntarily) advances technological complexity.
By identifying such an impact of innovation policy, this study advances the growing literature on(technological) complexity by addressing a neglected question: What factors drive the evolution ofcomplexity over time? Previous studies have often assumed that complexity grows as a “naturalprocess” resulting from the cumulative nature of knowledge (Balland et al., 2022; Hidalgo, 2015).
However, this does not account for the temporal variation in the rate of complexity increase(Broekel, 2019; van der Wouden, 2020). Our findings suggest that societal conditions, such as the35level of government support for innovation in complex technologies, influence the pace of thisprocess. This invites further research to explore other factors that shape the direction and speed ofcomplexity’s development and assess their relative importance.
Our study has several policy implications. Complex technologies tend to be spatially concentrated
and diffuse slowly across regions (Balland & Rigby, 2019; Broekel et al., 2023), which implies
that the support of complex technologies may exacerbate spatial inequalities in R&D. Moreover,complex technologies have high economic growth potential (Hidalgo & Hausman, 2009; Mewes& Broekel, 2022), which may further widen the economic gap between regions. Importantly, thisoccurs even without policy explicitly targeting complex technologies, e.g., Germany’s former
HighTech strategy (BMBF, 2006), as many complex technologies are related to and benefit frompolicy pursuing other socially or economically desirable goals, such as achieving the sustainability
transition. Therefore, policy faces a trade-off between fostering (directly or indirectly)
technological progress in complex domains and promoting spatial economic cohesion.
This trade-off also needs to be considered in the debate about using complexity and relatedness inregional smart-specialization policies (Balland et al., 2019). Here, (technological) complexity isargued to indicate the attractiveness of domains for regional diversification. This makes complexity
an explicit policy dimension. Our results raise the question of whether such a policy position isnecessary or desirable.
In the case of necessity, we showed that government R&D support in the USA is already skewed
toward more complex technologies. It can be argued that by focusing on other dimensions, such assustainability and digitalization, policy ensures indirect support for complex technologies.
However, we also observed that a large part of policy influence stems from stimulating private
R&D activities. This suggests that private investments in these domains are limited until policy

36
ensures government support or helps overcome bottlenecks. Therefore, further research is needed
to clearly identify differences in the role played by government support between simple andcomplex technologies.
In the case of desirability, our study casts some doubts on government R&D supporting complex
technologies. Despite potential positive effects such as larger growth potentials and increased
diversification opportunities, government support pushes the levels of technological complexity
further than the levels achieved without government intervention. Higher complexity makes
progress harder and more expensive. Hence, today’s benefits may come at the price of moredifficult and resource-intensive research in the future. This is not just a theoretical notion, as theresults of Strumsky et al. (2010) and Bloom et al. (2017) suggest. Research has become morecostly, and R&D productivity has been falling. It may not be too far-fetched to hypothesize,
although evidence is lacking, that declining R&D productivity is related to growing complexity. If
so, the support of complex technologies may have a negative side effect: to advance thesetechnologies, more resources need to be mobilized. This implies that, if qualitative dimensions ofresearch output are disregarded, government support for complex technologies may reduce
research productivity in the future.
Due to government intervention or other factors, humankind may have created and widened thegap between the capabilities and requirements of R&D. This might be driven by the diminishingreturns of the last scientific revolution and the need for a new technological paradigm that boosts
innovation and reduces resource requirements of R&D. Artificial intelligence may have thepotential to turn these developments around. We currently lack the evidence to support thesearguments and call for more research. Whether research productivity can be adapted by taking
output quality into account may be debated, for instance, by looking at the levels of complexity

37
achieved. Our study confirms that political decisions are associated with not only the direction oftechnological advancement but also the speed at which future R&D becomes increasingly
expensive.
Another implication of this study is concerned with the use of different types of government
support. We observed variations in their impact, which depended on the levels of complexity ofthe technologies. Hence, when designing and evaluating R&D support policies, attention needs tobe paid to the level of technological complexity. However, we lacked information about the actual
costs of the types of government support and, therefore, could not assess their effectiveness atvarying levels of technological complexity. Nevertheless, our study may encourage further
research on this issue.
Crucially, these implications are derived from an empirical study with several limitations that may
affect the findings. Most importantly, we did not observe the true investments in R&D, nor theexact share of the government’s contribution to it. The empirical insights were also restricted topatented innovation activities. Since such innovations usually have market potential and are rather
application-oriented, market failures are less likely or are already reduced by the patent system.
That is, our empirical analysis focused on the part of the R&D system for which the relevance of(other) government support is potentially the least likely. Moreover, because of our use of patentdata, we could not observe service and process innovations, which constitute a large proportion of
the innovation output. Other shortcomings of our empirical study are the lack of information on
the importance of military technologies and the specific aims of policy schemes that are importantfactors for the distribution of R&D support. In addition, the category “Government R&D cited” israther broad. It captures patents that refer to patents and publications funded or owned by thegovernment or affiliated with a government agency. It would be interesting to subdivide this38
category in future research. Hence, further studies and better data are needed to disentangle theinterplay between technological complexity, research productivity, and government support for
R&D.

Declaration of generative AI and AI-assisted technologies in the writing process
During the preparation of this work the author(s) used ChatGPT in order to improve language and readability. Afterusing this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for thecontent of the publication.

39

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Appendix
Details of the empirical model
Measuring structural diversity
The structural diversity measure starts from the idea that technologies are developed through (re-)
combinatorial processes and that they can be expressed as (combinatorial) networks of their(knowledge) components. These networks are characterized by different (sub)topologies, i.e., ways
in which the knowledge components are combined. For instance, some components are combinedin a star-like fashion, while others are in the form of a lattice. Both topologies require very little
information for their individual description; however, the information required to describe theentire combinatorial network will generally increase with the number of distinct topologies thatcharacterize its structure. Broekel (2019) argued that the increasing information content of
networks with greater diversities of (sub)topologies reflects the levels of complexity oftechnologies, as the information content is correlated with the difficulty of inventing, learning, andmastering it.
In practice, this diversity can be approximated with the network diversity score (NDS) (EmmertStreib & Dehmer, 2012) applied to the binarized co-occurrence network of 10-digit CPC codes(G ) for all patents that are associated with technology c (four-digit CPC code). Network nodes (V)are the 10-digit CPC codes, and links (E) are established whenever these co-occur on a patent thatfeatures the four-digit CPC code representing the focal technology (Broekel, 2019).18 Following
Emmert-Streib and Dehmer (2012), from the empirically observed network G , a series of G
subnetworks were randomly drawn from G by means of a Walktrap algorithm with w = 200 steps
and an initial random sample of S = 125 nodes. For each subnetwork, an individual network
diversity (iNDS) score was calculated:
iNDS(G ) =

α
v

∗r
∗v

)

,

where α= represented the share of modules in the network, M was their number, and V
was the number of nodes. Modules were identified with a random walk approach, as suggested byPons and Latapy (2006). αwas multiplied by the ratio of graphlets of sizes three and four.
The product obtained was set in relation to the product of the variability of the network's Laplacian(∧( )((L) matrix (ν =) and the variance of the module sizes m (v=). The( )∧( )subsampling of networks yields S distinct values of iNDS(G ), for which we calculated the average
to obtain the final value of the NDS:
1
NDS({G |G }) = ∑iNDS(G ).
S
The measure represents the structural diversity of a technology’s combinatorial network. It wasconverted to the final measure of technological complexity structural diversity (cpx ) with thefollowing equation:

18

The complexity values are freely downloadable from www.tombroekel.de.

47cpx = log

1.
NDS({G |G })The conversion ensured that the empirical values were in an application-friendly range and thatlarge values corresponded to higher levels of complexity.
Patent numbers fluctuate strongly for smaller technologies, which may introduce substantial
distortions to the measure. To reduce this effect, we used a three-year moving window approach.
That is, the combinatorial network of a technology in the year 𝑡 included all patents in the years 𝑡
to 𝑡 − 2 that featured its four-digit CPC code. Finally, we had one individual complexity score foreach of the 655 technologies per year (corresponding to the four-digit CPC classes).
The estimation procedure of VAR-LiNGAM
Structural vector autoregression (SVAR) models are commonly used to explore the causal
relationships between a set of variables (Coad & Binder, 2014; Coad & Grassano, 2019; Lanne etal., 2017; Moneta et al., 2013; Pearl, 2009; Spirtes et al., 2000). In this study, a Vector
Autoregressive Linear Non-Gaussian Acyclic model (VAR-LiNGAM) (Hyvärinen et al., 2010;
Moneta et al., 2013) was estimated to infer the relationship between government support andtechnological complexity. The SVAR model with 𝑞 lags was defined as
𝒚 = 𝑩 𝒚 +∑𝑩𝒚

+ 𝜺 (6),

where 𝒚 was the vector of variables at time 𝑡, 𝑩 was the matrix of instantaneous effects, 𝑩 , with𝑖 = 1, … , 𝑞, were the matrices of lagged effects, and 𝜺 was the vector of residuals. For the VARLiNGAM approach, the structural residuals 𝜺𝒕 were assumed to be independent of each other andover time and to have non-Gaussian distributions. Furthermore, VAR-LiNGAM assumed that 𝑩
could be permuted to be lower triangularity, implying that the instantaneous (causal) effects wereacyclic. Note that inferring causality from data using probability distribution information is a wellestablished concept (Pearl, 2009; Spirtes et al., 2000).
For the estimation of SVAR models, and in particular the VAR-LiNGAM model, three steps arenecessary (Hamilton, 1994; Hyvärinen et al., 2010):
1. Estimation of the coefficients of the reduced-form VAR model:
𝒚 = ∑

𝑨𝒚

+ 𝒆 (7).

As stated above, in our case, the variables 𝒚 were stationary such that ordinary leastsquares (OLS) or least absolute deviations (LAD) could be used to estimate the coefficientsof the lagged effects. Note that the reduced-form VAR model does not include
instantaneous effects. Several information criteria exist (Akaike Information Criterion,
Hannan–Quinn Information Criterion, and Schwarz Information Criterion) for selecting thenumber of lags 𝑞.
2. Estimation of the instantaneous causal effects matrix using the LiNGAM approach(Shimizu et al., 2006):
𝒆 = 𝑩 𝒆 + 𝜺 (8).

48
Re-writing this equation yields 𝒆 = (𝑰 − 𝑩 ) 𝜺 , where 𝑰 denotes the identity matrix.
With the non-Gaussianity assumption of the structural residuals 𝜺𝒕 and by applying
independent component analysis (ICA; Hyvärinen et al., 2001) to the reduced-form
residuals 𝒆 , the matrix (𝑰 − 𝑩𝟎 ) 𝟏 and the statistically independent residuals 𝜺 can be
identified up to the scaling and permutation indeterminacy inherent in ICA. These
indeterminacies can be resolved using the lower triangularity assumption of 𝑩𝟎. For thealgorithmic details see Shimizu et al. (2006); the intermediate results of this step of thealgorithm are shown in the appendix. Finally, the matrix 𝑩𝟎 can be straightforwardly
inferred. 
3. Calculation of the lagged causal effects matrices of the SVAR model:
𝑩 = (𝑰 − 𝑩 )𝑨 , 𝑖 = 1, … , 𝑞 (9).
The code package with an implementation of VAR-LiNGAM in R released by Moneta et al. (2013)
was used in this study with minor adaptations to estimate the models. The estimates were calculated
and compared based on the OLS and LAD methods with several lags. The information criteria for
selecting the number of lags to be considered (Akaike Information Criterion, Hannan–Quinn
Information Criterion, and Schwarz Information Criterion; see Tables A7 and A8 in the appendix)
delivered rather similar numbers for both estimation techniques (OLS and LAD). Thus, a specificmodel was not clearly indicated based on these information criteria. Further characteristics of awell-fitting model are the triangularity of the instantaneous effects matrix 𝑩 (see Tables A7 andA8 in the appendix) and the lack of autocorrelation of the residuals. The triangularity, i.e.,
acyclicity of the instantaneous effects, was nicely given in the OLS models with two and three lags
and the LAD models with one to five lags. The lower triangularity of the matrix 𝑩𝟎 , i.e., that there
were no feedback loops within one time period, was also backed up by theoretical considerations:
government support influencing technological complexity or vice versa is a slow process. Since
the residual autocorrelations were not significant in the OLS models but significant (though small)in the LAD models, we proceeded with OLS and two lags.19 After estimating the reduced-form
VAR model (results are reported in Table A10 in the appendix), we investigated the distribution of
the residuals. Histograms and QQ plots of the residuals (Figure A1 in the appendix), as well as thenormality tests (Table A11 in the appendix), implied that all residuals were non-Gaussian. Thisconfirmed the applicability of the VAR-LiNGAM approach. Furthermore, a block-bootstrap
approach, following the implementation of the code package of Moneta et al. (2013), using 500
bootstrap samples was adopted not only to evaluate the robustness of the model but also to infer
statistical significance of the estimated coefficients using a t-test. A further robustness analysis was
carried out using different pre-processing steps of the data (see section 4.3).
LiNGAM and ICA: Estimation of the instantaneous effects matrix
Above the estimation procedure of VAR-LiNGAM is explained. In Step 2, the LiNGAM method
was used to infer the instantaneous effects matrix 𝐵 . LiNGAM is based on ICA, which is19

Due to our data structure and theoretical considerations, we decided to proceed with a time lag of two instead ofthree. Given our data structure (aggregation into three-year periods), a lag of two already led to an observational periodof six years. We saw this as a good compromise between reliably observing an effect of government support and thegenerally slow phenomenon of complexity growth.

49
accompanied by scaling and permutation indeterminacy, both of which can be resolved due to thelower triangularity assumption. Here, we show the single steps of how matrix 𝐵 was calculated.
Following Shimizu et al. (2006), the ICA model is given by 𝑒 = (𝐼 − 𝐵 ) 𝜀 , with 𝐴 ≔(𝐼 − 𝐵 ) being the mixing matrix and 𝑊 ≔ 𝐴 = (𝐼 − 𝐵 ) being the un-mixing matrix. The
ICA model was estimated using the R package FastICA (Hyvärinen et al., 2001). 20
A column-permutation indeterminacy of the mixing matrix was inherent in the ICA, with rowpermutation indeterminacy of the un-mixing matrix and scaling indeterminacy. The latter was
solved by permuting the rows of 𝑊 such that the sum of the inverted, absolute value of the diagonal
entries of 𝑊 was minimized (if there were no estimation errors, there was only one permutation of
the rows such that all entries along the diagonal were non-zero). With the small dimensionality offive variables, the permutation was performed using a brute force approach, i.e., by calculating thesum for each row permutation. The matrices are shown in Table A1 below. In the first row, the unmixing matrix 𝑊 is listed, showing that each row of 𝑊 has exactly one entry which is larger than
all other entries of that row (highlighted in bold). This is a sign that the ICA model fits the datawell. The rows were permuted in such a way that these large entries were shown in the diagonal
results in the matrix (shown in the second row of Table A1). Then, each row was divided by its
diagonal element resulting in 𝑊 with all ones on the diagonal (the third row in the table).
A first estimate of the instantaneous effects 𝐵 is then given by 𝐵 = 𝐼 − 𝑊 , shown in the fourth
row of Table A1. Again, since there were small estimation errors when estimating matrix 𝑊 , thismatrix could not be permuted to strictly lower triangularity. Therefore, by simultaneous row andcolumn permutations, a matrix that minimized the entries in the upper triangle was sought. In
addition, a brute force approach was used since it was feasible with the small number of only fivevariables. The simultaneous row and column permutation yielding the best lower triangular matrix
was (4, 2, 5, 3, 1). The resulting matrix is shown in the fifth row of Table A1, which indicatesthat all entries are very small, except for the one in the third row and fourth column (in italics,
0.1041), although compared to the largest values, it is still rather small (e.g., 0.4434 or 0.1659).
The final matrix 𝐵 was then calculated with the Cholesky decomposition using the inferred orderof the LiNGAM model. This is a common approach for estimating the instantaneous effects matrix
when the causal order is known and follows the VAR-LiNGAM code package of Moneta et al.
(2013). These matrices are shown in rows 6 and 7 of Table A1. There are some minor differencescompared to the instantaneous effects matrix calculated using LiNGAM; however, the signs andrough magnitude of the values agree.
Un-mixing matrix 𝑊

1.0348 0.0195 -0.1879 -0.0051 -0.3880-0.0238 -0.3858 2.3258 -0.1302 -0.5835
0.0440 0.2025 0.3076 0.1136 -2.9561
0.0056 -2.1120 0.0923 0.9365 0.0634-0.0124 -0.1191 0.0192 -2.0091 0.0070

20

The R-package is available at https://www.rdocumentation.org/packages/fastICA/versions/1.2-3/topics/fastICA.

50
Row-permuted version of 𝑊
minimizing the inverse, absolute valueof the diagonal element

1.0348 0.0195 -0.1879 -0.0051 -0.3880
0.0056 -2.1120 0.0923 0.9365 0.0634-0.0238 -0.3858 2.3258 -0.1302 -0.5835-0.0124 -0.1191 0.0192 -2.0091 0.0070
0.0440 0.2025 0.3076 0.1136 -2.9561

Row-permuted and with unit diagonal
matrix 𝑊

1.0000 0.0188 -0.1816 -0.0049 -0.3749-0.0027 1.0000 -0.0437 -0.4434 -0.0300-0.0103 -0.1659 1.0000 -0.0560 -0.2509
0.0062 0.0593 -0.0096 1.0000 -0.0035-0.0149 -0.0685 -0.1041 -0.0384 1.0000

Estimated instantaneous effects matrix
𝐵 before permuting it in causal order

0.0000 -0.0188 0.1816 0.0049 0.3749
0.0027 0.0000 0.0437 0.4434 0.0300
0.0103 0.1659 0.0000 0.0560 0.2509-0.0062 -0.0593 0.0096 0.0000 0.0035
0.0149 0.0685 0.1041 0.0384 0.0000

Estimated instantaneous effects matrix
𝐵 in causal order

0.0000 -0.0593 0.0035 0.0096 -0.0062
0.4434 0.0000 0.0300 0.0437 0.0027
0.0384 0.0685 0.0000 0.1041 0.0149
0.0560 0.1659 0.2509 0.0000 0.0103
0.0049 -0.0188 0.3749 0.1816 0.0000

𝐵 calculated using the Cholesky
decomposition with the inferred causal
order from LiNGAM, arranged in theoriginal order of the data

0 -0.0259 0.2199 -0.0308 0.4819
0 0.0000 0.0000 0.3987 0.0000
0 0.1874 0.0000 0.0385 0.4187
0 0.0000 0.0000 0.0000 0.0000
0 0.1164 0.0000 0.0356 0.0000

𝐵 calculated using the Cholesky
decomposition with the inferred causal
order from LiNGAM, arranged in thecausal order of the data

0.0000 0.0000 0.0000 0.0000 00.3987 0.0000 0.0000 0.0000 00.0356 0.1164 0.0000 0.0000 00.0385 0.1874 0.4187 0.0000 0-0.0308 -0.0259 0.4819 0.2199 0

Table A1. Matrices in the estimation of the instantaneous effects matrix 𝐵 .

51
VariableGovernment ownership

Government funding

Government R&D citedComplexity

Number of private patents

Definition
This variable represents the number of patents for each technology in eachperiod owned by the government. It was calculated by taking the mean valueof the yearly number within each period, taking the first difference, andperforming a log-transformation.
This variable represents the number of patents for each technology in eachperiod funded by the government. It was calculated by taking the mean valueof the yearly number within each period, taking the first difference, andperforming a log-transformation.
This variable represents the number of patents for each technology in eachperiod that cited government research. It was calculated by taking the meanvalue of the yearly number within each period, taking the first difference,and performing a log-transformation.
This variable represents the technological complexity of each technology ineach period. It was calculated using the measure of structural diversity(Broekel, 2019) and was log-transformed. For each period, we took the mean
complexity value and the first difference.
This variable represents the number of private patents for each technology
in each period. It was calculated by subtracting the number of governmentsupported patents from the total number of patents, taking the firstdifference, and performing a log-transformation.

Table A2. Definitions of variables in the main model.
Note: This table shows the five variables used in the main empirical model.

52
Variable
PeriodComplexity
mean minmax

Number of private patents
mean
min
max

Government R&D citedmean
min max

Government fundingmean
min max

Government ownership
mean
min
max

1981–1983
1984–1986
1987–1989
1990–1992
1993–1995
1996–1998
1999–2001
2002–2004
2005–2007
2008–20102011–20132014–2016
1981–1982
1983–1984
1985–1986
1987–1988
1989–1990
1991–1992
1993–1994
1995–1996
1997–1998
1999–2000
2001–2002
2003–2004
2005–2006
2007–2008
2009–20102011–20122013–20142015–2016
1981–1984

5.99
5.97
6.27
6.74
7.23
7.71
8.16
8.37
8.45
8.39
8.71
9.07
6.01
5.94
6
6.19
6.52
6.81
7.15
7.46
7.79
8.1
8.3
8.4
8.49
8.42
8.37
8.65
8.89
9.14
5.95

13.32
13.47
11.82
12.46
12.26
13.6
13.42
13.25
14.82
12.91
13.29
13.24
13.2
13.5
13.48
11.87
11.84
13.41
12.2
13.64
13.62
13.63
13.61
13.12
14.79
14.78
12.82
13.2
13.19
13.41
13.35

161.29174.67198.59221.84239.65290.02364.18358.4
326.04351.41475.35573.39112.04107.56116.78124.81144.63151.6
158.93168.99201.75240.87245.25236.88220.88209.22248.86300.59369.3
381.94
218.6

22.21
27.31
36
41.59
49.28
68
90.39
104.59111.13130.18181.22
209.5
15.04
15.77
18.76
22.16
26.48
29.05
32.21
36.41
48.66
57.97
65.65
71.49
74.13
74.38
93.32
115.48136.28140.13
30.68

6.32
7.51
7.91
9.42
10.98
14.23
17.59
17.8
17.72
21.82
31.18
35.5
4.12
4.79
4.94
4.96
5.67
6.72
7.43
7.45
10.32
11.5
12.19
11.72
11.88
11.75
15.98
19.96
23.05
23.87
8.87

5.59
5.92
4.53
5.83
6.05
4.98
4.78
4.07
3.46
3.32
4.35
4.29
3.77
3.98
3.78
3
3.27
4.11
4.26
3.42
3.35
3.28
2.81
2.76
2.33
2.14
2.33
2.82
3.05
2.8
7.72

0
0
0
0
0
0
0
0
0
0
0.53
1.17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

2715
2538
2753
2820
4358
9420
13687
15104
17834
23647
32516
44882
2026
1474
1753
1775
1921
2067
2629
4116
7033
9059
9351
10381
11815
12706
16960
20123
27049
30226
3500

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

474
602
857
1021
1248
1721
2797
3814
3860
5125
7548
9868
329
331
416
503
655
720
792
968
1342
1652
2380
2579
2583
2520
3810
4634
6084
6698
660

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

146
214
232
301
358
885
1087
852
807
1001
1381
2102
91
111
152
128
193
212
231
311
706
755
627
557
516
538
752
835
1181
1472
202

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

137
189
145
182
206
161
162
134
140
123
157
144
94
101
131
96
107
124
143
125
111
113
94
89
103
75
85
96
117
88
195

53
1985–1988
1989–1992
1993–1996
1997–2000
2001–2004
2005–2008
2009–20122013–2016

6.09
6.67
7.3
7.95
8.35
8.44
8.5
9.01

0
0
0
0
0.54
0
0.4
0.88

11.86
11.8
12.29
13.57
13.37
14.78
12.95
13.3

241.16295.71
327.92442.62481.71428.58548.38749.22

0
1
1
1
1
0
0
1

3528
3780
6745
16092
19732
24521
37083
57275

40.85
55.44
68.62
106.63137.01147.98208.39275.66

0
0
0
0
0
0
0
0

919
1375
1760
2741
4959
4949
8444
12782

9.88
12.37
14.89
21.83
23.89
23.55
35.88
46.79

0
0
0
0
0
0
0
0

280
405
524
1461
1184
1054
1587
2653

6.76
7.37
7.68
6.63
5.57
4.46
5.13
5.83

0
0
0
0
0
0
0
0

227
231
268
212
183
178
181
205

Table A3. Extensive descriptive statistics.
Note: The table shows the mean value across all technology classes and the minimum and maximum values of a technology class within a (three-year, two-year,
and four-year) period. The government support variables and the number of private patents are total numbers (no first-difference transformation and no logtransformation), and the complexity value is log-transformed (but no first-difference transformation).

54

VariableGovernment R&D
cited (sum)Government
funding (sum)Government
ownership (sum)Number of private
patents (sum)Complexity (log)Government R&D
cited (sum)Government
ownership(sum)

Government
funding (sum)Number ofprivate patents(sum)Complexity
(log)

1
0.920

1

0.879

0.942

1

0.779

0.576

0.527

1

0.546

0.512

0.411

0.452

1

Table A4. Full rank correlation analysis.
Note: This table shows the results of the rank correlation analysis performed for variables different than those in our
final model dataset as described in Table A2. The data used for this correlation analysis are cross-sectional. The
government support variables and the number of private patents are total numbers (no first-difference transformationand log-transformation) and the complexity value is log-transformed (but no first-difference transformation).

VariableGovernment
R&D cited
Government
funding
Government
ownership
Number ofprivate patents
Complexity

Government
R&D cited1

Government
funding

Government
ownership

Number ofprivate patents

0.21

1

0.13

0.39

1

0.29

0.14

0.08

1

0.14

0.05

0.03

0.20

Complexity

1

Table A5. Correlation analysis.
Note: This table shows the results of the correlation analysis performed with the final model dataset with the variables
explained in Table A2.

VariableComplexity last value
Complexity first value
Complexity mean value

Complexity last value
1
0.88
0.97

Complexity first value

Complexity mean value

1
0.96

1

Table A6. Correlation analysis of the complexity measure.
Note: This table shows the results of the correlation analysis performed for two alternative operationalizations of ourstructural diversity measure of technological complexity. We computed the correlation between the first value withina period of three years, the last value, and the mean value. The values are log-transformed, but no first-differencetransformation has been performed.

55
VariableComplexity
Government funding
Government ownership
Government R&D cited
Number of private patents

Technologies
384
384
384
384
384

AWB
0.00150.00000.00050.00000.0015DWB
0.00400.00100.00100.00050.0040SWB
0.00000.00000.00000.00050.0005

Table A7. Unit root test for all variables in the first differences (p-value).
Note: The table shows the p-values of the unit root test for all five variables in the first differences. The null hypothesisis that all series have a unit root. The alternative hypothesis is that some series are stationary. All p-values are
significant at the 0.05 level. This means that we can reject the null hypothesis. Thus, we conclude that our variables
sufficiently fulfil the stationarity assumption (in first differences).21

Lags

AkaikeHannan–Quinn

Schwarz

Triangularity of LiNGAM matrix

1-6.0174-6.0079-5.9901

Causal B only somewhat triangular2-6.2234-6.2028-6.1642

Causal B nicely triangular3-6.3481-6.3141-6.2510

Causal B nicely triangular4-6.3663-6.3158-6.2231

Causal B only somewhat triangular5-6.3783-6.3073-6.1780

Causal B only somewhat triangular6-6.4739-6.3761-6.2003

Causal B only somewhat triangular7-6.5094-6.3751-6.1374

Causal B only somewhat triangular

Table A8. Lag selection in the ordinary least squares analysis.
Note: For the lag selection, three information criteria (Akaike, Hannan–Quinn, and Schwarz) were used. The maximum
number of lags possible was 7, so they were calculated with all values. The triangularity of the instantaneous effects
matrix was judged heuristically based on the percentage of the added values in the upper triangle compared to the totalsum of all matrix entries. If less than 5% were in the upper triangle, the matrix was judged as “nicely triangular”; if
between 5% and 20%, it was judged as “somewhat triangular”; and if otherwise, as “not triangular at all,” following
the initial implementation of the VAR-LiNGAM code package (Moneta et al., 2013).

21

The unit root test required a balanced panel and a certain level of variability in the values of the variables; theserequirements were not fulfilled for all the technologies. At the level of each technology and variable, the same value
could not occur eight or more times. This occurred if a technology had too often received no government support.
Thus, to perform the unit root test, we had to restrict the data to technologies (cpcs) with sufficient variability (i.e.,
occurrences of government support). This restricted the data for the unit root test to 384 of the 561 technologies.

56
Lags

AkaikeHannan–Quinn

Schwarz

Triangularity of LiNGAM matrix

1-5.9166-5.9071-5.8893

Causal B nicely triangular2-6.0987-6.0780-6.0394

Causal B nicely triangular3-6.1658-6.1317-6.0686

Causal B nicely triangular4-6.1882-6.1378-6.0451

Causal B nicely triangular5-6.2126-6.1415-6.0122

Causal B nicely triangular6-6.2770-6.1791-6.0033

Causal B only somewhat triangular7-6.3109-6.1766-5.9389

Causal B only somewhat triangular

Table A9. Lag selection in the least absolute deviations (LAD) analysis.
Note: For the lag selection, three information criteria (Akaike, Hannan–Quinn, and Schwarz) were used. The maximum
number of lags possible was 7; therefore, they were calculated with all the values. The triangularity of the instantaneous
effects matrix was judged heuristically based on the percentage of the added values in the upper triangle compared tothe total sum of all matrix entries. If less than 5% were in the upper triangle, the matrix was judged as “nicely
triangular”; if between 5% and 20%, it was judged as “somewhat triangular”; if otherwise, as “not triangular at all,”following the initial implementation of the VAR-LiNGAM code package (Moneta et al., 2013).

57
A1

A2

Complexity
(cpx)

Gov.
funding

Gov.
R&D
cited

Gov.
ownership

No. ofprivatepatents

Complexity
(cpx)

Gov.
funding

Gov.
R&D
cited

Gov.
ownership

No. ofprivatepatentscoeff-0.4107-0.00290.05080.01520.5434-0.18180.00960.0453-0.0204

0.0629SD

0.01880.03640.0447

0.03670.06360.01770.03530.0406

0.0344

0.052

coeff

0.0043-0.4825

0.071

0.00280.1271-0.0037-0.20240.03710.00230.0191SD

0.00470.01680.01480.01830.02020.00470.01590.01340.01530.0167Gov. R&D
cited

coeff

0.0172

0.0943-0.44480.00980.29070.00290.0718-0.1946

0.01930.1243SD

0.00530.01340.01750.012

0.02350.00540.01330.01560.01160.0185Gov.
ownership

coeff

0.00510.02920.0301-0.5276

0.0779-0.0056

0.03490.0173-0.2346

0.0039SD

0.005

0.01320.01220.01840.02040.00490.01650.01240.01920.0171

N. of priv.
patents

coeff

0.0151

0.02240.07520.0002-0.0989

0.00210.00590.022

0.0061-0.0293SD

0.00420.00890.01070.00940.02350.00420.00990.01120.01160.0148Complexity(cpx)
Gov. funding

Table A10. Results of the vector autoregression model.

58
MeasureShapiro–Wilk
Shapiro–Francia
Jarque–Bera

Technologicalcomplexity
2.5517e-39
5.1790e-38
0Government
funding
2.2965e-19
5.0228e-19
0Government
R&D cited
1.8902e-48
4.7964e-20
0Government
ownership
3.8140e-31
3.0972e-30
0Number ofprivate patents
1.7508e-26
7.9308e-260Table A11. P-values of the normality tests to confirm non-Gaussianity.
Note: The normality tests (Shapiro–Wilk, Shapiro–Francia, and Jarque–Bera) all resulted in very small p-values,
indicating that the null hypothesis that the residuals were normally distributed should be rejected.

59
Model

Specifications

Causalordering
Gov.
ownership,
Gov. funding,
No. of private
patents, Gov.
R&D cited,
Complexity

Bootstrap

2-year periods(561
technologies), 2
lags

Gov.
ownership,
Gov. funding,
No. of private
patents, Gov.
R&D cited,
Complexity

500
samples,
320 withsame order(64%)

4-year periods(561
technologies), 2
lags

Gov.
ownership,
No. of private
patent, Gov.
funding, Gov.
R&D cited,500
samples,
151 withsame order(30%)

3-year periods(561
technologies), 2
lags
1
(main
model)

500
samples,
324 withsame order
(65%)

2

3

Result compared to the main model (Model 1) result

B0: Equal significance of coefficients and effectdirection
B1: Nearly equal significance of coefficients (equal
effect direction of significant coefficients)
One additional significantly positive effect from
Gov. funding  Gov. ownership
B2: Differences in the significance of coefficients (equal
effect direction of significant coefficients)
Additional positive effects from:No. of private patents  Gov. funding
No. of private patents  Gov. ownership
Gov. funding  N. of priv. patents
Gov. R&D cited  No. of private patents
Lost significant effects (effects that were significant in
our main model but not here):Gov. funding  Complexity
Gov. R&D cited  Complexity
B0: Nearly equal significance of coefficients (equal
effect direction of significant coefficients).
One additional significantly positive effect fromNo. of private patents  Gov. funding
One lost significant effect from
Gov. funding  No. of private patents

Interpretation
Government support is driving thenumber of private patents, which is themain driver of an increase intechnological complexity. We observed
this effect within time (B0) and over time
(B1, corresponding to a period of 3
years). The effect did not hold over alonger period, when the number ofprivate patents was still driving
complexity, but government support was
not driving the number of private patents
anymore (B2, corresponding to a periodof 6 years). Instead, over a longer period,
government funding negatively
influenced complexity.
As in our main model, government
support drove the number of private
patents, which was the main driver of theincrease in technological complexity. We
observed this effect within time (B0) andover time (B1 and B2, corresponding to aperiod of 4 years).

As in our main model, government
support drove the number of private
patents, which was the main driver of theincrease in technological complexity. We
observed this effect within time (B0) andover time (B1, corresponding to a period

60Complexity(different thanin our mainmodel)

43-year periods,
only withtechnologies forwhich the unit
root test runs inwhich at least
one variable pertechnology wasstationary 
326technologies), 2
lags

Gov.
ownership,
Gov. funding,
No. of private
patents, Gov.
R&D cited,
Complexity

500
samples,
205 withsame order(41%)

B1: Nearly equal significance of coefficients (equal
effect direction of significant coefficients)
Two additional significantly positive effects from
Gov. ownership  No. of private patents
Gov. funding  Gov. ownership
Two lost significant effects from
Gov. funding  No. of private patents
No. of private patents  No. of private patents(negative autocorrelation)
B2: Differences in the significance of coefficients (equal
effect direction of significant coefficients)
Additional positive effects from:No. of private patents Gov. funding
Gov. ownership  Gov. R&D cited
Gov. funding  Gov. ownership
Lost significant effect from
Gov. R&D cited  Complexity
Gov. R&D cited  Gov. funding
Gov. funding  Complexity
B0: Nearly equal significance of coefficients (equal
effect direction of significant coefficients).
One lost significant effect from
Gov. ownership  Gov. R&D cited
B1: Nearly equal significance of coefficients (equal
effect direction of significant coefficients).
Two lost significant effects from
Gov. R&D cited  Gov. funding
No. of private patents  Gov. ownership
B2: Differences in the significance of coefficients (equal
effect direction of significant coefficients).
Now positive autocorrelations (all variables
apart from no. of private patents) instead of
negative (as in the main model)
Two lost significant effects from
Gov. funding  Complexity
Gov. R&D cited  Gov. funding
Additional significantly positive effects from:of 4 years). In this specification,
government ownership was relevant for
an increase in private patents. We foundno relationship between government
support and complexity over a longer
period (B2, corresponding to a period of
8 years).

As in our main model, government
support drove the number of private
patents, which was the main driver of theincrease in technological complexity. We
observed this effect within time (B0) andover time (B1, corresponding to a periodof 3 years).

61

5

6

3-year periods,
pre-process:estimation ofmedianregression withtechnologicalfield dummies
and taking theresiduals for theestimation (561technologies), 2
lags
Same as in 5with theaddition ofstandardizationof growth rates
with a mean of 0
and deviation of
1 (561technologies), 2
lags

Gov.
ownership,
Gov. funding,
No. of private
patents, Gov.
R&D cited,
Complexity

500
samples,
326 withsame order
(65%)

Gov.
ownership,
Gov. funding,
No. of private
patents, Gov.
citing,Complexity

500
samples,
204 withsame order(40%)

No. of private patents  Gov. funding
B0: Equal significance of coefficients and effectdirection.
B1: Equal significance of coefficients and effectdirection
B2: Nearly equal significance of coefficients (equal
effect direction of significant coefficients).
Two lost significant effects from
Gov. funding  Complexity
Gov. citing  Gov. funding

B0: Equal significance of coefficients and effectdirection
B1: Equal significance of coefficients and effectdirection
B2: Nearly equal significance of coefficients (equal
effect direction of significant coefficients)
Two lost significant effect from
Gov. funding  Complexity
Gov. R&D cited  Gov. funding

Table A12. Detailed information on robustness models.

As in our main model specification, we
observed government support driving thenumber of private patents, which was themain driver of the increase intechnological complexity. We observed
this effect within time (B0) and over time
(B1, corresponding to a period of 3
years). The technological field did not
influence this relationship.

As in our main model specification, we
observed government support driving thenumber of private patents, which was themain driver of the increase intechnological complexity. We observed
this effect within time (B0) and over time
(B1, corresponding to a period of 3
years). We observed a change incoefficient size due to thestandardization, but the relationshipbetween the coefficients in terms of size
corresponded to our main model.

62

Figure A1: Histograms and quantile-quantile (QQ) plots to confirm non-Gaussian distribution.
Note: The top row shows histograms of the residuals overlaid with the Gaussian distribution with the same mean andvariance. In all plots, the histograms deviate from this reference distribution. The bottom row shows QQ plots of thesame residuals. Both plots indicate non-Gaussianity of the residuals. The variable order of the plots is (1)technological complexity, (2) government funding, (3) government R&D cited, (4) government ownership, and (5)number of private patents.

63

(a)

(b)
Figure A2 (a and b): Full graphical representation of structural vector autoregression resultsfrom Table 2.
Notes: Solid arrows indicate significant positive effects, dashed arrows significant negative effects. The size of thearrow reflects the magnitude of each effect (thin: 0.03–0.19; medium: 0.2–0.39; thick: ≥0.4; equivalent for the negative
scale thin: -0.03 to -0.19, etc.). For simplicity and to maximize visibility, this figure does not show autocorrelations.
Instantaneous effects are shown on the right side of Figure A2a, and lagged effects on the left side (with a lag of one
period in A2a and with a lag of two periods in A2b). The row order corresponds to the empirically inferred causal
ordering: government ownership first, followed by government funding, number of private patents, government citing,and, lastly, complexity.

64(a) Least absolute deviations (LAD) estimator(b) Ordinary least squares (OLS) estimator
Figure A3 (a and b): Frequencies of inferred causal orders.
Note: The two panels show which causal orders were inferred among the bootstrap samples (for OLS and LAD). While
there is no strict rule for what constitutes a “good agreement” in bootstrap samples, a higher percentage of consistent
results generally indicates more robust findings. There are in total 120 possible orderings with five variables; therefore,
inferring 65–80% of the times (with OLS and LAD) the exact same ordering is far beyond random (which would beless than 1% of the times, i.e., about 4 out of the 500 bootstrap samples). Some variability is expected when usingbootstrapping, especially with smaller sample sizes.

65(a) Least absolute deviations (LAD) estimator(b) Ordinary least squares (OLS) estimator
Figure A4 (a and b): Variable positioning in the causal ordering.
Note: As mentioned before, some variability is expected when using bootstrapping, especially with smaller sample sizes. The key was to assess whether thisvariability significantly impacted the interpretations and conclusions of our study. These figures show how often each variable was at a particular position in thecausal ordering (for OLS and LAD). Our key rankings of complexity (cpx in the plots) being the last and government ownership (owned in the plots) being the firstin the causal order remain largely consistent across bootstrap samples (more than 90% for both OLS and LAD). We used this to indicate a trend despite thevariability.