Proximities and the Intensity of Scientific Relations

Abstract

Several types of proximity affect knowledge flows with different strength. Insufficient attention has been paid to the interrelations between such forms of proximity at the same time, each one assumed to facilitate the flow of goods, ideas, and spillovers on its own but not in relation to one another. Moreover, if decreasing returns have been conceptually attributed to proximity effects on the intensity of scientific cooperation and learning processes, empirical evidence about nonlinearities in different proximity effects has never been demonstrated. This article aims to fill these gaps. Results on all Nomenclature of Territorial Units for Statistics (NUTS2) regions of the 27 Countries of the European Union (EU27) point toward the existence and relevance of synergic effects between different types of proximity. In particular, while social proximity has a positive impact on scientific cooperation, with decreasing magnitude as spatial distance increases, results on cognitive and technological proximity suggest that some form of complementarity seems to exist with spatial distance. In fact, when spatial distance increases, in order to cooperate, regions must also be cognitively and technologically close.

Keywords

technological social cognitive proximities synergies nonlinearities scientific collaborations

Introduction

Since the seminal contributions by early location theorists, space (and in particular geography) has been considered as a major factor hampering or, at times, facilitating, economic interactions.¹

More recently, some additional reflections emerged on the role of spatial proximity. Firstly, spatial proximity may actually hide other types of similarities among agents in the social, technological, and cognitive sphere, and in this sense is a proxy for other kinds of proximities, like social and cognitive proximities, that are higher in compact geographical areas. Secondly, the space where economic interactions take place is much more complex than that summarized by pure geography. In fact, modern theories emerged about the role of relational and institutional space in fostering the innovative behavior of regions. As a consequence, theories have been extended to encompass different ways to conceive space in the analysis of economic interactions (Capello 2014; Torre and Wallet 2014).

A vast literature has already been developed on this theme, with the goal to empirically highlight the role of complex forms of proximities on scientific cooperation, enriching the oversimplifying assumption that spatial proximity—via epidemic contacts—enhances higher knowledge spillovers (e.g., Maggioni and Uberti 2007; Mora and Moreno 2010; Autant-Bernard and LeSage 2011; Frenken, Ponds, and van Oort 2010).

There is still room for further research on this topic. In fact, if so far empirical analyses have extended the applied work to the inclusion of one type of aspatial proximity, they have not yet been attracted by simultaneously accounting for all types of proximities potentially relevant for the diffusion of knowledge. A simultaneous analysis of the role of different kinds of proximities can in fact provide evidence of synergies or complementarities among them. Besides, and more importantly, insufficient attention has been paid to the mutual influences that different types of proximities may exert in the presence/absence of spatial proximity. In particular, the effects of spatial proximity on the exchange of scientific knowledge may be influenced by other types of proximity, viz., cognitive, social, and technological proximity; in other words, synergies may exist between spatial and aspatial proximity measures. Thirdly, and lastly, the relationship between scientific cooperation and the different kinds of proximities may be subject to increasing or decreasing returns; the existence of nonlinearities is thus a relevant, and insufficiently studied, aspect in the field of scientific cooperation.

This article enters the debate on proximities and scientific cooperation, with the aim to fill the above mentioned gaps. In particular, the aim of the present article is to simultaneously include three main types of proximity, namely, social, cognitive, and technological proximity, that are expected to influence, jointly with spatial proximity, the intensity of scientific cooperation. The choice of these three types of proximities, among those existing in the literature, is not random; it is instead driven by the aim to take account of complementarity effects in the different concepts of proximity used in these analyses. Organizational and institutional proximities (Torre and Rallet 2005; Torre 2011; North 1990; Maskell and Malmberg 1999) mostly refer to the capacity of, respectively, firms (workers) and regions (citizens) to provide rules and norms that foster cooperative behavior and learning; these concepts are, in our view, properly captured, respectively, by social (as for social norms and incentives toward cooperation) and cognitive proximity (for common norms and rules fostering learning processes). Besides, both institutional and organizational proximities better fit either a national or a business environment and only indirectly pertain the regional dimension.

A novelty of this article is also the innovative way in which different types of proximity are measured. Most importantly, we build a new measure of “interregional cognitive proximity,” by extending the existing concept of related variety to an interregional setting (Boschma and Iammarino 2009; Frenken, Oort, and Verburg 2009); moreover, we identify technological and social proximities as similarities between pairs of regions in terms of the regional social and industrial specialization profiles. Each proximity has a clear definition, logically followed by a quantitative indicator.

This article is structured as follows. In the second section, the literature needed to correctly position this contribution is critically summarized and this section concludes with the three research questions this article answers to. The third section offers a description of the empirical strategy and the methodology to demonstrate the article’s research questions. In the fourth section, the data set assembled for this article and the indicators built to capture aspatial forms of proximity are described. The fifth section discusses the main empirical findings. Finally, the sixth section concludes.

Literature Review

Proximity and Knowledge Spillovers Measurement

Around the mid-1980s, the economic growth literature witnessed the emergence of theoretical and empirical evidence on the fact that the productivity level of a country, or region, is affected not only by the extent to which local firms invest in research and development (R&D) activities but also by the potential access to external R&D stocks (Coe and Helpman 1995). While initially based on pure geographical space as means of knowledge diffusion, empirical studies have in the last decade shed some light on the main channels of knowledge diffusion. Among such vehicles, much evidence has been identified for foreign direct investment (FDI; e.g., van Pottelsberghe de la Potterie and Lichtenberg 2001); in fact, through reverse engineering, firms can acquire technology embedded in traded goods (MacGarvie 2005; Padilla-Pérez 2008). However, a major role in this respect has been, and is still, played by spatial distance.

In fact, if knowledge is a partially public, partially nonrival good, it can at least partially diffuse in space. According to an epidemic viewpoint, knowledge diffusion decreases with spatial distance, because the probability of running into useful knowledge decreases as the distance between a knowledge-generating institution and the knowledge users increases. The idea that spatial distance hampers knowledge flows represents the rationale for the 1990s wave of studies on knowledge spillovers (Figure 1).

Figure 1.

Approaches to knowledge flows: a diachronic representation. Source: Authors’ elaboration.

Until the early 1990s, the lack of appropriate measures of knowledge flows and the insufficient computing power available to scholars made the empirical validation of the above mentioned theories complicated. Simultaneous effort by industrial and regional economics led to the emergence of two techniques to assess knowledge spillovers. Pioneering work by Jaffe (Jaffe 1986, 1989) identified knowledge spillovers as potential flows of knowledge originating from R&D-generating institutions within a knowledge production function (henceforth KPF) framework. Subsequently, the KPF approach was perfected with the improvement in spatial econometric techniques (Anselin, 1988). Spatial econometrics offered a convincing toolbox to quantify the spatial impedance offered by spatial features (and in particular distance) in knowledge diffusion processes; these techniques have been applied to both the KPF and the standard growth models extended to include the effects of spatially lagged productivity growth on local performance (Ertur and Koch 2007). Around the same years, the idea that knowledge does leave a paper trail in patent citations led to the patent citations literature (Jaffe, Trajtenberg, and Henderson 1993; Thompson 2006), which provided a concrete measure of knowledge spillovers, although limited to a specific type of knowledge, viz., technological contents embedded in inventions and manufactured products (Figure 1).

The spatial econometric literature is based on a set of simplifying assumptions, which help in the estimation process but reduce the interpretative power of these analyses. On the one hand, knowledge spillovers are only implicitly measured, by assuming that the spatial nearness or the technological interdependence once again driven by spatial proximity are enough to determine knowledge diffusion. On the other hand, most such studies model technological interdependence as taking place mostly in geographical space. However, as correctly pointed out, “countries may be considered as located in some general socio-economic and institutional or political space, defined by a range of factors. Implementation of spatial methods thus requires accurate identification of their localisation in such a general space. Ideally, such a matrix should be theory-based” (Ertur and Koch 2011, 236). If this statement is true for countries, it is even more binding for regions, where identity and the sense of belonging are most developed.

The second above mentioned critique (viz., the validity of geographical space as the only environment where knowledge diffuses) has been questioned both from a theoretical and from an empirical perspective, in particular calling for paying more attention to the cognitive dimension being implicitly assumed behind spatial proximity in the explanation of knowledge spillovers. In fact, cognitive, social, and technological proximity represent the most relevant difference between a simple cluster and an industrial district/innovative milieu (Boschma 2005; Breschi and Lissoni 2001; Capello 2009).² Critical issues motivated by the absence of a convincing explanation for knowledge diffusion channels have been subsequently verified empirically through spatial econometric studies where the definition of proximity underlying the construction of knowledge spillovers measures have been variously defined (Figure 1). Although the use of aspatial proximities in modeling knowledge spillovers has been sometimes criticized, “Proximity in geographical, industrial, and technical space matters here in that it provides reluctant and sceptic, risk-adverse adopters the opportunity to assess the actual profitability of the new technology and hence to adopt it” (Antonelli 2003, 9–10).

Empirical verifications of the role of aspatial proximities in shaping knowledge diffusion include, among others, Autant-Bernard (2001) and Autant-Bernard and LeSage (2011), which dealt with technological proximity; Spolaore and Wacziarg (2009), which bring genetic distance in shaping income differentials to the fore; Agrawal, Kapur, and McHale (2008), which focus on social proximity; and Basile, Capello, and Caragliu (2012), which deal with relational, social, and technological proximity.

Proximity and Knowledge Flows’ Determinants

In the studies above summarized, knowledge spillovers are mostly measured as potential flows, with the notable exceptions of works based on patent citations. In fact, spatial econometric models assume that the potential access to a wealth of external knowledge, mediated by one or more forms of proximity, represents a suitable proxy for real knowledge flows.

In order to complement such analyses, and partially solve the above mentioned limitation, a more recent literature dealt with the determinants of knowledge flows (Figure 1). Most such, mostly empirical, studies deal with the determinants of scientific cooperation, proxied in different manners. Along with the traditional spatial impedance offered by pure geographical space, as the previous literature on knowledge spillovers, these works relate the extent to which knowledge-generating institutions (such as research centers, individual inventors, and universities) cooperate for scientific purposes to originating institutions’ characteristics as well as to other forms of proximity. The aim of the knowledge spillovers literature moves therefore from the measurement of the effects of knowledge spillovers toward the explanation and interpretation of their existence.

Among the most influential studies in this sense, one can include Maggioni and Uberti (2007) and Maggioni et al. (2009) who focus on the role played by aspatial, hierarchical networks of cooperation in knowledge production; Mora and Moreno (2010) who demonstrate that technological proximity complements spatial nearness in fostering knowledge flows across space; Autant-Bernard and LeSage (2011) who analyze the extent of inter- and intra-industry knowledge spillovers channeled by industrial proximity; and Frenken, Ponds, and van Oort (2010) and Ponds, Van Oort, and Frenken (2007), focusing on the synergic nature of spatial and relational proximity in research collaborations.

Theoretically, the choice of collaborating for scientific purposes has been modeled as a bilateral decision based on cognitive, relational, and structural embeddedness (Cowan, Jonard, and Zimmermann 2007). Recent empirical work demonstrating this theoretical assumption includes Autant-Bernard et al. (2007), which relate scientific cooperation to the position of individuals within an international network (and therefore deal with social distance); Scherngell and Barber (2009, 2011), whose main result is the assessment of the differential impacts of spatial and technological proximities (with the addition of institutional factors in their 2011 contribution) on scientific collaborations, with the dependent variable measuring scientific collaborations, as in the present article, measured by co-participations to EU Framework Programme 5 (FP5) projects.

Simultaneously, around the mid-2000s, a relevant literature originated by the pivotal contribution by Jan Tinbergen (1962) on the determinants of trade flows included aspatial characteristics of partners in the explanation of trade flows (de Groot et al. 2004), FDIs (Lankhuizen, de Groot, and Linders 2011), and, more recently, migrations (Belot and Ederveen 2012 and Caragliu et al., 2013).

Much has been done so far. However, we believe there is still room for further reflections, since limitations in the existing literature can still be identified and possible solutions to such shortcomings can be suggested, namely:

Previous studies mostly included one or two additional proximity effects in the evaluation of the determinants of scientific collaboration. However, since spatial proximity is at most a good proxy for the underlying real proximity relations, omitting one or more relevant proximity effects may in fact overemphasize the real impact of spatial proximity on scientific collaboration.³ In this article, we extend the notions of proximity accounted for, by relating scientific collaboration to cognitive, technological, and social distance. In this work, such proximity effects are jointly measured.

Relatively neglected in previous analyses is the understanding of whether simple spatial proximity is enough to explain research collaboration, or if instead spatial proximity plays a more relevant role in selecting scientific partners when regions are also cognitively, technologically, and socially compatible. In this article, we investigate possible synergic effects between spatial and aspatial proximity measures. In particular, we verify the extent to which cognitive, technological, and social proximity interact with spatial distance in fostering scientific cooperation.

Previous work on the determinants of research collaboration has consistently assumed that the effects of aspatial proximity obey a linear or exponential law, which, by definition, has no maximum or minimum. However, a theoretical rationale has been suggested for the need to verify the possible existence of an “optimal” proximity defined over different concepts and with the underlying goal to maximize some innovative process “Not only too little, but also too much proximity may be detrimental to interactive learning and innovation” (Boschma 2005, 61). In this article, we inspect the existence of nonlinear effects in the impacts of aspatial proximities on scientific collaboration.

These three issues can be formalized in the following three research questions for this article:

Research Question 1: What is the joint effect of spatial and aspatial proximities on scientific collaboration?

Research Question 2: Does spatial proximity synergically interact with cognitive, technological, and social proximity in fostering scientific collaboration?

Research Question 3: Do nonlinearities exist in the effects of proximity on scientific collaboration?

The Empirical Model

Scientific collaborations are measured in this work with bilateral scientific collaborations in EU FP5 projects. Previous works in this line of research identified two main determinants of scientific collaboration:

internal (to the region/institution) scientific collaboration-enhancing factors and

external characteristics (bilateral, i.e., related to different types of closeness between pairs of regions).

In this article, we bring forward this research and provide a comprehensive analysis of the different impacts of both internal and external, scientific collaboration-enhancing factors.

Following Scherngell and Barber (2009), we model cross-regional research collaborations as a function of a set of distance-decay effects, or factors of spatial impedance, as well as of region-specific research determinants.

We define regions as either i or j, i ≠ j, i = 1, …, n, j = 1, …, n. This implies that we do not evaluate intra-regional collaboration (i.e., FP5 projects where more than a single knowledge-generating institution belonging to a certain region took part), and we observe the full set of scientific collaborations in the n × n matrix of possible cross-regional research partnerships.

Let p_ij be the number of projects to which knowledge-generating institutions of regions i and j took part in the period 1998–2002. All p_ij represent the elements in matrix P_ij , that is, a matrix of all possible pairs of regions where scientific collaboration took place.

The basic research collaboration model can be formalized as:

P_{i j} = X_{i j} + ∊_{i j},

with i ≠ j, where:

X_{i j} = R & D_{i} \cdot R & D_{j} \cdot P R O X_{i j} .

The model is based on a gravitational logic, where the intensity of interactions between pairs of regions is directly proportional to the characteristics of each region (the mass) and inversely to the distance between elements of the regions’ pair. In fact, equations (1) and (2) state that the probability P_ij that two regions cooperate for scientific purposes depends on internal (to the region) scientific determinants but also on the various forms of friction separating pairs of regions (PROX_ij ). Formally, we require $E [∊_{i j} | p_{i j}] = 0$ . In other words, in each pair of regions the probability of collaboration should depend only on the factors (internal scientific determinants and external/bilateral spatial friction) here described; on average, deviations from such model should be equal to 0. Empirically, since the ex ante probability to engage in scientific collaboration cannot be directly measured, we proxy the probability that institutions collaborate for scientific purposes with the ex post implementation of such probability, namely, the count of FP5 projects in which partners of each region pair actually cooperated.

Equation (2) is in implicit form. It is standard in most similar studies to (often implicitly) assume a Cobb-Douglas specification. This specification is, in fact, more tractable than most others and allows to avoid implausible assumptions about the elasticity of the function arguments (Uzawa 1962). Such choice allows in addition the log linearization of the main equation, thereby identifying elasticities when empirically estimating the model.

Besides, in this article the notions of proximity accounting for are extended. In fact, we tackle the role of cognitive, technological, and social proximity, along with the traditional spatial dimension, as a factor enhancing research collaboration. In addition, we also verify whether regions characterized by relevant differentials in R&D investment and product innovation intensity also tend to cooperate more.

Including both the formalization of equation (2) as a Cobb-Douglas specification, and the above mentioned notions of proximity, we can state the following explicit function:

P_{i j} = (\begin{array}{l} S I Z E_{i j}^{α} \cdot G E O_D I S T_{i j}^{β_{0}} \cdot C O G_P R O X_{i j}^{β_{1}} \cdot T E C H_P R O X_{i j}^{β_{2}} \cdot S O C_P R O X_{i j}^{β_{3}} \cdot R & D_D I F F_{i j}^{β_{4}} \cdot \\ P R O D I N N_D I F F_{i j}^{β_{5}} \end{array}) + ∊_{i j},

where the variables refer, respectively, to the size of the analyzed regions (in terms of both knowledge size and physical size), the spatial distance, the cognitive, technological, and social proximities, and finally structural differences in R&D and innovation activity difference between regions, respectively.

Finally, equation (3) can be log linearized to obtain:

p_{i j} = α_{0} + α_{1} s i z e_{i j} + β_{0} g e o_d i s t_{i j} + β_{1} c o g_p r o x_{i j} + β_{2} t e c h_p r o x_{i j} + β_{3} s o c_p r o x_{i j} + β_{4} R & D_d i f f_{i j} + β_{5} p r o d i n n_d i f f_{i j} + ∊_{i j},

where lowercase letters refer to the log linearized variables. Equation (4) is our baseline model. The fourth section presents now the indicators used to measure the complex set of proximity measures present in this analysis.

Indicators

The data set comprises several proximity matrices calculated on the basis of proximity concepts presented in the second section, as well as a matrix of scientific cooperation, described hereafter.⁴

Scientific Cooperation

Following the road paved by previous works on the topic of scientific collaboration (e.g., Scherngell and Barber 2009, 2011; Autant-Bernard et al. 2007), we measure scientific collaboration with bilateral scientific collaborations in EU FP5 projects, actually measuring the ex post intensity of cooperation.

The indicator of scientific cooperation has been calculated by the authors as the count of framework research programs to which institutions belonging to each of the 69,696 (= 264²) possible pairs of NUTS2 regions jointly participated. The matrix has been next triangularized (i.e., each co-participation has been counted just once), and the main diagonal, bearing the FP5 projects where institutions of the same NUTS2 region co-participated, eliminated. This implies a total number of possible observations equal to ([264 × 264] − 264)/2 = 34,716.

Measuring scientific collaboration with regions’ co-participations in EU FP5 projects implies that a specific weight is given to transnational cooperation, which is fostered by the very nature of FPs. In fact, the EU believes the FP should be best targeted toward selecting “only objectives which are more efficiently pursued at the community level by means of research activities conducted at that level,” while at the same time meeting the “need to establish a ‘critical mass’ in human and financial terms, in particular through the combination of the complementary expertise and resources available in the various Member States.”⁵ As such, it is highly likely that scientific cooperation measured by FP5 projects is negatively associated with the fact that regions belong to the same country. We control for this issue with a dummy which takes on value 1 if indeed regions belong to the same country and 0 otherwise.

In terms of how large these cooperation activities could get, the Community Research and Development Information Service (CORDIS) data base shows a large variety of possible situations. Figure 2 shows that, while a relatively large number of projects only presents cooperation between two partners, the remaining (about 85 percent of the total sample) is characterized by cooperation between three or more partners, with the mode around six or seven partners.

Figure 2.

Share of Framework Programme 5 projects by the number of partners. Source: Authors’ elaborations on European Commission/CORDIS (2005).

Spatial Proximity

Spatial proximity is defined as the matrix comprising elements calculated as the inverse of distance d_ij between NUTS2 centroids in kilometers. Each distance d_ij is in turn calculated with the following formula:

d_{i j} = \sqrt{{(x_{i} - x_{j})}^{2} + {(y_{i} - y_{j})}^{2}} .

Following the recent theoretical call for an extension of the notions of space beyond pure geography (see the second section), the use of spatial proximity as a factor facilitating scientific collaboration between regions should actually capture other underlying effects related to other forms of relatedness between pairs of regions. Econometrically, this could be demonstrated by showing that after including other forms of proximity, the absolute relevance of spatial proximity abates, as it will be demonstrated later in this article (see the fifth section).

Cognitive Proximity

A recent approach to proximity posited by evolutionary economic geography analyzed in depth the two main components of knowledge base diversity externalities, that is, those externalities accruing to regional growth and stemming from a diversified knowledge composition. In particular, such externalities have been classified into those stemming from cognitive distance (i.e., those arising from pure knowledge diversity) and those originating from cognitive proximity, viz., those externalities connected to the presence within an area of knowledge neither too distant nor too close (Boschma 2005). The idea, following Noteboom (2000), is that in order to trigger learning mechanisms, industries must enjoy a certain degree of knowledge distance in order to have something to learn, while at the same time being technologically compatible. In fact, “it is unclear what a pig farmer can learn from a microchip company even though they are neighbors” (Boschma and Iammarino 2009, 292).

So far, the concept of cognitive proximity (based on related variety) has been operationalized at the regional level by calculating indicators of technological relatedness across sectors. This concept has been mostly proxied by means of entropy measures (e.g., Frenken, Oort, and Verburg 2009) on the basis of employment or value-added data at various levels of sectoral disaggregation. In particular, entropy would be best captured by elaborating indicators which correlate positively with sectoral diversity at high levels of disaggregation (e.g., five-digit industrial classes), while negatively correlating with differences in specialization at low levels of disaggregation (e.g., two-digit technological classes). Following this approach, “related variety [would] be the indicator for Jacobs externalities because it measures the variety within each of two-digit classes. It is expected that the economies arising from variety are especially strong between subsectors, as knowledge spills over primarily between firms selling related products” (Frenken, Oort, and Verburg 2009, 689).

The concept of cognitive proximity has been applied in regional analysis in order to capture the positive spillover effect stemming from sectoral diversity, which ultimately relates to the notion of cognitive proximity between actors. In this article, a major step forward is made by extending the concept of cognitive proximity to the case of interregional knowledge flows. This leads to the definition of the concept of interregional cognitive proximity.

Definition 1: Interregional cognitive proximity

Two regions are cognitively proximate if they enjoy a complementary set of skills and competences pertaining to a common knowledge base, characterizing a technological domain.

In order to learn from each other, agents in distant regions must have compatible sets of skills (i.e., they have to share a common technological domain), within which sufficient cross-regional complementarity must exist. The extent to which a specific knowledge base matters within an interregional cognitive proximity depends on the relevance with respect to the overall knowledge present in the region.

In order to operationalize the concept of interregional cognitive proximity, we resort on regional patent data, which represent a good proxy for the knowledge profile of a region (see the Appendix for more details on the patent data).

Empirically, the common technological domain is approximated by a common specialization of pairs of regions into the same technological class (two digits) of patents; potential for advancements is approximated by differentiation and complementarity in terms of specialization in subclasses of patents (three digits) in two regions. The higher the difference between the two regional shares of patents in three-digit technological classes, the higher the complementarity between regions. The higher the share of two-digit technological classes in the pair of regions analyzed, the higher the common knowledge base in the region. The latter should be adjusted for the difference in the size of the same technological domain in the two regions; the higher the difference in size, the lower the cognitive proximity.⁶

Interregional cognitive proximity (between region i and j) indicator (cog_ij ) is therefore measured as:

c o g_{i j} = \sqrt{\sum_{s_{2 d} = 1}^{z} [\frac{(x_{s_{2 d} i} \times x_{s_{2 d} j})}{| x_{s_{2 d} i} - x_{s_{2 d} j} |} (\sum_{s_{3 d} = 1}^{m} (| x_{s_{3 d} i} - x_{s_{3 d} j} |))]},

where z and m are the numbers of classes partaining to a given category (in this specific case IPC 2-digit classes for z and 3-digit classes for m), i and j indicate two regions, $x_{s_{2 d} i}$ is the share of patents in each two-digit industry in region i, and, analogously, $x_{s_{3 d} i}$ is the share of patents in each three-digit industry in region i. The first part of the indicator captures the common specialization of pairs of regions into the same technological class (two digits) of patents adjusted for the difference in the size of the same technological domain in the two regions. The second part of the indicator measures the complementarity in terms of specialization in subclasses of patents (three digits) in two regions.

This indicator is a positive function of the within three-digit class variety (complementarity of knowledge among regions), and a positive function of the two-digit specialization (common knowledge base between a pair of regions).

Finally, the whole indicator is square rooted in order to reduce the variance of otherwise extreme data, typical of indicators based on patent counts as also suggested in the literature (Hollanders, Tarantola, and Loschky 2009). As a final step, the values of cog have been normalized on the maximum, so that the indicator ranges from 0 to 1.

This measure of cognitive inter-regional proximity may present endogeneity issues in relation with scientific cooperation that could have fostered patent activities among partners.⁷ Although no direct evidence is available against such aspect, it is worth examining the type of partners participating in the projects. Table 1 presents the types and the cumulative distribution of organizations participating in FP5 projects and demonstrates that only a relatively small portion of FP5 project partners can actually be ascribed to commercial and profit-oriented activities, whose scope is the protection of intellectual property as the project produces something worth commercialization. On the contrary, a vast number of organizations can be related to the education industry, whose cooperation can be safely related to the emergence of relational capital among participating institutions, and is expected to be only marginally devoted to the patenting activity, and the protection of intellectual property of the results found in the project funded by the FP.⁸

Table 1.

Types and Cumulative Distribution of Organizations Participating to Framework Programme 5 Projects.

Organization type	Frequency	Percentage	Cumulative
Commission external service	3	0.00	0
Consultancy	33	0.02	0.37
Education	16,508	20.98	21.02
Industry	7,723	9.81	30.83
NA	4,663	5.92	36.76
Noncommercial organization	83	0.11	36.86
Other	34,272	43.55	80.41
Research	15,417	19.58	100
Total	78,702	100

Note: NA = Not Applicable.

Source: Authors’ elaborations on European Commission/CORDIS (2005).

Interregional Social Proximity

Social capital has been used in order to formalize the cultural characteristics of a society facilitating interactions, reducing transaction costs, and improving the ease with which knowledge spreads (Capello, Caragliu, and Nijkamp 2011; Basile, Capello, and Caragliu 2012).

This article interprets inter-regional social proximity as the similarity existing between pairs of regions in terms of their endowment in social capital. Pairs of regions with similar social capital are more prone to exchange their knowledge, while regions with different social capital face higher transaction costs in the process of absorbing, understanding, and decoding external knowledge. In fact, regions whose social values comprise a high level of trust and sense of belonging will be more inclined to interact with regions with a high level of social capital. By the same token, regions with low social capital can most easily interact with regions endowed with low levels of social capital. This is not a choice but a natural consequence of the poverty of social capital; in fact, no region with higher social capital will find cooperation with socially poor regions attractive. The sharing of similar social values among regions facilitates interactions and, most importantly, reduces transaction costs. Borrowing from the jargon of contract theory, not only do regions with similarly high social capital take advantage of lower transaction costs, but also regions with similarly low social capital complete contracts in a less expensive way, thanks to their experience of doing business in a risky environment.

In this article, we follow Putnam’s definition of social capital “social capital here refers to features of social organization, such as trust, norms, and networks, that can improve the efficiency of society by facilitating coordinated actions” (Putnam, Robert, and Nanetti 1993, 167). Given the paramount relevance of coordination in the complex research activities being explained in the present work, and the even higher relevance of coordination-enhancing societal characteristics, it follows that regions with different stocks of social characteristics may find it harder to structure complex R&D cooperation networks. At the same time, such impedance factor may ceteris paribus (viz., with similar absolute differences in social capital characteristics) be reduced as regions are simultaneously characterized by higher levels of social capital.

In order to construct the social proximity matrix, first a measure of social capital must be built. The empirical definition of social capital is based on the seminal work by Putnam and coauthors (Putnam 2000; Putnam, Robert, and Nanetti 1993). This measure is calculated by averaging out percentage scores to questions in the individual questionnaires administered in the 2000 wave of the European values study (henceforth, EVS).⁹ For each of the theoretical domains of social capital originally identified as crucial elements of this concept in Putnam (2000), a proper proxy has been identified among EVS questions. Individual answers have next been aggregated at the European NUTS2 level.¹⁰ In particular, the choice of the questions selected to represent the domains of the Putnam literature are shown in Table 2.

Table 2.

Indicators of Social Capital Used for the Social Proximity Matrix.

Domain	Question	Scale
Community organizational life	How often do you spend time in clubs and voluntary associations?	1. Every week
		2. Once or twice a month
		3. A few times a year
		4. Not at all
Engagement in public affairs	Do you participate in any form of social activity?	0–1
Community volunteerism	Do you take part to voluntary work in any community activity?	0–1
Informal sociability	Do you agree that “most people can be trusted”	1. I trust them completely
		2. I trust them a little
		3. I neither trust nor distrust them
		4. I do not trust them very much
		5. I do not trust them at all

Once a proper indicator for each of Putnam’s social capital axes has been defined, and the economic rationale for the assessment of interregional differences in terms of social capital explained, the concept of interregional social proximity can be defined as follows:

Definition 2: Interregional social proximity

Two regions are socially proximate if they enjoy similar sets of social values. In fact, in order to learn from each other, agents in different regions must have compatible sets of values.

Empirically, social distance between regions i and j is computed in terms of normalized Euclidean distances between regional social capital characteristics with the formula:

s o c_{i j} = \sqrt{\sum_{q = 1}^{Q} {(x_{q i} - x_{q j})}^{2}} / \sum_{q = 1}^{Q} (x_{q i} + x_{q j}),

where x_q is the social capital indicators, respectively, of region i and j (with Q = 4). The indicator ranges from 0 to 1. The numerator of the indicator measures the difference in the regional social capital endowment of the two regions. The denominator discounts for the size of the social capital endowment in the two regions.

The way in which the indicator is built guarantees that what matters in generating more/less social proximity between pairs of regions is the lower/higher distance in their stock of social values, whatever the stock of social capital is in the two regions. A pair of regions with a low stock of social capital but a similar social capital profile has a higher social proximity than a pair of regions with a higher stock of social capital but very different social capital profiles, which is exactly what we mean by social proximity.

Interregional Technological Proximity

In order to be inclined to cooperate for scientific purposes, regions must enjoy a compatible productive context, which guarantees a similar technological profile; therefore, similar specialization patterns in manufacturing sectors are expected to increase the likelihood of research collaboration between pairs of regions. This leads to the following definition of interregional technological proximity:

Definition 3: Interregional technological proximity

If two regions enjoy similar specialization in manufacturing industries, they are technologically proximate. In order to learn from each other, regions must have compatible levels of specialization in manufacturing industries, where scientific activity is performed (i.e., they must have technological similarities).

In fact, it has been noted that “Similarities in technological knowledge (…) facilitate technological learning as well as the anticipation of technological developments (…). Technological proximity between actors facilitates the acquisition and development of technological knowledge and technologies” (Knoben and Overmans 2006, 77).

It may be claimed that the concept of technological proximity hides a certain similarity with the concept of cognitive proximity; industrial specialization can explain the technological performance of a region and therefore its knowledge profile. This explains why in the related literature technological proximity is measured through patent specialization and therefore conceptually associated with the cognitive proximity concept (e.g., Walukiewicz 2007; Marrocu, Paci, and Usai 2011). However, we prefer to keep these two concepts separated, since technological proximity adds something to our understanding of cognitive processes, by:

overcoming a limit of patents as a proxy of knowledge used in the cognitive proximity measure. In fact, the use of patents captures formal knowledge but leaves aside all informal, tacit knowledge embedded in specific technological capabilities that can exist in specific industries and regions;¹¹

defining that research cooperation is easier among actors operating in similar industrial, and not only technological, contexts.

The matrix of interregional technological proximity is operationalized as follows. In the first place, location quotients for manufacturing employment (Table 3 shows the Nomenclature statistique des Activités économiques dans la Communauté Européenne [NACE] 2 classes used in this process) are calculated, with the EU27 as the reference value.

Table 3.

Manufacturing Industries Used for the Calculation of the Technological Proximity Matrix.

Industry code	Industry name
DA	Food, beverages, and tobacco
DBDC	Textiles and leather, etc.
DFDGDH	Coke, refined petroleum, nuclear fuel, and chemicals, etc.
DL	Electrical and optical equipment
DM	Transport equipment
OM	Other manufacturing

Next, distances between pairs of regions with respect to the location quotients are calculated. Each entry of the interregional technological proximity matrix, therefore, takes on the following formula:

t e c h_{i j} = \frac{\sqrt{\sum_{q = 1}^{Q} {(L Q_{q i} - L Q_{q j})}^{2}}}{Q},

where LQ stands for region-specific location quotients, indices i and j indicate regions (with the EU27 as the reference area), while Q is the number of manufacturing industries here considered (in our case 6, as shown in Table 2), so that the indicator ranges from 0 to 1.

Other Variables

The main determinants of scientific collaboration between regions used in this article are of two types.

The first category of control variable captures the physical size and the size of the knowledge produced by the pair of regions measured, respectively, as the average number of inhabitants of each pair of regions and the average R&D expenditure over gross domestic product (GDP) of each pair of regions. In order to overlap as perfectly as possible with the dependent variable, and reduce the potentially distorting impact of business cycles, the two size variables are calculated as averages of the yearly values in 1998–2002, exactly the period when FP5 projects were funded.

The second category of control variable measures the difference in the capability of the pair of regions to produce either knowledge or innovation measured, respectively, as the absolute difference in R&D expenditure over GDP and in the share of firms performing product innovation according to the 2002–2004 wave of the community innovation survey (CIS¹²) between the pairs of regions. These variables allow to control for differences that can explain the interest of regions for cooperation, irrespective of all other types of proximities to other regions. In fact, ceteris paribus, scientific cooperation is expected to take place among regions with similar research capabilities and with similar skills in translating knowledge into a commercialized and high value-added product. The inclusion of these two variables allows to further reduce the role played by spatial proximity in mediating scientific collaboration, by stressing the arguably negative contribution of large differences in R&D investment and product innovation intensity between pairs of regions on their likelihood to cooperate.

Table 4 shows finally the correlation between the four main proximity matrices. Not necessarily such concepts of proximity are linked—in fact, in some cases they even correlate negatively. This first statistical analysis reinforces the case to add alternative proximity measures to the explanation of cross-regional research cooperation.

Table 4.

Pearson’s Correlations between Proximity Measures.

	Cognitive proximity	Technological proximity	Social proximity	Spatial proximity
Interregional cognitive proximity	1 (.00)
Interregional technological proximity	−.0237 (.45)	1 (.00)
Interregional social proximity	−.0122 (.00)	.0297 (0.00)	1 (.00)
Spatial proximity	−.0164 (.00)	−.1810 (.00)	−.0947 (.00)	1 (.00)

Note: Standard errors are given in parentheses.

Empirical Results

The Joint Effect of Spatial and Aspatial Proximities on Scientific Collaboration

In this section, results of estimating equation (4) with the use of the indicators described in the fourth section are presented. Each subsection aims at answering one of the research questions described in the second section.

Across all estimates, in this section robust standard errors are used, in order to correct for potential heteroskedasticity in the data.

Our baseline estimates (Table 5) start from equation (4); first, in columns 1 and 2, we include only two measures of the sheer size of the regions potentially involved in scientific collaboration (namely, the average percentage expenditure in R&D over GDP in both regions belonging to each regions’ pair and their average populations), along with the dummy variable indicating when regions belong to the same country; these variables are maintained throughout the estimates.

Table 5.

Empirical Results—Linear Estimates.

Dependent variable	(Log of) scientific collaboration
Estimation method	OLS	OLS	OLS	OLS	OLS	OLS	OLS	Negative binomial	Zero-inflated negative binomial
Model	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Constant	−0.07(0.08)	0.96***(0.11)	1.05***(0.12)	1.12***(0.12)	1.16***(0.12)	0.62***(0.12)	0.50***(0.12)	−4.44***(0.23)	−2.78***(0.21)
Cooperation determinants
Size of knowledge produced (average R&D expenditure/GDP in region pair)	0.92***(0.01)	0.89***(0.01)	0.91***(0.01)	0.91***(0.01)	0.91***(0.01)	0.97***(0.01)	0.96***(0.01)	0.95***(0.01)	0.57***(0.01)
Physical size of region (average population levels in region pair)	0.02(0.01)	0.03**(0.01)	0.05***(0.01)	0.05***(0.01)	0.05***(0.01)	0.04***(0.01)	0.05***(0.01)	0.40(0.75)	2.18***(0.67)
Proximity measures
Spatial distance	—	−0.14***(0.01)	−0.14***(0.01)	−0.13***(0.01)	−0.11***(0.01)	−0.07***(0.01)	−0.06***(0.01)	−0.0000454**(0.00)	−0.0000293***(0.00)
Interregional cognitive proximity	—	—	0.04***(0.01)	0.04***(0.01)	0.04***(0.01)	0.03***(0.01)	0.03***(0.01)	0.06***(0.01)	0.02***(0.00)
Interregional technological proximity	—	—	—	1.03***(0.01)	1.02***(0.11)	0.97***(0.11)	0.93***(0.11)	2.40***(0.21)	2.00***(0.19)
Interregional social proximity	—	—	—	—	0.96***(0.08)	0.93***(0.08)	0.88***(0.08)	2.00***(0.15)	1.43***(0.14)
Difference in knowledge production between pairs of regions	—	—	—	—	—	−0.19***(0.01)	−0.19***(0.01)	−1.86***(0.05)	−1.00***(0.05)
Difference in innovation production between pairs of regions	—	—	—	—	—	—	−0.05***(0.01)	−0.24***(0.05)	−0.29***(0.05)
Dummy, equals 1 if regions belong to the same country	0.19***(0.02)	0.01(0.02)	−0.003(0.02)	−0.02(0.02)	−0.09***(0.03)	−0.07**(0.03)	−0.08**(0.03)	−0.12***(0.04)	−0.16***(0.04)
Robust standard errors	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Number of observations (nonzero)	21,012	21,011	20,646	20,646	20,646	20,479	21,012	34,716	34,716 (21,012)
R ²	.18	.18	.19	.19	.19	.22	.22	.21	.21
Joint F-test (OLS)/Wald χ² test (Poisson)	1,533.01***	1,175.51***	951.77***	816.98***	728.00***	753.81***	662.12***	7,570.55***	3,542.69***

Note: Standard errors are given in parentheses. OLS = ordinary least squares; R&D = research and development; GDP = gross domestic product.

*Significant at 90 percent level.

**Significant at 95 percent level.

***Significant at 99 percent level.

Next (columns 2–7), we progressively include all distance measures described in the previous section (in the order spatial distance, cognitive proximity, technological proximity, social proximity, R&D difference, and product innovation difference). Finally, in columns 8 and 9, we also verify whether our results are driven by the use of linear log transformations or instead hold with the use of count models.

Results show remarkable significance, with all signs in line with theoretical expectations, and stability across all specifications. The only (expected) exception is the spatial distance parameter, which decreases with the inclusion of more measures of proximity (Figure 3). This is in line with the theoretical rationale already pointed out in Ertur and Koch (2011): in this literature, geographical space is at best a good proxy for the real underlying mechanisms driving the diffusion of knowledge. While its importance cannot be ignored, the magnitude of its true impact should probably be revised with the inclusion of richer ways to conceive space.

Figure 3.

Values of the estimated parameter for the spatial distance measure, as additional proximity measures are included. Source: Authors’ elaboration.

The results are not driven by the use of standard ordinary least squares (OLS) techniques. Columns 8 and 9 show in fact that negative binomial estimates obtain qualitatively comparable results, with similar signs (although with different magnitudes, which is in line with analogous studies).¹³ Column 9, besides, takes also into account the existence of zero observations in the data set, that is, regions’ pairs which never collaborate during the 1998–2002 FP cycle. In this case, the zero-inflation problem is modeled with a zero-inflated negative binomial technique, which fits two models, a first-step regression which explains the probability that two regions embark in scientific cooperation; and next, a second (main) equation, which identifies the partial correlations between actual scientific cooperation (i.e., nonzero observations in the dependent variable) and right-hand side determinants.¹⁴

The difference in the estimated parameters between the zero-inflated negative binomial estimates and OLS becomes particularly relevant mainly for the spatial distance indicator. This can be easily explained with the nature of this model, which first accounts for the probability that institutions in two regions cooperate, and then only explains the determinants of such cooperation (if any). Clearly, institutions in regions located far away from each other are less likely to cooperate. After taking this selection process into account, what is left is a less relevant role played by spatial distance in interregional scientific cooperation patterns, which likely explains the smaller magnitude of the parameter associated with spatial distance in Table 5, column 9.

Since our results hold with the use of count techniques, and given the following two research questions, in the remaining of the article, we opt for classical OLS estimates.¹⁵

A last consistency check on the results presented in Table 5 relates to possible nonlinearities in the relations tested. In fact, applying a simple linear functional form to the whole sample comprising 34,716 observations could hide the existence of possible multiple regimes characterized by spatial nonconvexity. In the spatial econometrics literature, this issue is usually tackled by applying nonlinear semi-parametric estimators (Basile 2008; Basile, Capello, and Caragliu 2012), in turn based on potentialized partial differential equation representations (Paelinck and Mur 2013). However, these estimators are based on cross-sectional data with observations collected for individual regions.

In the case of our analyses, on the contrary, the unit of observation is the regions’ pair. We thus follow Ertur, Le Gallo, and Baumont (2006) who tackle the possible existence of multiple spatial regimes by clustering observations in terms of the main factors of interest (in their case, the level of development, which is expected to influence the speed of the convergence process). Empirically, this translates into using quantile regressions in order to take account of the possible structural groupwise heteroskedasticity that may affect the decision to cooperate for scientific purposes. We opted for splitting the scientific cooperation flows in quartiles, and, while in general we obtain qualitatively similar results, we also find an interesting pattern for the proximity variables in Table 5. Estimated parameters for the quartiles are represented in Figure 4 below.

Figure 4.

Intensity of the effects of different interregional proximities by scientific cooperation quartiles. Source: Authors’ elaboration.

Results show that all types of proximity, both geographic and nongeographic, are indeed characterized by different impact intensities depending on the degree of interregional cooperation activity. Proximity seems to matter more as the intensity of scientific cooperation increases, with a peak reached in correspondence of the third quartile. Then, for very high levels of scientific cooperation, our results suggest that interregional proximities no longer matter witnessed by a nonstatistically significant parameters estimates for the fourth quartile. This suggests some form of hysteresis, with regional institutions cooperating because they already did so in the past, irrespective of their mutual characteristics.

These findings further strengthen the case for inspecting nonlinearities in interregional proximity effects, an issue that will be discussed in the subsection “Nonlinearities in the Impact of Proximity on Scientific Collaboration”.

Synergies between Spatial and Aspatial Proximities

In this subsection, we deal with the second research question (Table 6). In particular, we verify whether synergies exist between different forms of proximity: do regions cooperate more easily with regions being not only spatially, but also cognitively, technologically, and socially similar? This question is answered by interacting the main measures of proximity of interest (namely, interregional cognitive, technological, and social proximity) with the measure of spatial distance.

Table 6.

Empirical Results—Interaction Estimates.

Dependent variable	Log of scientific collaboration
Model	(1)	(2)	(3)
Constant	−0.56**(0.28)	0.15(0.15)	0.20(0.33)
Cooperation determinants
Size of knowledge produced (average R&D expenditure/ GDP in region pair)	0.96***(0.01)	0.96***(0.01)	0.96***(0.01)
Physical size of region (average population levels in region pair)	0.05***(0.01)	0.05***(0.01)	0.05***(0.01)
Proximity measures
Spatial distance	0.11***(0.04)	0.01(0.01)	−0.13***(0.03)
Interregional cognitive proximity	−0.57***(0.13)	0.07***(0.01)	0.06***(0.01)
Interregional technological proximity	0.93***(0.11)	−3.56***(0.84)	0.93***(0.11)
Interregional social proximity	0.88***(0.08)	0.89***(0.08)	3.35***(0.79)
Difference in knowledge production between pairs of regions	−0.19***(0.01)	−0.19***(0.01)	−0.19***(0.01)
Difference in innovation production between pairs of regions	−0.05***(0.01)	−0.04***(0.01)	−0.05***(0.01)
Interaction spatial distance-cognitive proximity	0.09***(0.02)	—	—
Interaction spatial distance-technological proximity	—	0.67***(0.13)	—
Interaction spatial distance-social proximity	—	—	−0.35***(0.11)
Dummy, equals 1 if regions belong to the same country	−0.09***(0.02)	−0.07***(0.03)	−0.15***(0.03)
Robust standard errors	Yes	Yes	Yes
Number of observations	20,332	20,332	20,332
R ²	.22	.22	.22
Joint F-test	601.91***	603.01***	595.72***

Note: Standard errors are given in parentheses. R&D = research and development; GDP = gross domestic product.

*Significant at 90 percent level.

**Significant at 95 percent level.

***Significant at 99 percent level.

Table 6 shows the results of estimating the main model with the inclusion of each of the interacted terms: column 1 shows the synergic interaction between spatial distance and cognitive proximity, column 2 between spatial distance and technological proximity, and column 3 between spatial distance and social proximity.

The first column shows that all three components of the interaction terms display high significance. However, as usual with interaction terms between continuous variables, the results for individual parameter estimates are interesting for different values of the interaction term. For this reason we resort to graphical analysis.

Figures 5 –7 show the marginal effects of, respectively, cognitive, technological, and social proximity as spatial distance increases.

Figure 5.

Marginal effects of interregional cognitive proximity on scientific collaboration for different spatial distances. Source: Authors’ elaboration.

Figure 6.

Marginal effects of interregional technological proximity on scientific collaboration for different spatial distances. Source: Authors’ elaboration.

Figure 7.

Marginal effect of interregional social proximity on scientific collaboration for different spatial distances. Source: Authors’ elaboration.

Figure 5 shows an interesting and counterintuitive result. For low levels of spatial distance, the effect of cognitive proximity on scientific collaboration is negative, while when regions are located far away, the negative effect of cognitive proximity on cooperation decreases, and even become positive, witnessing that cognitive proximity is required for scientific cooperation when a strong spatial distance is in place. This is in line with similar findings obtained on the basis of a large micro data base in Boschma, Eriksson, and Lindgren (2009).

Figure 6 shows, for given levels of technological proximity, its marginal effect on scientific collaboration as spatial distance increases. This figure can be interpreted along the same lines of Figure 5, the effect of technological proximity on scientific cooperation is positive only when regions are located far away. Similarities in industrial profiles, and therefore in technological knowledge, are required for scientific cooperation in the case of distant locations. These similar results are welcome, given the similar conceptual interpretation of the cognitive and technological proximities.

Finally, Figure 7 displays the impact of social proximity on scientific collaboration as spatial distance increases. In this case, the impact of social proximity on scientific collaboration remains positive throughout the range where spatial distance is defined; this positive impact, nevertheless, decreases in magnitude as spatial distance between regions engaging in scientific cooperation increases. This implies that, even at large spatial distances, regions being characterized by different social values find it difficult to collaborate for scientific purposes.

Nonlinearities in the Impact of Proximity on Scientific Collaboration

This final subsection verifies whether nonlinear effects exist in the role of proximities on scientific collaboration. In order to maintain throughout the paper similar techniques, possible nonlinearities are inspected by means of robust OLS estimates of not only the linear but also the parameters of quadratic terms. Results of the third empirical exercise are shown in Table 7.

Table 7.

Empirical Results—Nonlinear Estimates.

Dependent variable	Log of R&D collaboration
Model	(1)	(2)	(3)	(4)	(5)
Constant	0.50***(0.12)	4.03***(0.40)	3.84***(0.40)	3.88***(0.39)	3.89***(0.39)
R&D determinants
R&D intensity (average R&D expenditure/GDP in region pair)	0.96***(0.01)	0.97***(0.01)	0.97***(0.01)	0.97***(0.01)	0.97***(0.01)
Size of region (average population levels in region pair)	0.05***(0.01)	0.05***(0.01)	0.05***(0.01)	0.05***(0.01)	0.05***(0.01)
Proximity measures
Spatial distance	−0.06***(0.01)	−1.10***(0.12)	−1.11***(0.12)	−1.05***(0.11)	−1.04***(0.11)
Square of spatial distance	—	0.08***(0.01)	0.08***(0.01)	0.08***(0.01)	0.08***(0.01)
Interregional cognitive proximity	0.03***(0.01)	0.06***(0.01)	0.21***(0.05)	0.21***(0.05)	0.21***(0.05)
Square of interregional cognitive proximity	—	—	−0.08**(0.02)	−0.08**(0.02)	−0.08**(0.02)
Interregional technological proximity	0.93***(0.11)	0.93***(0.11)	0.94***(0.11)	3.95***(0.24)	3.94***(0.24)
Square of technological proximity	—	—	—	6.88***(0.47)	6.86***(0.47)
Interregional social proximity	0.88***(0.08)	0.90***(0.08)	0.92***(0.08)	0.88***(0.08)	1.25***(0.77)
Square of interregional social proximity	—	—	—	—	−0.16***(0.03)
Difference in knowledge production between pairs of regions	−0.19***(0.01)	−0.19***(0.01)	−0.19***(0.01)	−0.18***(0.01)	−0.18***(0.01)
Difference in innovation production between pairs of regions	−0.05***(0.01)	−0.05***(0.01)	−0.05***(0.01)	−0.04***(0.01)	−0.04***(0.01)
Dummy, equals 1 if regions belong to the same country	−0.08**(0.03)	−0.16***(0.02)	−0.16***(0.03)	−0.20***(0.03)	−0.21***(0.03)
Robust standard errors	Yes	Yes	Yes	Yes	Yes
Number of observations	20,332	20,332	20,332	20,332	20,332
R ²	.22	.22	.23	.23	.23
Joint F-test	662.12***	603.82***	550.99***	526.62***	486.32***

Note: Standard errors are given in parentheses. R&D = research and development; GDP = gross domestic product.

*Significant at 90 percent level.

**Significant at 95 percent level.

***Significant at 99 percent level.

The results are organized as follows. The baseline model in the section “The Joint Effect of Spatial and Aspatial Proximities on Scientific Collaboration”, Table 5, column 8 is for easing the cross-readability of our results reproduced in column 1 in Table 7. In the rest of the table, we add the squares of all the main distance/proximity measures, one per column. For instance, column 2 adds the square of spatial distance, column 3 the square of cognitive proximity, and so forth.

Results present interesting patterns:

for spatial distance, the squared parameter estimate displays a positive value, which implies a full-fledged distance-decay effect, with a negative, but less than proportional, impact of spatial distance on scientific collaboration. Decreasing returns seem to be present;

for cognitive and social proximity, the squared parameter estimates display negative and significant values, which, along with the positive estimate for the linear parameter, implies that scientific collaboration increases, but at a decreasing rate, with all above mentioned proximity measures, displaying therefore decreasing returns;

finally, the technological proximity squared parameter turns out to be positive and extremely large; this implies that the probability that two regions cooperate for scientific reasons increases, and more than proportionally so, as their technological profiles get more similar.

Such findings can be summarized in a qualitative way as shown in Figures 8 –11, where on the x-axes the measures of spatial distance, and interregional cognitive, technological, and social proximities are plotted, while on the y-axes we represent the marginal effects of, respectively, spatial distance, and interregional cognitive, technological, and social proximities on scientific collaboration.

Figure 8.

Marginal effect of spatial distance on scientific collaboration as spatial distance increases. Source: Authors’ elaboration.

Figure 9.

Marginal effect of interregional cognitive proximity on scientific collaboration as cognitive proximity increases. Source: Authors’ elaboration.

Figure 10.

Marginal effect of interregional technological proximity on scientific collaboration as technological proximity increases. Source: Authors’ elaboration.

Figure 11.

Marginal effect on scientific collaboration of interregional social proximity as social proximity increases. Source: Authors’ elaboration.

Figure 8 shows how the marginal effects of spatial distance on scientific collaboration change for different levels of spatial distance. For regions that are far away, the contribution of being spatially close is very limited compared to when two regions are very close by, showing that strong distance-decay effects exist in scientific cooperation.

Figure 9 tells a completely different story. It shows the way in which the marginal effect of interregional cognitive proximity adds to scientific cooperation for different levels of cognitive proximity. The result shows that, contrary to spatial distance, when two regions are cognitively proximate, they take advantage of their proximity in terms of scientific cooperation. This advantage, however, decreases when interregional cognitive proximity increases, showing increasing returns to cognitive proximity, at decreasing rates. This result is in line with the theoretical expectations in Boschma (2005) who claims that “cognitive proximity may easily lead to cognitive lock-in, in the sense that routines within an organization (or in an inter-organizational framework) obscure the view on new technologies or new market possibilities” (Boschma 2005, 64).

Figure 10 shows a third and different picture. While interregional technological proximity increases, its marginal effects on scientific cooperation increases, suggesting increasing returns at increasing rates. Any increase in technological proximity, in fact, increases scientific cooperation. Similarities in sectoral specialization imply similar informal knowledge, similar labor market skills, similar competences; all these elements push regions to develop specialized knowledge that helps in scientific research.

The same result is obtained for social proximity, which in Figure 11 shows increasing returns at increasing rates. Commonality of norms and incentives, therefore, turns out to be strategic for scientific cooperation; the higher such characteristics are, the easier the scientific collaboration between regions.

Conclusions

This article enters the debate on the ways space can be conceived in modeling economic interactions and provides empirical evidence in three main directions.

Firstly, evidence is provided on the role of a large number of proximity concepts, which widens the evidence on the distance-decay effects affecting scientific cooperation, in line with previous research on this topic.

Secondly, the results point toward the existence and relevance of synergic effects between different forms of space. In particular, while social proximity impacts positively scientific cooperation, with such impact decreasing in magnitude as spatial distance increases, the results on cognitive and technological proximity suggest that some form of complementarity seems to exist with spatial distance. At low spatial distance, some degree of interregional cognitive and technological distance seem to be bearable for the purpose of scientific cooperation, with regions filling the interregional cognitive and technological gap exactly by means of such low spatial distance. When, however, spatial distance increases, such bridge ceases to exist and work, which implies that in order to cooperate, regions must be cognitively and technologically close.

Thirdly, and lastly, our results point, for the first time to our knowledge, toward the existence of nonlinearities in the impacts of aspatial distance on scientific cooperation. While such results are per se interesting, they call for further research, possible with the use of partially, or fully, nonlinear estimators, thereby allowing the mapping of such nonlinear effects.

Far from being merely academic, these results call for profound policy implications. Currently, the future EU research agenda is being shaped and discussed at the highest policy levels. Ignoring possible synergies between distance-decay effects, for instance, may imply that the (formal and informal) rules for shaping transnational research groups may be misleading, and ultimately ineffective. Along the same lines, ignoring nonlinearities in distance-decay effects may lead to over- or underfunding of specific research lines or even wrongly assume that multidisciplinarity can afford the formation of large transnational research groups with various scientific backgrounds, ultimately leading to a cost-ineffective provision of research funds.

This last point, in connection with the decrease in research funds in most countries, because of the ongoing financial crisis, may lead to the failure to reach the “more with less” goal that most policy makers currently seem to have as a major mind-set.

Footnotes

Appendix

The two-digit and three-digit classes have the following summary statistics for our sample of 264 regions (Tables A1 and A2).

The main descriptive statistics for the dependent and independent variables employed in the empirical estimates are presented in Table A3.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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