Rosina Moreno
email: rmoreno@ub.edu.

-Innovation and Invention: Processes and Incentives

Keywords: inventors' mobility, networks of co-inventors, knowledge production function, spatial econometrics, European regions JEL: J61, O31, O33, R1

We investigate the importance of the labour mobility of inventors, as well as the scale, extent and density of their collaborative research networks, for regional innovation outcomes. To do so, a knowledge production function framework at the regional level is used. The empirical approach presented here takes full account of spatial interactions by estimating a spatial lag model, together, where necessary, with a spatial error model. In addition, standard errors are calculated using spatial heteroskedasticity and autocorrelation consistent (SHAC) techniques. The results suggest the existence of a robust positive correlation between intra-regional labour mobility and regional innovation, whilst the relationship with networks is less clear.

Introduction

Knowledge diffusion between individuals and firms is critical for innovation and growth (GROSSMAN and HELPMAN, 1991;[START_REF] Lucas R | On the mechanics of economic development[END_REF][START_REF] Romer | Increasing Returns and Long-run Growth[END_REF][START_REF] Romer | Endogenous Technological Change[END_REF]. At firm and geographical level, knowledge is known to flow through a variety of mechanisms [START_REF] Döring | What do we know about geographical knowledge spillovers and regional growth?: A survey of the literature[END_REF], among which the labour mobility of highly skilled personnel and the existence of research collaboration networks are considered pivotal.

The goal of this paper is to analyse the contribution made by these collaborative networks and the labour and geographical mobility of inventors to the process of knowledge creation. To do so, we investigate the quantitative relationship between these two key Specifically, the empirical analysis is based on a regional knowledge production function (KPF hereafter) framework, which is used to model the aforementioned relationship for a large sample of European NUTS-2 regions.

Drawing on patent data and computerized algorithms to identify individual inventors, a large dataset of individuals containing information such as their personal address(es), their patenting history, the owners of their patents (i.e. a firm, a university or other public institution, or the inventors themselves), the co-authors of their patents, and so on, is created. Given the lack of data on single, individual inventors, very few studies have examined the influence of these features on regional innovation.

Among the questions addressed in this study are the following: What is the contribution of inventor networking and inventors' labour mobility to the regional intensity of patenting? Do cross-regional mobility and cross-regional networking play an important role? What impact is attributable to mobility and networking once spatial interactions have been controlled for?

Our choice of the term knowledge "flows" instead of, for instance, knowledge "spillovers" or "externalities" is not accidental and requires an explanation before proceed. As [START_REF] Breschi | Mobility of skilled workers and co-invention networks: an anatomy of localized knowledge flows[END_REF] point out, knowledge may flow locally, but not necessarily as an externality. When knowledge is transferred following the hiring of an employee from another firm, or by means of a cooperation agreement, market mechanisms are operating and no externalities or spillovers can be said to exist. Clearly, these flows may include pure externalities if all the knowledge transferred is not compensated accordingly, but in all instances it will only constitute a marginal part. With these thoughts in mind, the However, it is very difficult to do this empirically, first because the mechanisms defined as market-based may bring pure externalities with them, and second because the ones acknowledged as pure spillovers, e.g., agglomeration externalities, may be partially paid off. So this is an important theoretical discussion that cannot be fully addressed in an empirical framework like the present one. 1 The econometric approach takes full account of the spatial structure of the data by applying spatial econometric techniques. Unlike previous studies of innovation, however, the spatial lag model is not used to the exclusion of the error model or vice-versa, but rather a rich spatial specification is allowed for. To achieve this, first the spatial lag model is estimated and then the non-parametric heteroskedasticity and autocorrelation consistent (HAC) estimator of the variance-covariance (V-C) matrix in a spatial framework (following [START_REF] Kelejian | HAC estimation in a spatial framework[END_REF] is applied is performed. To the best of our knowledge, no previous studies have estimated a knowledge production function using both a spatial lag model and the robust spatial HAC estimation of the V-C matrix.

The rest of the paper is organized as follows: section 2 reviews the literature on inventor networking and mobility, and their relationship with knowledge diffusion and creation; section 3 describes the model and the hypotheses proposed; section 4 presents the data; whilst section 5 includes the results. Finally, section 6 presents the conclusions and identifies certain limitations in the approach. The literature on collaborative research networks, and their impact on knowledge diffusion and innovation, has expanded greatly in recent years. 2 This is particularly true in the case of networks of co-inventors, thanks to the availability of relevant data (that is, copatent data). Part of this literature has been devoted to explaining the determinants of these collaborative patterns [START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF]MAGGIONI and UBERTI, 2008), while another important strand has focused on networks as mechanisms for inter-regional R&D spillovers [START_REF] Kroll | Spillovers and proximity in perspective: A network approach to improving the operationalisation of proximity[END_REF]PONDS et al., 2007PONDS et al., , 2010)), and, in particular, networks as the means by which knowledge diffuses between individuals and across firms (BRESCHI andLISSONI, 2004, 2006;2009;GOMES-CASSERES et al., 2006;[START_REF] Singh | Collaborative Networks as Determinants of Knowledge Diffusion Patterns[END_REF]. SINGH (2005) finds strong evidence in the US that the existence of interpersonal ties in the form of co-patents increases the probability of knowledge flows, as measured by patent citations. Indeed, he hints that these ties are important in determining patterns of intra-regional and intra-firm knowledge flows. SINGH claims that geography matters especially because interpersonal networks tend to be regional in nature (Op. cit.). Similar results are found by [START_REF] Breschi | Knowledge networks from patent data: methodological issues and research targets[END_REF] for Italy. Recent findings by [START_REF] Breschi | Mobility of skilled workers and co-invention networks: an anatomy of localized knowledge flows[END_REF], using patent applications to the European Patent Office (EPO) in certain technological fields (biotechnology, organic chemistry, and pharmaceuticals), suggest that networking activity across firms (and locations) is to a large extent responsible for the localisation of knowledge flows, indicating that the residual effect of non-market externalities is not as great as was previously believed.

Background

All these studies stress the importance of networks as mechanisms of knowledge transmission, and hence of knowledge creation. Co-location and shared space are reported to be neither necessary nor sufficient for knowledge flows; rather it appears to be closely involved with innovative activities, that is critical for the effective diffusion of knowledge [START_REF] Boschma R | Proximity and Innovation: A Critical Assessment[END_REF]. If this is the case, the features of the inventors' network structure at any given location will play a significant role in regional innovation outcomes.

A number of empirical analyses have recently been conducted in a knowledge production function framework by BETTENCOURT et al. (2007a,b), FLEMING et al. (2007[START_REF] Lobo | Metropolitan patenting, inventor agglomeration and social networks: A tale of two effects[END_REF] for the case of US metropolitan statistical areas (MSAs). Broadly speaking, various features of the inventors' network are found to have different and significant effects on creativity. While the scale and extent of networks are reported to have a positive impact, the density of these networks seems to have a negative effect, which has been attributed to the existence of superfluous information (BETTENCOURT et al., 2007a,b;[START_REF] Lobo | Metropolitan patenting, inventor agglomeration and social networks: A tale of two effects[END_REF]. However, the importance of inventors' networks is not equally significant in all the analyses conducted (FLEMING et al., 2007), and further research in this field is still required. At present, few empirical studies of inventors' networks have been performed and the evidence of their benefits remains scarce.

The present analysis is closely related to these recent studies, since it also uses a KPF to assess the effect of networks and their particular structure on aggregate innovation outcomes. However, here the production function is applied to European regions as opposed to US MSAs. 3 Moreover, in contrast to the earlier studies, spatial relationships across regions are taken fully into account by applying spatial econometric techniques.

Yet, no significantly different results are expected a priori vis-à-vis those previously reported for the US. Similarly, earlier studies have examined how the labour mobility of inventors acts as a key mechanism in the diffusion of knowledge [START_REF] Almeida | Localisation of knowledge and the mobility of engineers in regional networks[END_REF][START_REF] Rosenkopf | Overcoming Local Search Through Alliances and Mobility[END_REF][START_REF] Saxenian | Regional Advantage. Culture and Competition in Silicon Valley and Route 128[END_REF]. However, this line of research has been less prolific. 4 One strand of this literature has shown the relationship between mobility and the flow of knowledge as measured by patent citations, as well as the knowledge gain by a firm hiring an inventor from another firm. For example, in a pioneering study, [START_REF] Almeida | Localisation of knowledge and the mobility of engineers in regional networks[END_REF] show that inter-firm mobility of patent holders in the US semiconductor industry influences the local transfer of knowledge across firms. Similar findings are reported in BRESCHI and LISSONI (2009)'s study mentioned above for US inventors in selected technological fields making patent applications to the EPO. In a similar vein, [START_REF] Agrawal | Gone but not forgotten: labour flows, knowledge spillovers, and enduring social capital[END_REF] stress that when inventors leave their workplace they maintain interpersonal ties with their former colleagues, who may well later cite their work. In addition, several studies [START_REF] Crespi | The mobility of university inventors in Europe[END_REF]CORREDORIA and ROSENKOPF, 2006;[START_REF] Lee | International Knowledge Flows: Evidence from an Inventor-Firm Matched Data Set[END_REF][START_REF] Singh | Recruiting for Ideas: How Firms Exploit the Prior Inventions of New Hires[END_REF][START_REF] Song | Learning-by-hiring: When is mobility more to facilitate interfirm knowledge transfer?[END_REF] have stressed the role of mobility in increasing the hiring firm's use of a hired inventor's prior knowledge.

Parallel to these studies, another line of research has studied mobility by focusing attention on inventors' performance itself. For instance, mobility-productivity relationships have been studied by [START_REF] Hoisl | Does mobility increase the productivity of inventors?[END_REF][START_REF] Hoisl | Tracing mobile inventors: The causality between inventor mobility and inventor productivity[END_REF] for German, by [START_REF] Lenzi | Patterns and determinants of skilled workers' mobility: evidence from a survey of Italian inventors[END_REF] for Italian, and by [START_REF] Shalem | Software patents, inventors and mobility[END_REF] for Israeli inventors. Broadly speaking, it has been shown that mobility may in fact enhance productivity [START_REF] Hoisl | Does mobility increase the productivity of inventors?[END_REF], although results in this direction are not as robust as one would expect [START_REF] Shalem | Software patents, inventors and mobility[END_REF], a fact that these authors attributed to what they identified as the short-term costs of mobility. If an individual's innovative output increases on moving, and if the new host firms acquire more knowledge and are more efficient in their innovative activities, the innovative capacity of a region as a whole should increase as the degree of inventors' mobility rises across firms within a region. To the best of our knowledge, there have been few empirical attempts at quantifying the effect of this feature of the local labour market for inventorsin other words, the degree of their job-to-job mobility -on regional innovation outcomes.

As such, this constitutes one of the main contributions of this paper.

Model and hypotheses

Baseline specification

In order to meet the goals identified above in the introduction, the knowledge production function framework at the regional level is used. First used in the seminal studies of GRILICHES (1979) and[START_REF] Hausman | Econometric models for count data with an application to the patent-R&D relationship[END_REF] at the firm level, this framework was subsequently extended by [START_REF] Jaffe | Technological opportunity and spillovers of R&D: evidence from firms patents, profits and market value[END_REF][START_REF] Jaffe | Real effects of academic research[END_REF]) to the regional level. Since then, regional KPF has been the standard tool for assessing the influence of regional innovation efforts on regional innovation output. However, many empirical exercises have sought to test this relationship by simultaneously considering a number of regional structural characteristics, which would also tend to have a positive impact on regional innovation output. The KPF has been widely estimated for the case of the US [START_REF] Acs | Patents and innovation counts as measures of regional production of new knowledge[END_REF]ANSELIN et al., 1997) and Europe (ACKÇOMACK and TER [START_REF] Akçomak | Social capital, innovation and growth: Evidence from Europe[END_REF][START_REF] Bottazzi | Innovation and spillovers in regions: Evidence from European patent data[END_REF]DE DOMINICIS et al, 2007;MORENO et al., 2005a).

Our point of departure is the simplest specification of this model:

F o r P e e r R e v i e w O n l y 9 ) , ( • L K f A Y δ = , ( 1
)
where Y is the innovative output of a given region, which depends on two knowledge inputs, i.e., the knowledge capital of a given region ( K ), and the R&D employment of that region ( L ) -see GRILICHES (1979), footnote 3. Moreover, the innovation output is allowed to depend on an R&D productivity index 5 for that region, A . For simplicity, it is assumed that the KPF follows a Cobb-Douglas functional form:

, • • • α β δ i i i i L K A C Y = 1 0 < < α , 1 0 < < β , 1 = + β α (2)
where i denotes the region, and C the constant term capturing the impact of all common factors affecting innovation. In order to guarantee reliable results in the estimations, the regional observations need to be comparable in size: equation 2 is pre-multiplied by a factor of N 1 , where N is the total population of each region.

α β δ i i i i l k A C y • • • = , (3)
where

N Y y / = , N K k / =
, and

N L l / =
. In this way, the innovative intensity of regions (patent applications per capita) depends on the stock of knowledge per capita and the number of R&D employees as a proportion of the total population.

From a neoclassical perspective, all kinds of R&D efforts will systematically lead to a larger number of inventions, so regions investing more heavily in R&D will tend to innovate more. However, this argument overlooks the importance of a set of factors that [START_REF] Rodríguez-Pose | Research and Development, Spillovers, Innovation Systems, and the Genesis of Regional Growth in Europe[END_REF]. To capture a variety of returns that might affect innovation outcomes, the R&D productivity index is assumed to be a function of a number of (Hicks neutral) control variables. In addition to pure externalities and other controls, this index is assumed to be affected by the level of inventors' labour mobility within a given region, and by the scale and density of its collaborative research networks.

The hypotheses to be tested here are:

H1. Collaborative research networks of inventors boost regional innovation capability.

Networks of inventors may have a direct influence on innovation. The rationale behind this is that the simple cross-fertilization of previously unconnected ideas will lead to better knowledge outputs [START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF] and that individuals connected within a collaborative framework are more willing to learn from each other than is the case of isolated inventors. Moreover, collaborative research projects may achieve scale economies and may lower research costs by reducing the duplication of research efforts among the participants in the network. On the other side, indirect effects of networking may be due to knowledge diffusion -and subsequent innovation -and the formation of social capital. Thus, close network links should prove more useful in transferring complex knowledge (COWAND and JONARD, 2004), especially knowledge with a high component of "tacitness" [START_REF] Singh | Collaborative Networks as Determinants of Knowledge Diffusion Patterns[END_REF]. Additionally, professional relationships of this nature enhance trust and cooperative behaviour between individuals (hence raising the level of social capital) which has been shown to be a further element in innovation and knowledge transmission (AKÇOMAK and TER [START_REF] Akçomak | Social capital, innovation and growth: Evidence from Europe[END_REF][START_REF] De | Human capital, social capital, and innovation: A multi-country study[END_REF]MIGUÉLEZ et al., 2008). In line with the literature (see Section 2), social network analysis (SNA) tools are employed to investigate empirically the quantitative relationship between inventors' collaborations and levels of inventiveness. 6 We are particularly interested in measuring two aspects of inventors' networks. The first is the scale of these networks, i.e., whether a greater number of social ties, or just simply more inventors involved in co-innovations, are beneficial for inventive intensity. Here, three distinct variables are used to proxy the scale of the networks in a community. However, we are reluctant to include the three variables at the same time in the regressions because of their high degree of collinearity and so three separate models are estimated. Clearly, a positive effect on creativity is expected.

The second aspect that concerns us is the strength of the inventors' community ties, measured as the network density. The naïve, expected effect of density on innovation is positive. However, we should bear in mind GRANOVETTER's (1985) warning that overly strong interpersonal ties may well hamper innovation because, at some point, the information flowing across those ties becomes redundant. As shown in Section 5 below, the findings of the empirical analysis of network density are in agreement with those encountered for the case of the US.

H2. The mobility of inventors within the local labour market of a region enhances innovative intensity.

Recent studies have shown that mobile inventors are more productive than non-mobile ones, measured either by patent applications or by citations received to their work [START_REF] Singh | Recruiting for Ideas: How Firms Exploit the Prior Inventions of New Hires[END_REF][START_REF] Hoisl | Does mobility increase the productivity of inventors?[END_REF][START_REF] Hoisl | Tracing mobile inventors: The causality between inventor mobility and inventor productivity[END_REF][START_REF] Shalem | Software patents, inventors and mobility[END_REF]. Hence, communities of inventors within regions with larger degrees of labour mobility are expected to be more productive and innovation intensive. On the other hand, mobility may also favour knowledge diffusion. As knowledge is embedded in individuals, when they move they also take with them the knowledge capital they have accumulated. Their movement across firms therefore contributes to knowledge exchange between firms [START_REF] Boschma R | How does labour mobility affect the performance of plants? The importance of relatedness and geographical proximity[END_REF]. Skilled workers take their knowledge with them and share it in a new workplace with their new employer and colleagues. In return, they acquire new knowledge from their new colleagues, establish new links and social networks for future collaborations based on trust and, in general, promote new combinations of knowledge [START_REF] Laudel | Studying the brain drain. Can bibliometric methods help?[END_REF]TRIPPL and MAIER 2010).

Given these two hypotheses, the R&D productivity index is a function of the following variables ) , , , , , (

i i i i i C i X Z DENS NET MOB A g A = , ( 4
)
where MOB is the measure of mobility, NET is the scale of the networks in a given region, DENS is a measure of the density of regional networking, Z is a set of variables controlling for the existence of externalities and other knowledge flow mechanisms derived from agglomeration economies, specialization, urbanization, and market access; and X is a set of technical controls to capture differences in economic structures across regions. Moreover, C A is a country-specific effect capturing both institutional differences across countries affecting innovation and the existence of so-called national systems of innovation. Thus, equation 3 becomes The R&D productivity index is modelled as a simple multiplicative function of locationspecific features:

[ ] α β δ i i i i i i i C i l k X Z DENS NET MOB A g C y • • ) , , , , , ( • = . (5)
n j i i i i i C i X Z DENS NET MOB A A φ φ φ φ φ • • • • • 3 2 1 = . ( 6
)
Expressing this in log form yields the following specification,

i n i j i i i C i X Z DENS NET MOB A A •ln •ln •ln •ln •ln ln ln 3 2 1 φ φ φ φ φ + + + + + = . ( 7
)
Expressing 3 in log form and substituting 7 in the resulting expression gives the following empirical model, to which an (a priori) random error term is now added, i ε :

it i N it n it j it it it it it it EFFECT COUNTRY DUMMY X Z DENS NET MOB l k y ε ω ω ω ω ω ω α β ξ + + + + + + + + + + + = - - - - - - - _ _ •ln •ln •ln •ln •ln •ln •ln •ln ln 1 1 1 3 1 2 1 1 1 1 , ( 8
)
where

C ln = ξ , δ φ ω • r r = , it it PATpc y = , 1 1 _ - -= it it RDpc STOCK k and 1 1 - -= it it HRST l
. We also add the subscript t denoting the time dimension, because although a cross-section regression is going to be estimated, we should be aware that all the explanatory variables pre-date the period of analysis of the dependent variable and can be assumed, in principle, to be exogenous. It is acknowledged that innovation and knowledge variables are, by and large, spatially correlated, irrespective of the level of regional disaggregation, the time span, or the sample of regions analysed [START_REF] Acs | Patents and innovation counts as measures of regional production of new knowledge[END_REF], ANSELIN et al., 1997;AUTANT-BERNARD and LESAGE, 2011;[START_REF] Bode | The spatial pattern of localized R&D spillovers: an empirical investigation for Germany[END_REF]MORENO et al., 2005b). Indeed, knowledge tends to flow locally, but there is no reason to assume that it stops flowing because of regional borders (AUDRETSCH and FELDMAN, 2004). Here we are interested in elucidating whether the preliminary findings are robust to the correct specification of these spatial effects. Thus, the following hypothesis is considered:

Spatial structure of innovation

H3. The spatial structure of the data also matters.

To step in this direction, the R&D productivity index is now assumed to be a function of the innovation intensity of the neighbouring regions of a given region,

∏ ≠ = N i j j w j ij y 1 ρ
, where ij w are bilateral spatial weights, which will depend on the distance between regions i and j , while ρ is the output elasticity of cross-regional effects of innovation intensity.

) , , , , , , (

1 i i i i i N i j j w j C i X Z DENS NET MOB y A g A ij ∏ ≠ = = ρ . ( 9
)
Expressing this in log form in the multiplicative version of 9 and 3, and making the necessary rearrangements, we obtain the following model for estimation, including once again a random error term, i ε :

F o r P e e r R e v i e w O n l y 15 i N it n it j it it it it it it i j ij it EFFECT COUNTRY DUMMY X Z DENS NET MOB l k PATpc w PATpc ε ω ω ω ω ω ω α β ρ ξ + + + + + + + + + + + + = - - - - - - - ≠ ∑ _ _ •ln •ln •ln •ln •ln •ln •ln •ln ln • ln 1 1 1 3 1 2 1 1 1 1 , (10)
Thus, equation ( 10) suggests the estimation of the spatial lag model -as opposed to the spatial error model (see [START_REF] Anselin | Spatial Econometrics: Methods and Models[END_REF]. Indeed, this model implies an economically meaningful interpretation, i.e., spillovers across regions captured in the spatial lag of the dependent variable, whereas the spatial error autocorrelation can be attributed to noise [START_REF] Anselin | Spatial Econometrics: Methods and Models[END_REF] or even to a misspecification of the model [START_REF] Andersson | Spatial dependence and the representation of space in empirical models[END_REF]. However, checks for any remaining spatial correlation in the residuals following the estimation of this model will be presented.

As far as the spatial econometric techniques are concerned, the inclusion of the spatial lag of the dependent variable as an additional regressor introduces endogeneity and, therefore, OLS estimations are no longer consistent. Thus, these models are usually estimated by maximum likelihood, though this method requires specific assumptions regarding the distribution and properties of the variables [START_REF] Kelejian | A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances[END_REF].

Moreover, the need to estimate the spatial lag and error model simultaneously will make the use of the technique cumbersome, if not impossible (FINGLETON and LE GALLO, 2008). In this setting, spatial two stage least squares (S2SLS) procedures are preferred, where the instruments are the spatial lags of the remaining explanatory variables. 7

A crucial decision in spatial econometrics is the choice of the weighting matrix to characterize the spatial relationships between regions. Different matrices can lead to different conclusions (HARRIS and KRAVSTOVA, 2009) However, instead of simply using contiguity matrices, the concept of k-nearest neighbours is used. Thus, we measure the distance to a fixed number of neighbours, k, using a matrix where k=5, because both the mean and the median number of neighbours for the contiguity matrix is located around 5.

Networks and mobility: Cross-regional linkages

Continuing with the idea of exploiting specific relationships across regions, explicit interlinkages are now taken into account. If they are relevant for regional innovation, their omission will lead to biased and inconsistent estimates.

H4. Cross-regional collaborations and inter-regional mobility enhance creativity. The more inventors collaborate with fellow inventors outside the region, the greater are the returns on innovation. Similarly, the greater the number of inventors moving into a given region, the greater is the patenting activity of that region.

To check this hypothesis, two additional variables are now included. Thus, the last specification includes the variable OUT_COLL, which compares the number of coinventors outside the region with the total number of inventors within a region. They also include the variable Inward Migration Rate (IMR), which is calculated counting the number of inventors moving into the region compared to the total number of inventors 17 identified in that region. Other things being equal, a positive and significant effect for both variables, for the same reason that a positive effect was expected for the scale of networks and labour mobility within the region, is expected. This cross-regional knowledge is likely to be critical for innovation because imported knowledge is even more relevant than that already held locally.

Data

Innovation intensity is measured by patent applications per capita (PATpc), a variable widely used in the literature to proxy innovation outcomes. As is well known, this proxy presents serious caveats since not all inventions are patented, nor do they all have the same economic impact, as they are not all commercially exploitable (GRILICHES, 1991).

In spite of these shortcomings, patent data have proved useful for proxying inventiveness as they present minimal standards of novelty, originality and potential profits, and as such are a good proxy for economically profitable ideas [START_REF] Bottazzi | Innovation and spillovers in regions: Evidence from European patent data[END_REF]. Patent R&D expenditure data are drawn from Eurostat and are used to construct the R&D stock proxy (STOCK_R&Dpc). The accumulation of R&D is described as 18 rate set at 5%. Other depreciation rates, however, do not affect the results. The initial stock of R&D has been calculated using the perpetual inventory method,

1 & & & - - = ∆ t t D R D R D R
) ( & & 0 δ + = - g D R D R n t
, where

n t D R - &
is the first year for which the data were available, and g is the geometric average annual growth rate of R&D expenditure between 1996 and 2000. R&D employment has been proxied using Human Resources in Science and Technology (HRST) data extracted from Eurostat. Ideally, direct data on R&D employment, also available from Eurostat, should be used, but the number of missing figures is considerable and so we opted not to use this dataset.

The data for constructing the mobility and network variables are also taken from the REGPAT database. In spite of the vast amount of information contained in patent documents, a single ID for each inventor and anyone else is missing. However, in order to draw the mobility and networking history of inventors, it is necessary to identify them individually by name and surname, as well as via the other useful details contained in the patent document. The method chosen for identifying the inventors is therefore of the utmost importance in studies of this nature. Here, then, the methodology proposed by MIGUÉLEZ and GÓMEZ-MIGUÉLEZ ( 2010) is followed, who, in line with a growing number of researchers in the field, suggest several algorithms for singling out individual inventors using patent documents. In the present study, this procedure has been used for a subsample of inventors whose patent applications have been made from one of 17 countries (see Appendix 1) between 1993 and 2002. Additionally, and unlike the dependent variable, we only apply the algorithms to EPO patents also filed under the Patent Cooperation Treaty (PCT). This condition was adopted for two main reasons. The first is that patents filed during an international phase (the PCT) can be assumed to be more technologically and economically exploitable, since applying for EPO patents under PCT procedures is more expensive and time-consuming; therefore, the knowledge Eventually, however, the procedure provides us with a sample of 646,678 records, from which 285,831 individual inventors are identified.

Once each inventor has been assigned an individual identification, mobility and network data can be calculated for each region. A "mobile" inventor is broadly defined as an individual who moves across different organisations offering his/her services [START_REF] Breschi | Mobility of skilled workers and co-invention networks: an anatomy of localized knowledge flows[END_REF]. Therefore, mobility can refer either to labour mobility understood in its strictest sense (an employee leaving a firm to take up a position in a new one), or to that demonstrated by consultants, freelance workers, university inventors, and the like.

We assume that both constitute sources of knowledge flows to the extent that in the two instances knowledge is transferred from former employers or customers to new ones.

Mobility is then proxied as the average number of assignees 9 for each inventor identified per region. To make this calculation, the recent study by THOMA et al. (2009a,b) and the OECD Harmonised Applicants' Names (HAN) database (October, 2009), aimed at identifying single applicants in patent documents, is used. Additionally, all patents with more than one applicant, or assignee, are discarded, as we were unable to discriminate labour relationships between applicants and inventors in a multi-applicant patent.

However, from the initial sample of 646,678 records, only 59,687 were discarded.

The design of the network variables is based on the theory of SNA. The inventors form the nodes in the network, and these are grouped via edges or ties (in this instance, copatents) into different components. A component, therefore, is formed by all the inventors in the network who are linked in such a way that a continuous path via the edges The largest component is the largest set of inventors that can be linked through direct and indirect collaboration ties.

The scale of the network structure in each region -each regional community of inventors -is proxied using three different variables. Among them, two measures of connectivity of the network are included. Connectivity is measured counting the number of edges (ties)

between inventors within a given region. Thus, both the absolute number of ties (CONN_ABS) and its relative measure (CONN_INV -the absolute number of ties with respect to the number of inventors within each region) are considered separately. As a third measure, the size of the largest component (SIZE_LC -the number of inventors that belong to the largest component with respect to the total number of inventors, in each region) is included as well. A positive and significant coefficient is expected for both the mobility and the networking variables.

The strength of these ties is proxied by the network density, which is the number of ties between inventors within the region divided by the possible number of ties within that region. Formally, where i T stands for the number of edges (ties) within a given region, and i Q is the total number of inventors within that region. As stressed earlier, the expected effect (be it positive or negative) of innovation density is not so clear a priori.

2 ) 1 ( - = i i i i Q Q T DENS , (11)
In the specification, up to four variables are included to capture the effect of other knowledge flow mechanisms ( ) Likewise, a set of four controls ( ) X capture differences in the technological and economic structures across regions: the shares of manufacturing employment in each region (MAN), and the shares of biotechnology (BIOTECH), organic chemistry (CHEM), and pharmaceuticals (PHARMA) in their patenting activity, according to the IPC classification; since these three sectors tend to be more research intensive, controls for their presence in each region are necessary. 12 A summary of the variable descriptions and the data sources can be found in Appendix 2. 13 The empirical analysis is conducted for the NUTS 2 regions of 17 Western European countries (EU-15 plus Norway and Switzerland, see Appendix 1). However, due to data

Z

Results

Results on the role of research networks and labour mobility of inventors

Table 1 presents the results of the OLS estimations with robust standard errors to control for heteroskedasticity of unknown form. In columns (i), (ii), and (iii) the estimations are presented without country dummies. It should be borne in mind that three specifications using alternative proxies for the network scale have been estimated. In principle, the coefficients can be interpreted as elasticities, since the variables in the regression are expressed in natural logarithmic form: the proportional increase in patenting activity in response to a 1% increase in a given explanatory variable. In this way, the interpretation of R&D stock and human capital coefficients is straightforward. In the case of the remaining coefficients, some doubts must remain regarding their direct interpretation. Since the functional relationship between these variables and their response is decided in an ad-hoc fashion, their sign and significance can be fairly informative, although any interpretation of their magnitude should be treated with caution [START_REF] Bode | The spatial pattern of localized R&D spillovers: an empirical investigation for Germany[END_REF].

Some specific results are worth highlighting. The R&D stock and human capital parameters are, in general, strongly significant; they have the expected sign and present similar values to those reported elsewhere in the literature. The control variables tend to be significant and with the expected sign, although there are a number of exceptions. The specialisation index is only significant (and positive) when country dummies are included, and the same is true in the subsequent tables. The share of patents in organic chemistry has a positive impact on innovation, whilst, surprisingly, biotechnology and pharmaceutical shares correlate negatively (and in the latter case, the correlation is always significant). We believe that manufacturing employment (strongly positive and significant) must capture part of the effect of these three sectors on innovation. Strikingly, population density is significant, but contrary to our expectations, it is negative. This can be interpreted in several ways: first, the positive effects of market potential may already be taken into account with the inclusion of GVA per capita, which is always significant and positive. Moreover, it might be that overly dense areas suffer several costs related to the congestion effects of agglomeration (negative externalities). Alternatively, the result may also reflect the fact that the regions in the sample are particularly heterogeneous. Finally, the significant yet negative effect of population density on innovation may point to the absence of urbanisation (inter-industry) economies, at the expense of specialisation economies. 15 The focus variables of this study are also significant. Mobility, for example, is always significant at 1%, presenting parameters around 0.26 and 0.29, whilst the relationship between the scale of the networks and innovation is always positive and strongly significant, except in the case of the size of the largest component variable. Thus, hypotheses 1 and 2 of the theoretical section are confirmed. In addition, network density shows a negative impact on innovation intensity, which supports GRANOVETTER's (1985) arguments about weak ties and innovation. Encouragingly, the results are broadly similar to the findings reported for the US, although the approach adopted here is slightly different.

[ In short, the empirical analyses undertaken here support the hypotheses concerning the importance of labour mobility and networks in the local labour market for the diffusion and creation of regional innovations. However, several extensions to this initial approach can now be made, in order to relax the initial assumptions concerning the error term of the empirical model.

Results on the spatial structure of the data

As can be seen at the end of Table 1, Moran's I tests and Lagrange Multiplier (LM) tests (robust and non-robust) are also calculated. OLS residuals remain spatially correlated after the estimations -even when country dummies are included, although quantitatively their importance is relatively small. Moreover, LM tests seem to point to the need to estimate the spatial lag model, as was suggested in equation 10. Again, however, tests for residual spatial autocorrelation after the estimation of the spatial lag model will be performed.

Thus, Table 2 shows the results of the spatial lag model presented in equation 10, and corresponding to hypothesis 3. As can be seen, the parameter for the spatial lag is positive and strongly significant, suggesting the existence of relevant knowledge flows across regions affecting their respective innovation outcomes and thus confirming the hypothesis.

Again, this result is in line with findings reported elsewhere. Comparing these results for the remaining explanatory variables with the previous OLS estimations, it can be seen that both the value of the parameters and their significance remain practically unchanged.

[Insert ANSELIN and KELEJIAN (1997), which points to the existence of a residual correlation (albeit not very strong) in at least three of the estimations (iv, v, and vi). Given these results, we believe that spatial correlation is no longer a problem, although we will confirm this below. To address this issue, recent developments in spatial econometrics by [START_REF] Kelejian | HAC estimation in a spatial framework[END_REF] are implemented which, in contrast to earlier work, do not impose a specific functional form of the spatial correlation of the error term 16 , i.e. the spatial HAC estimator of the V-C matrix. The rationale behind this technique is drawn from the time-series results; basically it is a non-parametric technique for estimating the V-C matrix using the averages of cross-products of residuals, the range of which is determined by a kernel function. This kernel will determine which pairs of regions, i,j, are included as cross-products. In the present paper, the kernel is formulated as

) / ( d d K ij ,
with ij d the distance between regions i and j, and d the bandwidth.

) / ( d d K ij equals 0 when d d ij ≥ . The triangular kernel, ) / ( 1 ) / ( d d d d K ij ij - =
, is used here as the form of the function. The bandwidth used is calculated based on distances to the 10 nearest neighbours. As will be shown in the final section, robustness checks using both different forms of the kernel -Epanechnikov and bisquare -and alternative numbers of nearest neighbours to calculate the bandwidth are performed, but these checks do not alter the results.

Table 3 summarises the results of the estimation of the spatial model with a spatial lag and the spatial heteroskedastic and autocorrelation consistent estimation of the V-C matrix. Encouragingly, the significance of the parameters in even though this variable presents smaller parameters than those presented by other networking variables, it is significant in the specifications that include country dummies.

The same results are not found in the case of the IMR, where positive parameters are only slightly significant in the OLS estimation without country dummies, and they are not significant for any of the other specifications. The interpretation of these results is as follows: the geographical mobility of inventors is quite localised [START_REF] Breschi | Mobility of skilled workers and co-invention networks: an anatomy of localized knowledge flows[END_REF], and the aggregate unit of analysis (NUTS2, and some NUTS1 and NUTS0) fails to identify a number of movements that occur within the region and between, for instance, NUTS3 regions. Networks, however, can connect points further apart in space (PONDS et al., 2010), and thus help to overcome geographic distances [START_REF] Singh | Collaborative Networks as Determinants of Knowledge Diffusion Patterns[END_REF]. In addition, it could be argued that the actual origin of these inventors -that is, whether or not they come from a more innovative region -also matters. Comparing the spatial residual tests at the bottom of Table 4 with those at the bottom of Tables 1 and2, it is unfortunately impossible to assert categorically that the inclusion of economically meaningful linkages across regions has any significant effect on the residuals in the previous estimations. In short, a reduction in the OLS spatial residual tests (especially those of the spatial LM and RLM) is observed if Table 1 (columns i and iv)

and Table 4 (columns i and ii) are compared. However, comparing Table 2 (columns i and iv) and Table 4 (columns iii and iv), no reduction in the value of the Moran's I is observed. Consequently, it seems that the inclusion of these variables does not completely eliminate the spatial correlation in the residuals. Obviously, these results may depend on the (spatial) weights matrix chosen for the analysis, though several (spatial) alternatives have been tried without relevant changes in the results. However, further research on this question is required.

[Insert Table 4 about here]

Conclusions, implications and limitations

The research conducted here has sought to assess the importance of specific knowledge flow mechanisms, namely networks of co-invention and labour mobility, on regional Strong support for the positive relationship between regional labour market mobility and regional innovation intensity is found. The influence of networks is also fairly important, but the strength of these ties (measured as the network density) was found to have a negative influence on innovation. In line with previous studies, we rely on the explanations proffered by GRANNOVETTER (1985) concerning the importance of weak ties for innovation. This idea is further strengthened with the inclusion in the regressions of a proxy for the number of collaborations with inventors outside the region -hypothesis 4, positive and significant -which leads us to conclude that weak, distant ties are indeed more important for innovation.

Contrary to our expectations, however, the inflow of inventors from other regions does not have a markedly significant impact on innovation outcomes. In principle, these findings can be attributed to the level of regional disaggregation at which the analysis was conducted, although, as [START_REF] Shalem | Software patents, inventors and mobility[END_REF] state, the existence of certain short-term costs of a change in location should not be overlooked.

However, the results reported here reveal certain tendencies from which a number of policy implications can be directly derived. Research collaborations across firms and regions are pivotal for acquiring external knowledge (see similar claims in SINGH, 2005), and for promoting the creation of new knowledge. The promotion of distant, weak ties embracing as many actors as possible is therefore a plausible and beneficial policy option from a regional perspective. Policy recommendations regarding mobility within the local labour market are not so straightforward. Although mobility seems to be desirable at an aggregate level, and also at the inventor level, it could be understood as a zero-sum game for firms. A policy option might be, therefore, to promote competition for talent at interregional and, in particular, at international levels.

Our approach has several limitations. Below, we note some of the drawbacks to the analysis, which should serve as the basis for improved approaches.

Patenting activity does not take into account all the research collaboration relationships that exist between individuals or all the mobility patterns of those individuals. In so far as other variables capturing similar concepts can be assembled, the analysis conducted should be repeated. Related to the first of these shortcomings, extending the sample to include all EPO patents and not just those that had been filed under the PCT will shed more light on the relationships analysed here.

As regards the raw data used, improvements to the suggested algorithms are likely to provide variables with fewer measurement errors and, ultimately, more consistent estimations. Moreover, even though outside collaborators are included here as a regressor, our method of measuring regional networks imposes implicitly artificial boundaries on the administrative limits of the region, thereby failing to identify possible strong links between inventors located in separate regions, or links between co-located inventors via a third inventor located outside the region. Suitable variables reflecting the structure of the whole network and able to capture these two phenomena might alter some of the results. However, additional theoretical developments should be carried out before proceeding along these lines. across regions in the production of knowledge, on which to base the estimated model is lacking in this paper and, arguably, throughout the literature of spatial econometrics and knowledge spillovers. Analogously, a specific, more meaningful modelling of these interactions in the spatial weights matrix is needed. Fortunately, co-patenting and mobility data are opening up a promising line of research in this direction, on which we will no doubt focus our attention sooner rather than later. Moreover, lagging variables of the right hand side of the models seeks to reduce the problems of endogeneity and reverse causality, thus implicitly assuming that weak exogeneity is sufficient to obtain consistent results. However, we should acknowledge the possibility that patenting activity in earlier years may well have influenced the levels of certain independent variables, and therefore consistency will be affected. To the best of our knowledge, suitable instruments have still to be found for the explanatory variables, and so further research along these lines must first be undertaken. 17 Notes: Robust standard errors are presented in parentheses. Significance levels: *** p<0.01, ** p<0.05, * p<0.1. Pseudo R2 is calculated as the ratio between the variance of the fitted value and the variance of the dependent variable. The Moran's I in iii and iv is the version suggested by ANSELIN and KELEJIAN (1997). We would like to acknowledge the referees for raising this point.

2 Recent special issues on the subject include: "Spatial knowledge diffusion through collaborative networks"

Guest editors: CORINNE AUTANT-BERNARD, JACQUES MAIRESSE and NADINE MASSARD, Papers in Regional Science 2007, 86(3): 341-525; and, more specifically on the subject of networks of co-inventors, the special issue "Embedding network analysis in spatial studies of innovation". Guest editor: EDWARD M.

BERGMAN, The Annals of Regional Science, 2009, 43(3): 559-833.

3 Very recently a working paper by [START_REF] Kroll | Spillovers and proximity in perspective: A network approach to improving the operationalisation of proximity[END_REF] examined the effect of the characteristics of inventors' networks on innovation outcomes; however, both the features it focuses on and the approach it adopts are slightly different from ours. 4 The number of these studies has been limited by data constraints, and only recently have researchers begun using patent data to identify inventors and their subsequent movements. The reason for this limitation is basically the cumbersome nature of singling out inventors on the basis of the names disclosed in patent documents. 5 The R&D productivity index in the knowledge production function would be equivalent to the Total Factor Productivity index in a production function. 6 Aside from the aforementioned studies, SNA has been widely applied to collaboration in research and innovation studies, although a review of detailed methodological contributions falls outside the scope of this paper. In fact, in recent years many contributions have been made to economics and economic geography using SNA tools, most notably BALCONI et al. (2004[START_REF] Breschi | Tracing the linkages between science and technology: An exploratory analysis of the research networks among scientists and inventors[END_REF]), and TER WAL and BOSCHMA (2009). For a more complete theoretical discussion of the methods and applications of SNA, see WASSERMAN and FAUST (1994). 7 We use the first and second order spatial lags, as suggested in KELEJIAN et al. (2004). 8 In the case of the mobility and networking variables, however, we do not calculate averages but rather total labour movements and co-patents between 1993 and 2002. We do so because of the very small number of these variables, and indeed we had to extend the period of analysis to ensure sufficient variation. There is no a priori reason to believe that this difference in procedure might affect the spatial differences in our sample and, therefore, our estimation results. 9 In our study, we use the term firm, applicant, or assignee interchangeably to refer to the owner of the patent listed in the patent document -although clearly they are not always the same. where PAT is the number of patents in each region i for each sector j, expressed as a difference for the whole sample (C). Thus, a positive and significant coefficient for this variable would point to the existence of MAR externalities.

12 Although overall employment in these sectors would be a better proxy, these data are not available. 13 We added a small value, 0.0000001, to all the explanatory variables presenting zero values in at least one observation to allow for a logarithmic transformation. Three Greek regions filed no patent applications in our period of analysis and so were removed from the study. 14 We also consider the German land of Sachsen-Anhalt as a single NUTS 1 region, and we have omitted the regions of Las Canarias, Ceuta, Melilla, Madeira, Açores, Guadeloupe, Martinique, Guyane and Reunion due to their distance from continental Europe. Moreover, the two NUTS2 regions of Trentino-Alto Adige/Südtirol (Italy) are considered as a single region. 15 To see these points, the quadratic form of population density was also included in all the models. By doing so, the population density variable becomes positive and significant, whilst its quadratic form remains negative. These results would therefore confirm the existence of congestion effects. For the sake of brevity, the results are not reported here but can be provided upon request from the authors. 16 Although the inclusion of a spatial lag of the dependent variable to summarise a broader set of externalities is theoretically straightforward, the a priori functional form of the spatial process in the disturbance term is less clear and that is why we find the validity of the approach proposed by K-P (2007) more convincing here.

17 An earlier version of this article sought to deal with endogeneity problems by instrumenting the focus variables using the three-group procedure suggested by [START_REF] Kennedy | A guide to econometrics[END_REF]. The method is thought to cope with measurement errors, and the results of the procedure have to be treated with caution. The three-group method involves sorting the variables into three groups of equal size, taking the value 1 if the observation is in the highest third of the variable, 0 if it is in the middle, and -1 if the value is in the lowest third of the regressor. The results -available upon request -make few changes to our conclusions, with the exception of the "outside collaborators" variable, which was no longer significant at 10%.

  local labour market and regional innovative capability is investigated.

  the present empirical approach was to disentangle the effects of market and non-market knowledge flows on innovation in a multivariate estimation framework.

  or the quality and quantity of interactions between those individuals most

  how innovation is generated at the regional level (RODRIGUEZ-POSE

  data come from the REGPAT database (January 2009 edition), which is the result of the OECD's regionalisation of the PATSTAT dataset (all EPO patents). Since these data are prone to exhibit lumpiness from year to year, we have averaged out patent figures from 2001 to 2003, thereby mitigating the effects of annual fluctuations in this variable, especially in the less populated areas. The same procedure is repeated for the explanatory variables, for the period1996-2000. 8

  δ-see PERI (2005) -where δ is an arbitrary depreciation

  patents is presumably of greater worth for innovative activities. The second reason is related to time constraints, because the chosen methodology still requires a considerable amount of manual work to ensure minimum levels of reliability.

  across them. In this way, even if a given pair of inventors has not copatented an invention but they share a co-invention with a third inventor, they will form part of the component: i.e., components may comprise both direct and indirect links.

  . Thus, gross value added per capita (capturing market access, general economic conditions, and wealth -GVApc), the number of technological firms to the total number of manufacturing establishments in that region (capturing agglomeration of firms engaged in patenting activity -TECH_FIRMS), population density (capturing agglomeration economies and urbanization economies -inter-industry economies -POP_DENS), and a technological specialization index (capturing specialization economies -intra-industry economies -constructed using the eight technological classes of the IPC 10 classification 11 -SPIN) are considered in the regressions.

  have also been considered for the UK, and NUTS 0 for Denmark and Switzerland.14

  Additionally, since most of the knowledge flows across regions in the knowledge production process are driven by networks of research collaborations and labour mobility, one would expect the values of the spatial autocorrelation tests to fall significantly when these two variables are included in the regressions. This appears to be the case of the residual spatial correlation tests after the estimation of the spatial lag model. If this is indeed the case, a way to model interdependences across regions in the production of knowledge has been found.

  regards the KPF framework, a theoretical model of spatial interactions occurring

  Miguélez, from the Ministerio de Educación, AP2007-00792.However, any mistake or omission remains ours. ,VARGA A. and ACS Z. (1997) Local Geographic Spillovers between University Research and High Technology Innovations, Journal of Urban Economics 42, 422-48; ANSELIN L. and KELEJIAN H. H. (1997) Testing for spatial error autocorrelation in the presence of endogenous regressors, International Regional Science Review 20, 153-82; AUDRETSCH D. B. and FELDMAN, M. (2004) Knowledge Spillovers and the Geography of Innovation, in V. HENDERSON and J. THISSE (Eds) Handbook of Urban and regional Economics, Volume 4; AUTANT-BERNARD C. and LESAGE J. (2011) Quantifying Knowledge Spillovers using Spatial Econometric Models, Journal of Regional Science 51, 471-96; AUTANT-BERNARD C., MAIRESSE J. and MASSARD N. (2009) Spatial knowledge diffusion through collaborative networks. Introduction, Papers in Regional Science 86, 341-50; BALCONI M., BRESCHI S. and LISSONI F. (2004) Networks of inventors and the role of academia: an exploration of Italian patent data, Research Policy 33, 127-45; BERGMAN E. M. (2009) Embedding network analysis in spatial studies of innovation, The Annals of Regional Science 43, 559-65; BETTENCOURT L., LOBO J., HELBING D., KÜHNERT C., and WEST G. (2007a) Growth, innovation, scaling, and the pace of life in cities, Proceeding of the National Academy of Sciences 104, 7301-06; and LE GALLO J. (2008) Estimating spatial models with endogenous variables, a spatial lag and spatially dependent disturbances: Finite sample properties, Papers in Regional Science 87, 319-39; FLEMING L., KING C., and JUDA A. (2007) Small worlds and innovation, Organization Science 14, 375-93; GOMES-CASSERES B., HAGEDOORN J., and JAFFE A. B. (2006) Do alliances promote knowledge flows?, Journal of Financial Economics 80, 5-33; GRANOVETTER M. S. (1985) The strength of weak ties, American Journal of Sociology 78, 1360-80; GRILICHES Z. (1979) Issues in assessing the contribution of research and development to productivity growth, The Bell Journal of Economics 10, 92-116; GRILICHES Z. (1991) Patent Statistics as Economic Indicators: A Survey, NBER Working Papers No. 3301, National Bureau of Economic Research; GROSSMAN. G. M. and E. HELPMAN (1991) Innovation and Growth in the Global Economy. MIT Press, Cambridge, MA; HARRIS R. and KRAVTSOVA V. (2009) In Search of 'W', SERC Discussion Paper 17, A. and UBERTI T. E. (2008) Knowledge networks across Europe: which distance matters?, The Annals of Regional Science 43, 691-720; MIGUÉLEZ E. and GÓMEZ-MIGUÉLEZ I. G. (2010) Singling out individual inventors from patent data, IREA Working Paper 2011/05; MIGUELEZ E., MORENO R. and ARTÍS M. (2011) Does social capital reinforce technological inputs in the creation of knowledge? Evidence from the Spanish regions, Regional Studies 45, 1019-38; MORENO R., PACI R. and USAI S. (2005a) Spatial spillovers and innovation activity in European regions, Environment and Planning A 37, 1793-812; MORENO R., PACI R. and USAI S. (2005b) Geographical and sectoral clusters of innovation Europe, Annals of Regional Science 39, 715-39; PERI G. (2005) Determinants of Knowledge Flows and Their Effect on Innovation, The Review of Economics and Statistics 8, 308-22; PONDS R., VAN OORT F. and FRENKEN K. (2007) The geographical and institutional proximity of research collaboration, Papers in Regional Science 86, 423-43; PONDS R., VAN OORT F. and FRENKEN K. (2010) Innovation, spillovers and universityindustry collaboration: an extended knowledge production function approach, Journal of Economic Geography 10, 231-55; . L. J. and BOSCHMA R. (2009) Applying social network analysis in economic geography: framing some key analytic issues, The Annals of Regional Science 43, 739-56; TRIPPL M. and MAIER G. (2010) Knowledge spillover agents and regional development, Papers in Regional Science 89, 229-33; THOMA G. and TORRISI S. (2007) Creating Powerful Indicators for Innovation Studies with Approximate Matching Algorithms. A test based on PATSTAT and Amadeus databases, CESPRI Working Papers, No. 211; THOMA G., TORRISI S., GAMBARDELLA A., GUELLEC D., HALL B.H., and HARHOFF D.(2009a) Methods and software for the harmonization and combination of datasets: A test based on IP-related data and accounting databases with a large panel of companies at the worldwide level, mimeo; THOMA G., TORRISI S., GAMBARDELLA A., GUELLEC D., HALL B.H., and HARHOFF D. (2009b) Harmonizing and Combining Large Datasets: An Application to Firm-level Patent and Accounting Data, STI Working Paper, OECD, Paris; WASSERMAN S. and FAUST K. (1994) Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge.

  specialisation index is designed to control for the existence of Marshall-Arrow-Romer (MAR) externalities derived from the regional specialisation in certain technological sectors. To calculate this, we employ the following formula

  is expressly specified, although we are aware of the criticism that these matrices have received from a number of scholars who claim they are oversimplified[START_REF] Boschma R | Proximity and Innovation: A Critical Assessment[END_REF]. Nonetheless, as is shown in the next subsection, the interest is precisely in identifying what part is attributable to geographical space when other more meaningful variables describing interactions across regions are considered.

	geographical weights matrix
	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	16

, and it is therefore essential to ascertain which features illustrate the linkages across locations. In the present paper a

  Insert Table 1 about here]

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	24

Table 2

 2 It is shown at the bottom of Table2the modified Moran's I test for 2SLS suggested in

	about here]

Table 2

 2 Here, only the estimations with the absolute connectivity (CONN_ABS) variable are shown, though the other models do not change the conclusions greatly. The results (see Table4-columns i-vi) corroborate the importance of outside collaborators:

	remains virtually

Table 1 .

 1 OLS estimations with White robust standard errors. Dep. Var.: Patents pc. ratio between the variance of the fitted value and the variance of the dependent variable. The Moran's I is the version suggested byANSELIN and KELEJIAN (1997) which takes into account the existence of an endogenous regressor in the r.h.s. of the equation in the form of a spatial lag of the dependent variable. It is distributed as a Chi-square with 1 degree of freedom and presents significant spatial autocorrelation in models iv, v, and vi. Robust standard errors are presented in parentheses. Significance levels: *** p<0.01, ** p<0.05, * p<0.1. Pseudo R2 is calculated as the ratio between the variance of the fitted value and the variance of the dependent variable.

			(i)	(ii)	(iii)	(iv)	(v)	(vi)
			OLS	OLS	OLS	OLS	OLS	OLS
	Intercept		-5.25***	-5.44***	-5.20***	-3.43***	-3.13***	-3.37***
			(0.63)	(0.73)	(0.63)	(0.99)	(1.10)	(0.99)
	ln(STOCK_R&Dpc)	0.26***	0.39***	0.26***	0.16***	0.29***	0.17***
			(0.06)	(0.07)	(0.06)	(0.05)	(0.08)	(0.05)
	ln(HRST)		0.53**	0.58**	0.52**	0.75**	0.92**	0.74**
			(0.23)	(0.25)	(0.23)	(0.32)	(0.39)	(0.32)
	ln(MOB)		0.26***	0.29***	0.26***	0.27***	0.29***	0.27***
			(0.03)	(0.03)	(0.03)	(0.03)	(0.04)	(0.03)
	ln(DENS) F ln(CONN_ABS) o ln(CONN_INV) r -0.16*** (0.04) 0.08*** (0.02)	-0.05* (0.03)	-0.24*** (0.06) 0.16*** (0.04)	-0.21*** (0.03) 0.12*** (0.02)	-0.06 (0.04)	-0.33*** (0.05) 0.22*** (0.05)
	ln(SIZE_LC) ln(POP_DENS) ln(GVApc) ln(TECH_FIRMS)	0.03 (0.04) -0.06* (0.03) 1.06*** (0.19) e P -0.09*** (0.03) e 1.08*** (0.18) 0.14*** 0.15*** r (0.04) (0.04)	-0.09*** (0.03) 1.08*** (0.18) 0.14*** (0.04)	-0.15*** (0.04) 0.65*** (0.18) 0.39*** (0.11)	0.08* (0.04) -0.08** (0.04) 0.49** (0.23) 0.42*** (0.12)	-0.15*** (0.04) 0.66*** (0.18) 0.39*** (0.11)
	ln(SPIN) ln(BIOTECH) ln(PHARMA) ln(CHEM) ln(MAN)		0.05 (0.13) -0.01 (0.02) -0.06*** (0.02) 0.04* (0.02) 0.92*** (0.09)	-0.16 (0.14) R -0.01 (0.02) e 0.05 (0.13) -0.01 (0.02) -0.05** -0.06*** (0.02) (0.02) v 0.05*** 0.04* i (0.02) (0.02) e 0.26** (0.11) 0.01 (0.01) -0.05** (0.02) 0.01 (0.02) 1.04*** 0.92*** 0.85*** w (0.09) (0.09) (0.08)	0.02 (0.12) 0.01 (0.02) -0.04 (0.03) 0.03* (0.02) 1.04*** (0.08)	0.26** (0.11) 0.01 (0.01) -0.04** (0.02) 0.01 (0.00) 0.85*** (0.08)
						O n
							l y
					41

Notes:

Table 4 .

 4 OLS and S2SLS estimations. Includes outside collaborations and I.M.R.

		(i)	(ii)	(iii)	(iv)	(v)	(vi)
		OLS	OLS	S2SLS	S2SLS	SHAC	SHAC
	Intercept	-4.84***	-3.36***	-4.24***	-3.76***	-4.24***	-3.76***
		(0.62)	(0.93)	(0.56)	(0.75)	(0.56)	(0.63)
	W•lnPATpc			0.32***	0.26***	0.32***	0.26***
				(0.05)	(0.07)	(0.05)	(0.07)
	ln(STOCK_R&Dpc)	0.25***	0.15***	0.32***	0.19***	0.32***	0.19***
		(0.06)	(0.05)	(0.05)	(0.05)	(0.06)	(0.05)
	ln(HRST)	0.45*	0.65**	0.40**	0.72***	0.40**	0.72***
		(0.23)	(0.30)	(0.17)	(0.24)	(0.17)	(0.24)
	ln(MOB)	0.25***	0.27***	0.25***	0.27***	0.25***	0.27***
		(0.03)	(0.03)	(0.03)	(0.02)	(0.03)	(0.03)
	ln(IMR)	0.03**	0.00	0.02	0.00	0.02	0.00
		(0.01)	(0.01)	(0.01)	(0.01)	(0.01)	(0.01)
	ln(DENS)	-0.16***	-0.22***	-0.14***	-0.21***	-0.14***	-0.21***
		(0.04)	(0.04)	(0.03)	(0.03)	(0.03)	(0.03)
	ln(CONN_ABS)	0.08***	0.12***	0.07***	0.11***	0.07***	0.11***
		(0.02)	(0.02)	(0.02)	(0.02)	(0.02)	(0.02)
	ln(OUT_COLL)	0.02	0.03**	0.02	0.03**	0.02	0.03**
		(0.02)	(0.01)	(0.01)	(0.01)	(0.01)	(0.01)
	ln(POP_DENS)	-0.08**	-0.15***	-0.03	-0.11***	-0.03	-0.11***
		(0.03)	(0.04)	(0.03)	(0.03)	(0.03)	(0.03)
	ln(GVApc)	1.09***	0.75***	0.44***	0.38**	0.44***	0.38**
		(0.18)	(0.16)	(0.16)	(0.15)	(0.16)	(0.15)
	ln(TECH_FIRMS)	0.14***	0.39***	0.05	0.27***	0.05*	0.27***
		(0.04)	(0.10)	(0.03)	(0.09)	(0.03)	(0.08)
	ln(SPIN)	0.10	0.28**	0.14	0.28***	0.14	0.28***
		(0.13)	(0.11)	(0.11)	(0.10)	(0.11)	(0.10)
	ln(BIOTECH)	-0.01	0.01	-0.00	0.01	-0.00	0.01
		(0.02)	(0.01)	(0.01)	(0.01)	(0.01)	(0.01)
	ln(PHARMA)	-0.05***	-0.04*	-0.05***	-0.04***	-0.05***	-0.04***
		(0.02)	(0.02)	(0.02)	(0.02)	(0.02)	(0.02)
	ln(CHEM)	0.03	0.01	0.03**	0.01	0.03**	0.01
		(0.02)	(0.02)	(0.02)	(0.01)	(0.02)	(0.01)
	ln(MAN)	0.91***	0.84***	0.70***	0.67***	0.70***	0.67***
		(0.09)	(0.08)	(0.09)	(0.09)	(0.09)	(0.09)
	Country Dummies	no	yes	no	yes	no	yes
	Moran's I	5.416	0.912	1.625	-4.303
	p-value	0.000	0.362	0.200	0.040
	Spatial error LM	21.053	0.504
	p-value	0.000	0.478
	Spatial error RLM	4.290	5.898
	p-value	0.038	0.015
	Spatial lag LM	41.062	10.935
	p-value	0.000	0.001
	Spatial lag RLM	24.299	16.329
	p-value	0.000	0.000
	Adjusted-R2	0.933	0.920	0.942	0.962	0.942	0.962
	Sample size	173	173	173	173	173	173
	Log-likelihood	-70.04	-86.26	-48.32	-11.27	-48.32	-11.27
	AIC	172.09	200.59	130.64	82.53	130.64	82.53
	Schwarz	222.54	244.66	184.24	177.13	184.24	177.13

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nlRegional Studies

Acknowledgements

Part of this work was carried out while Ernest Miguélez was visiting the Kiel Institute for the World Economy (Kiel, Germany). The use of the Institute's facilities is gratefully acknowledged. The authors would also like to share their appreciation of helpful comments received from Wan-Hsin Liu, Aïda Solé-Auró, and the participants of the "XXXIV Simposio de la Asociación Española de Economía" (Valencia, December 10 th -12 th 2009). The work made by Ismael Gómez-Miguélez is sincerely appreciated. We also acknowledge financial support from the Ministerio de Ciencia e Innovación, ECO2008-

< O3 -Technological Change|Research and Development < O -Economic Development, Technological Change, and Growth, O33 -Technological Change: Choices and Consequences|Diffusion Processes < O3 -Technological Change|Research and Development < O -Economic Development, Technological Change, and Growth, R1 -General Regional Economics < R -Urban, Rural, and Regional Economics

Appendix 2: Variables, data construction, and data source http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl

Regional Studies