The strength of strong ties: How co-authorship affect productivity of academic economists?

The Econ tribe occupies a vast territory in the far North. Their land appears bleak and dismal to the outsider, and travelling through it makes for rough sledding; but the Econ, through a long period of adaptation, have learned to wrest a living of sorts from it. (…) The extreme clannishness, not to say xenophobia, of the Econ makes life among them difficult and perhaps even somewhat dangerous for the outsider. This probably accounts for the fact that the Econ have so far not been systematically studied. Information about their social structure and ways of life is fragmentary and not well validated. More research on this interesting tribe is badly needed.

Axel Lejonhufvud (1973, p. 327) our italics

Abstract

Increased specialization and extensive collaboration are common behaviours in the scientific community, as well as the evaluation of scientific research based on bibliometric indicators. This paper aims to analyse the effect of collaboration (co-authorship) on the scientific output of Italian economists. We use social network analysis to investigate the structure of co-authorship, and econometric analysis to explain the productivity of individual Italian economists, in terms of ‘attributional’ variables (such as age, gender, academic position, tenure, scientific sub-discipline, geographical location), ‘relational’ variables (such as propensity to cooperate and the stability of cooperation patterns) and ‘positional’ variables (such as betweenness and closeness centrality indexes and clustering coefficients).

Introduction

Co-authorship is an increasing phenomenon in science and economics makes no exception to this trend. Laband and Tollison (2000) show that in ‘three prominent economics journals: the American Economic Review, the Journal of Political Economy, and the Quarterly Journal of Economics’, the percentage of co-authored papers grew steadily between 1950 and 1994, <10 % in the 1950s and to around 70 % in 1994. Their data perhaps overemphasize the phenomenon, but are also consistent with the results of other studies. For instance, McDowell and Melvin (1983), for a sample of eight major economic journals, found the percentage of co-authored papers was about 30 % in 1976; Hudson (1996), based on a similar sample, found that the average number of co-authored papers in 1993 was over 50 %; Sutter and Kocher (2004) analyse 15 economics journals with the highest average impact factors, for the period 1977–1997, and found 44 % of papers on average were co-authored; Medoff (2003) surveyed ‘thirty-one top economics journals’, and found the percentage of papers with two authors, in 1990, was approximately 40 %; and Vieira (2008), for a sample of 168 journals available in the ‘economics’ class in the ISI database, found 47 % of papers were multi-authored (two or more authors) between 1986 and 1996.

In a previous paper (Cainelli et al. 2012), thanks to an purpose-built original database, we describe the structure of the Italian academic economists community and analyse the positive effects of collaborative national and international behaviours on the individual productivity. In this paper we build on the same database to investigate the attributional (age, gender, academic position, tenure, scientific sub-discipline, geographical location), relational (propensity to cooperate and stability of cooperation patterns) and positional (betweenness/closeness centrality indexes and clustering coefficient of the co-authorship network) variables in determining the productivity of Italian economists. To achieve this aim, in section “Co-authorship: causes and consequences” we briefly review the existing knowledge on the determinants and effects of co-authorship in the social sciences; section “The original database” describes in details the original database used in our analysis. Section “Relational structure of co-authorships” introduces social network analysis (SNA) methodologies and describes a number of relational and positional indexes used in the subsequent econometric analysis. Section “The econometric analysis” presents the results of three econometric exercises to show the role of attributional, relational and positional variables in determining the productivity of Italian economists. Section “Conclusions” concludes the paper.

Co-authorship: causes and consequences

Recent research studies (such as: Kalaitzidakis et al. 1999; Goyal 2005; van der Leij and Goyal 2011) and policy reports show an increasing relevance of multiple authorship in almost every field of science. In the meantime, universities’, government bodies’ and funding agencies’ throughout the world are evaluating scientific research output through ‘objective’ bibliometric indicators. These phenomena are strictly intertwined since the pressure on academics to publish has promoted more co-authorships based on the belief that co-authorship increases both the quantity¹ and quality² of research output in the form of published papers (Lee and Bozeman 2005). Thus, as the ‘publish or perish’ policy diffuses across national and disciplinary borders, the appeal of co-authorship increases among researchers.

This section is thus devoted to the review of a substantial, but not very prominent stream of literature, devoted to the theoretical and, above all, empirical analysis of the determinants and consequences of co-authorship.

While most of the theoretical literature (see among others: Laband 1987; Laband and Piette 1995; Laband and Tollison 2006; Butler 2007) concentrates on complementarities in skills and attitudes, Fafchamps et al. (2010, 2006, p. 8) underline that ‘if research output depends only on ability, collaboration is most likely between authors of a similar level of ability (assortative matching) but with non-overlapping competences (complementarity in competences)’. However ‘collaboration between high and low ability authors can arise if the low ability author provides more effort. In this manner the time-constrained high ability author can produce more research while the low ability researcher produces better quality output’ (ibid). In this process, each author faces a ‘matching’ problem in finding his co-author, and this problem is exacerbated by the fact that one of a co-author’s qualities is based on an ex ante evaluation of an unobservable variable (his/her effort). However, since ‘collaborating with someone reveals valuable information about their ability and motivation, it follows that a referral about a researcher i is particularly informative when it is provided by a previous coauthor of i. Referral by a coauthor can thus be construed as a vetting process, stating whether a coauthor is competent and can be trusted to do his or her share of the work’ (ibid., p. 12).³

The scale and scope of the empirical literature is definitely wider and calls for a brief survey of the different determinants and facilitators of co-authoring highlighted over 20 years of research.

• Specialization: ‘the explosion of knowledge in economics, as the sheer growth of knowledge resulted in increased efficiencies of specialization and co-authorship relative to working alone’ (McDowell and Melvin 1983, p. 156).

This argument has been developed by several other authors:

• Multi-disciplinarity: since it is often fruitful to bring different perspectives to the study of a single issue, this is easily achieved by a ‘multi-disciplinary configuration of the research team’⁴ (Sigelman 2009, p. 508). Further: ‘As authors work in areas outside of their major areas of specialty they tend to engage in co-authorship to a larger extent than the authors who published within presumably more familiar areas in terms of interest or expertise’ (Piette and Ross 1992, p. 281).Technological complementarities: the need to master very different analytical tools increases the importance of different expertise in order to manage numeric simulation packages, econometric estimation applications, and huge data bases⁵ (Hudson 1996). This point is further re-enforced as follows: ‘Only one specific type of complexity that matters. The combination of quantitative methods with other economic analyses is what appears to spurn co-authorship’ (Nowell and Grijalva 2011).

• Synergy: the gains from collaborative work may be the result of a sort of synergy where ‘multiple contributors develop ideas that none would have developed on his or her own. Synergy differs from skill complimentarily in the sense that it can exist between individuals with very similar skill sets’ (Hudson 1996, p. 157). Johnston et al. (2013) highlight that citations patterns in economics change over time and are different for empirical and theoretical papers. Regarding the co-authorships issue, they underline that the co-authorship is positively correlated with citation process since it indicates ‘the transfer of knowledge between those who created the original idea’ (Johnston et al. 2013, p. 1024).

• Opportunity cost of time: the increased emphasis on research output and the use of publication output as a criterion for promotion, increases the opportunity cost of time for typical researchers in economics. Every other activity than doing research and writing papers, tends to be shelved or minimized. This means that acknowledgement is no longer a sufficient ‘reward’ for pre-submission review by a colleague in the field and ‘this increased “price” often takes the form of co-authorship’ (Barnett et al. 1988, p. 540).

• Risk diversification: ‘the editorial review process contains a random element that many would agree is large (…) and a given review may motivate a rejection, revision, or acceptance depending upon the editor’s judgement concerning reader interest, the size of the journal’s backlog, or a host of other potential factors (…). Thus, the author of a paper faces considerable uncertainty (…) A natural response is to diversify against this risk by co-authoring papers. Through co-authorship, one is able to increase the total number of papers submitted within a given period of time, thereby reducing the variance of the random element inherent in the review process. Thus, even if the value of co-authored papers is discounted exactly by the number of authors, and if there are no synergistic or quality effects in co-authoring, there will still be incentives to collaborate’ (Barnett et al. 1988, p. 540).

• Assigned value of co-authored papers: department ‘chairmen ordinarily “assign a weight” to coauthored papers that exceeds l/n (with n being the number of authors), presumably to encourage collaborative research’ (Liebowitz and Palmer 1983, quoted in Sauer 1988, p. 857). Many universities and funding agencies promote and reward collaboration in the belief that it has a positive impact on research productivity (Laband and Tollison 2000).

• Social interactions and pressures: collaboration may be chosen based on consumption/leisure reasons. Working with co-authors ‘offers opportunities for friendship and camaraderie’ and is a way to escape academic isolation (Medoff 2003, p. 607; Acedo et al. 2006; Holder et al. 2000). Having co-authors acts also as a motivation to keep to self-imposed deadlines.

We can add also that innovations in information and communication technology (ICT) have made collaboration, even at a distance, easier and less costly⁶ although Sutter and Kocher (2004) based on a gravity model of the co-authorship patterns in US departments, and based on the top 15 economics journals, find that the coefficient of the variable for geographical distance is non-significant for all the periods investigated (1977, 1982, 1987, 1992, 1997).⁷

Finally, it must be acknowledged that co-authorship has some negative effects, otherwise every paper would be written in collaboration, and the number of collaborators per paper would be infinite. Looking at the ‘dark side’ of co-authorship, we may mention the following reasons acting against this collaborative practice:

• Compromise: ‘An individual author working with a group will have to agree to a certain approach, certain text, even certain conclusions that that person might not enunciate in the same way if working alone. Because multiple authorship inevitably involves compromise, thus it tends to reduce risk taking in academic papers. The result may be more technically proficient papers than in the past, but at the cost of the imaginative leap forward that starts economics in a new direction or gives fresh impetus to an old subject area’ (Hudson 1996, p. 157).

• Organization and communication costs: ‘multi-authored papers impose costs of organization and communication that may lead to diseconomies of scale. These are probably greater if all the collaborators are equally involved with all parts of the research and all parts of the paper. Developments in technology in recent years may have reduced the threshold at which these problems occur, but at some level they surely continue to exist’ (ibid., pp. 157–158).

• Reward structure: ‘Any net advantage of collaboration may disappear altogether if some individuals combine even though the sum of what each could achieve working alone exceeds their combined efforts. This may occur if an economist can achieve a greater gain in academic reputation from multi-authored rather than single-authored papers’ (ibid., p. 158). This results is confirmed by Hilmer and Hilmer (2005) who find that the estimated return (as measured by increases in annual salaries) to a sole authored article is twice the estimated return to an article with more than one author (Hilmer and Hilmer 2005, p. 520).

From the above, it is evident that we need to consider both ‘positional’ and ‘relational’ variables in estimating the determinants of scientists’ productivity. To achieve this, we built an original database in order to calculate positional and relational indexes for use as regressors in our econometric exercise.

The original database

Our analysis is based on an original dataset built by matching two different data sources: (1) the Italian economists population drawn from the official database of the Italian Ministry of Universities and Research, managed by Cineca (henceforth MIUR-Cineca) and (2) their scientific production extracted from the Econlit database of the American Economic Association.

The entire population of Italian academic economists, at 31st December 2006, is composed by 1,620 individuals holding one of the following academic positions: Tenured Full Professor (TFP), Full Professor (FP), Tenured Associate Professor (TAP), Associate Professor (AP), Senior Lecturer (SL) and Lecturer (L).⁸ According to MIUR,⁹ economists are sub-divided into six disciplinary groups; however for the empirical analysis we re-classified these groups into four sub-disciplines: Economics, Econometrics, Public Economics and Others.¹⁰ Table 1 presents the distribution of academic positions and scientific fields in the Italian academic population of economists.

Table 1 Academic position and scientific field

Once the population of Italian economists has been identified as described above, their scientific production can be traced in the Econlit database¹¹ recorded for the period 1969–2006. These records were downloaded between August 2007 and February 2008, and painstakingly corrected for errors in people’s names and double entries. Since the aim of this paper is to analyse the effects of co-authorship on scientific productivity of Italian economists, we chose to measure the productivity of an individual as the total number of journal articles (henceforth: JA) published, per year.¹² The total number of JA published by the Italian economists in the period under analysis is equal to 8,679.

Before describing in details the Econlit database, it is useful to highlight its strengths and limitations. Dolado et al. (2003) suggest that Econlit contains missing information on authors and includes some errors and omissions with respect to publications, number of pages, etc. Furthermore, especially in the 1970s, the geographical coverage was limited to certain countries and to international publishers. Finally, the database does not include any evaluation or publication weight (i.e. impact factor or similar) for “scientific product”.¹³ However, the use of Econlit allowed to include, in the analysis, the publication activity on Italian scientific journals which are almost absent in the ISI-Thomson dataset and to record data on collective volume articles (CVA) which have been used as instruments in the econometric analysis (see section “The econometric analysis”).

Relational structure of co-authorships

This section introduces the SNA indexes and analytical tools, and their application to study the structure and evolution of the scientific collaboration behaviour of Italian economists.

Selection and treatment of networks

SNA is a scientific method of analysis that investigates the structure of the relations between social units of analysis, using graph theory, mathematics and statistics tools. Key SNA concepts are actors (i.e. players or nodes in the network); relational ties (i.e. the links connecting the actors) and groups/subgroups (i.e. the subsets of the actors and the relations among them).

Having defined the sample of actors and relations to be studied, SNA distinguishes the type or mode of the networks, i.e. the ‘number of sets of entities on which structural variables are measured’ (Wasserman and Faust 1994, p. 35). Most SNA studies relate to ‘one-mode networks’ (i.e. where all entities or nodes belong to the same set of actors); however, some deal with two sets of social entities¹⁴ (and the relations connecting one set to the other). These are called ‘two-mode networks’ or ‘affiliation networks’.

In this paper we build a two-mode network, where one set of nodes, i.e. mode 1, is composed of journal articles (JA) and the other set of nodes, i.e. mode 2, is the papers’ authors (AU) (see Fig. 1a). We transform this into a ‘one-mode network’ in which AU are the nodes and the papers are the links between co-authors (see Fig. 1b).

Fig. 1

One-mode versus two-mode representation of co-authorship networks

More formally Fig. 1a is a two-mode network defined as X = (JA, AU, R, w), where the two disjoint sets are respectively JA, i.e. 8,679 articles, and AU, i.e. 2,972 authors included in the analysis, the scientific collaborations are denoted as R ⊆ JA × AU and the mapping w:R → R represents a weight, i.e. the number of co-authored articles. The resulting affiliation matrix, X, is rectangular, i.e. 8,679 JA times 2,972 AU, with links originating from different authors and targeting the same paper representing cases of co-authorship. In order to emphasize the structure of co-authorship among economists we transformed the two-mode network into a one-mode network (depicted in Fig. 1b) where the network is defined as X ₁  = (AU, R ₁ , w ₁ ), representing the collaborations, R ₁ , among authors AU, i.e. a 2,972 times 2,972 squared matrix where nodes are authors, and w ₁ represents the number of scientific collaborations between dyads of authors. Then we performed a series of SNA analyses on the one-mode network for the whole period 1969–2006 and—given that co-authorship changes radically over time—we investigated the networks for four different historical periods (1969–1976; 1977–1986; 1987–1996 and 1997–2006).

Before discussing the structural features of collaborative networks, we describe how the network of 2,972 authors is defined. Figure 2 synthesizes the final population of economists investigated, defined using the snowball sampling procedure, from 1,620 Italian economists selected from the MIUR-Cineca database.

Fig. 2

Set representation of the populations in the dataset

First, we identify the entire population of Italian economists according to the MIUR-Cineca database (M) as defined in section “The original database”, i.e. the 1,620 Italian economists¹⁵ in an official academic position at the end of 2006. For each individual we identify the records indexed in the Econlit database, including details of year of entry, full records on JA, CVA, books and dissertations. This snowball procedure means that the number of individuals involved in writing JA increases with respect to the initial population M and we can identify a new Econlit population, E, that includes individuals belonging to set M, and all their co-authors (if any) including each affiliation,¹⁶ for a total of 2,972 individuals.

The intersection between sets M and E produces the intersection set P, which is composed of 1,317 ‘Italian’ Academic Economists who wrote at least one JA indexed in Econlit¹⁷ and 3 other complementary sub-sets: N, O and F. Subset N is composed of 262 ‘Italian’ academic economists with no JA entries in Econlit; F is composed of 806 ‘foreign’ economists with at least one co-authored JA recorded in Econlit, involving one or more Italian economists (included in P); O is composed of 849 ‘other Italian’ co-authors with the economists in set E, which do not belong to P because: (1) they are affiliated to non university institutions (e.g. Bank of Italy, CNR-National Research Council, ISTAT-National Statistical Office, foreign and international institutions); or (2) they belong to non economic sub-disciplines (i.e. business management, statistics, etc.).¹⁸

This ‘partial snowballing’ sampling procedure allows us to identify the structure of the scientific collaboration of the Italian academic economists (in set P). Since in this article we are interested in the Italian economists we do not investigate in detail the structure for the residual F and O populations.¹⁹

SNA indexes and network topology

Since our interest is in co-authorships and the effects on scientific production, we treat the data on the publications of Italian economists transforming the two-mode network into a one-mode network as described previously, and we calculate a number of different indexes measuring the structure of the network, the positions and relational roles of each node to be used as inputs for the econometric analysis in section “The econometric analysis”.

In order to synthesize the general features of the overall network, we calculate its density values (d and d _r), degree centralization (C _deg), clustering coefficient (CC), average path length (APL), diameter (δ), and average degree (av_deg).

Density (d) is defined analytically as the ratio between the total number of actual links (L) and all possible potential links among all nodes in the network (n):

$$ d = \frac{2L}{n \times (n - 1)} $$

(1)

This network index ranges from 0 (i.e. the network is disconnected) to 1 (i.e. the network is complete; i.e. all possible links are present) and represents the completeness of the network (Wasserman and Faust 1994).

Since it is not possible to compare densities for networks of different dimensions, we follow Maggioni (1995) and compute a relative density²⁰ value (d _r):

$$ d_{r} = \frac{L - (n - 1)}{{\frac{n \times (n - 1)}{2} - (n - 1)}} $$

(2)

Degree centralization index (C _deg) is a measure of the variance in the degree centrality values of the nodes in a given network (Freeman 1979), expressed analytically as:

$$ C_{{\rm deg}} = \frac{{\sum\limits_{i = 1}^{n} {\left[ {C_{{\rm deg }} (a^{*} ) - C_{{\rm deg }} (a_{i} )} \right]} }}{{n^{2} - 3n + 2}} $$

(3)

where C _deg(a*) and C _deg(a _i ) respectively are degree centrality index (i.e. the number of a node’s direct links) of the most central node, and degree centrality of a generic node i. As in the case of d, the index ranges from 0 (i.e. all nodes have the same degree centrality index) to 1 (i.e. there is one node that connects the entire network). This index, therefore, measures the hierarchization in the network and the presence (or absence) of pivotal node(s), i.e. a node(s) with a direct relation to most of the other nodes in the network.

While these network indexes occur frequently since early applications of SNA to sociological analysis, CC, APL and δ were recently introduced by mathematicians, physicists and computer scientists (Strogatz 2001; Albert and Barabasi 2002; Newman 2001, 2003). These indexes (and the underlying degree distribution) are computed to classify large and complex structures (i.e. networks characterized by thousands of nodes) with reference to standard ideal types (e.g. random, regular, scale-free or small world structures).

The clustering coefficient of node i (CC _i ) is the ratio of the existing links connecting a node’s neighbours to each other to the maximum possible number of such links. Its average across all nodes in a network (CC) summarizes the extent to which the nodes in a graph tend to group together (Watts 1999). More formally:

$$ {\text{CC}}_{i} = \frac{{\varLambda_{i} }}{{\nu_{i} }} $$

(4)

and

$$ {\text{CC}} = \frac{{\sum\limits_{i = 1}^{n} {\frac{{\varLambda_{i} }}{{\nu_{i} }}} }}{n} $$

(5)

where Λ _i is the number of edges in the neighbourhood of node i, v _i is the total number of possible edges of node i. CC _i and CC vary between 0 (i.e. no neighbour of any vertex is adjacent to any other neighbour of vertex i) and 1 (i.e. a node’s neighbours are also neighbours of each other).

Average path length (APL) is a measure of the degree of separation between two nodes along the shortest path of their intermediaries, i.e. the average number of intermediaries between all pairs of actors in the network (Uzzi and Spiro 2005). If APL is low, the actors in the network are close together and flows across the network are easy. Another measure of average distance in the network is diameter (δ), which measures network connectedness and corresponds to the maximal distance between any pair of nodes, i.e. the longest geodesic path, and therefore will be a positive number >1. In a disconnected network, δ is equal to infinity, but it can be computed for connected components.

To classify the topological structure of a network it is usual to compare the indexes of the ‘actual’ or ‘real’ networks, to equivalent (i.e. with the same number of nodes and edges as the real network) random networks (Watts 1999; Uzzi and Spiro 2005).²¹,²² A ‘small world’ network is a network in which most nodes are not neighbours of one another, but are separate only by a small number of steps.²³ Watts (1999) synthesizes some of the structural features of the topology comparing a given network’s APL and CC with the same indexes calculated for an equivalent random network.

In this paper we check whether the network of Italian economists is structured according to a ‘small world’ typology by computing the ‘small world quotient’ (Uzzi and Spiro 2005), Q _sw, as follows:

$$ Q_{\text{sw}} = \frac{{\frac{{{\text{CC}}_{\text{a}} }}{{{\text{CC}}_{\text{r}} }}}}{{\frac{{{\text{APL}}_{\text{a}} }}{{{\text{APL}}_{\text{r}} }}}} $$

(6)

where subscripts a and r respectively indicate the actual and the equivalent random networks CC and APL, in terms of average degree and density. The greater the Q _sw, (and particularly if the quotient is >1), the closer the structure of the network to a ‘small world’ structure.²⁴

In order to investigate the evolution of the co-authorship network, we also study the relationship between network structure at time t and its evolution over subsequent periods. Albert and Barabasi (2002) find that the evolution of scale-free networks²⁵ generally follows a ‘preferential attachment’ process where central nodes become increasingly central because new nodes tend to establish proportionally more links with more central nodes.

In the following analysis we calculate R(k), the relative probability of establishing new co-authorships, as follows:

$$ R(k) = \frac{{{\text{proportion of new links to nodes of deg }}k}}{{{\text{proportion of nodes with }} {\rm deg} \, k_{i} }} $$

(7)

If there is no preferential attachment, R(k) is equal to 1, and describes a growth process in which new authors enter the co-authorship network by establishing links to existing authors randomly. If R(k) is >1, then growth follows a preferential attachment process because more central authors are more attractive to new co-authors.

The following network indexes have been computed for each node (author) and used in the empirical analysis: degree, betweenness and closeness centrality,²⁶ and clustering coefficient.

The degree centrality²⁷ index is a measure of the number of direct links connecting a given node, which in our case is the number of co-authors of each individual economist, which measures the local centrality of the economist.

Betweenness centrality is a measure of the number of times a vertex occurs on all geodesic (i.e. shortest) paths within a network connecting every node to every other node. This index identifies the strategic value of a node and its potential ability to control the relations of a network. Analytically:

$$ C_{b} (a_{i} ) = \sum\limits_{j < k}^{n} {\frac{{g_{jk} (a_{i} )}}{{g_{jk} }}} $$

(8)

where $g_{jk} \left( {a_{i} } \right)/g_{jk}$ is the estimated probability of connecting two nodes and the numerator represents the number of geodesic distances connecting nodes j and k containing node i, while the denominator does not necessarily contain node i (Wasserman and Faust 1994).

Closeness centrality is an inverse function of the geodesic distances from one node to every other node in the network—hence it depends on both direct and indirect links—and reflects the efficiency of the communication channels of a given node with the rest of the network. Analytically:

$$ C_{c} (a_{i} ) = \left[ {\sum\limits_{j = 1}^{n} {d(a_{i} , a_{j} )} } \right]^{ - 1} $$

(9)

where d(a _i , a _j ) is the number of lines in the geodesic path linking nodes i and j (Wasserman and Faust 1994).

Since these last indexes are computed for each node of the network (i.e. each Italian economist included in the analysis), we consider them regressors in the econometric analysis since they measure different aspects of the positional role of an author in the co-authorship network.

SNA of Italian economists

In order to detect whether and how co-authorship behaviour has changed over time, and whether the structure of co-authorship is similar to one of the ideal typical network topologies we analyse the co-authorship patterns of Italian economists using SNA techniques.

First, we observe that collaboration is evolving over time, and is becoming a more common phenomenon of Italian economists’ scientific behaviour. For example, the number of co-authored JA has increased more than the number of single authored JA. In 1969, 20 out of 24 articles recorded in Econlit were single authored; in 2003, 272 out of 540, while in 2006, 328 out of 567 articles were multi-authored.

The structure of the whole period network is very complex (see Fig. 3; Table 2). In a network of 2,972 economists there is a main component (MC), i.e. the largest group of connected nodes, which includes 2,061 economists, several of these wrote together more than one article (represented by the thicker lines between nodes), while the number of isolated nodes (i.e. economists always writing alone) is quite small, under 10 %. There are several sub-groups of different dimensions in the whole network, which represent small communities of economists (i.e. discipline-bounded or geographically delimited).

Fig. 3

The co-authorship network of Italian economists (1969–2006). Note: colours identify different sub-groups and the thickness of links identify the number of collaborations

Table 2 Basic SNA statistics of the whole network (1969–2006)

Table 2 shows the results for a network dichotomized according to a threshold value equal to 1. This procedure identifies collaborations for at least one JA, which means that multiple collaborations with the same co-author do not influence the structure of the network.

The density value shows that the network is quite sparse: density value is very low for both the whole network and the MC. The centralization measure indicates a fairly non-hierarchical network, with no stars in a pivotal role, in the whole network or in the MC. Diameter δ indicates that although the network is quite complex, the biggest distance between two connected economists is 30, which is a relatively small value.

The average degree values show that Italian economists collaborate with over two people in the whole network, and around three people in the MC.

In the complexity of Fig. 3 we identify nodes far apart and a main component. We should highlight that nodes far apart are not exclusively isolated (only 282 nodes are completely disconnected), but several other apparently isolated nodes (200) are diads, triads and sub-networks identifying people writing in economics sub-subjects. On the main component a typical collaborative pattern (defined also by the literature and detailed in the econometric analysis) emerges: some people collaborate more and this is captured by the thickness of the link.

There are some other interesting features that emerge when we compare different groups of economists, especially subset P with subsets F and O, the groups of foreign and ‘other Italian’ economists. In this work, the group of P economists represents 44 % of the whole network and 37 % of the MC.

If we consider the international openness of Italian economists in terms of the nationalities of co-authors, we find that foreign economists accounts for 38 % of the network and this percentage is 46 % for the MC. This suggests an overrepresentation of foreign economists in the most connected sub-community of co-authors.

Since cooperation behaviour is changing dramatically over time, we identify four distinct periods from 1969 onwards, which demonstrate how network features are changing (see Table 3 for basic SNA statistics).

Table 3 SNA statistics for different periods

In the first period (1969–1976) no particularly cohesive network structure can be identified, and the network is mostly disconnected. In the second period (1977–1986), the network structure is very disconnected, and we can identify several isolated nodes (i.e. economists writing alone). In both these networks the Italian economists community is not very open to collaboration with foreigners and is mainly representative of the selected scientific sectors. In both networks average degree is <1, and more co-authorship among the Italian economists community does not emerge until the late 1980s. Hence due to this pattern of isolated and diads (at maximum) MC were very unlikely to appear.

The structure of the networks changes radically in the last two periods: 1987–1996 and 1997–2006. A MC emerges, while the number of isolated authors remains fairly constant; average degree increases and APL and diameter increase dramatically; and the maximum degree increased 6 times and a half, indicating a diffusive collaborative pattern. This shift in late 1980s could be due to the diffusion of the new ICT and to the intensification of post-doc experiences abroad.

The values for network density (both absolute and relative) are very low and are continuously decreasing over time.²⁸ This does not contradict the increasing values for average degree since, even if scientific collaborations increases over time, the increase in these values is less than the increase in the number of possible links in a growing network.²⁹

Table 4 presents the Q _sw index to detect the presence of a small world topology in the network structure of the Italian economists community. The value index (Q _sw) means that this network has features typical of a small world topology. Since the network is changing over time, and collaborative behaviour is increasing, we calculate this index for all the periods in which a MC is present.³⁰ All indexes are > 1, confirming the existence of a ‘small world phenomenon’ in the network of Italian economists.

Table 4 The ‘Small World’ of Italian economists

Finally, to identify the forces behind the resulting topology of the co-authorship network we investigate the presence of preferential attachment. Figure 4 describes the existence of a non-linear dynamics of preferential attachment in the MC of Italian economists, passing from period 3 to period 4. As already detailed, a value >1 signals the existence of preferential attachment dynamics in the growth of the network, with more central nodes (i.e. node with a higher degree) in the previous period receiving a more than proportional share of new links in the subsequent period. This is the case for the Italian economists community in the two most recent decades. Authors with more than four different co-authors in the 3rd period tend to show an increase in the number of their co-authors. This may be due to different reasons, including that: (1) previous co-authorship signals both a willingness and ability of an author to cooperate with other scientists; (2) scientists tend to look for this kind of person when looking for potential co-authors.

Fig. 4

Preferential attachment in the MC of the Italian economist network

The depiction in Fig. 4 suggests that the increasing returns to co-authorship are not linear; in particular, when the cumulated number of co-authors reaches 8, the relative probability of additional co-authors begins to decrease and becomes equal to 1 for 12 co-authors in period 3. This may be explained by an excessive level of transaction and communication costs for a subgroup of more than 12 co-authors, and a preference for stability in co-authorship relations, as described in section “The econometric analysis”. We also calculate the distribution of degrees, and find that it is very skewed, and very different from a normal distribution, which confirms the wide variation in the collaborative behaviour of Italian economists and suggests that the network topology is more similar to a scale-free than to a random network.

The econometric analysis

We use different econometric methods to identify empirically the determinants of the probability to publish and of the scientific productivity of economists working in Italian universities. As stated in the introduction, and discussed extensively in section “Co-authorship: causes and consequences”, we expect that these determinants will have three distinct dimensions:

• an attributive dimension related to the individual characteristics of the researcher (measured by variables for gender, academic position, tenure, location);

• a relational dimension representing the researcher’s connection to his/her scientific community (measured by variables such as the propensity for co-authoring, propensity to cooperate with foreign researcher);

• a positional dimension, which relates to the role of the researcher in the scientific community (measured by network variables such as betweeness centrality index and clustering coefficient).

In particular in Table 5 we identify the attributional determinants of the probability to publish using a probit model; in Table 6 we investigate the relational driving forces of an individual researcher’s scientific productivity, through an Instrumental Variables (IV) estimation strategy; finally we focus on the impact of the positional characteristics of the researcher within the scientific community using OLS methods and analysing the sole MC of the co-authorship network.

Table 5 Determinants of the probability to publish

Table 6 Determinants of scientific productivity: complete sample

While some econometric results on the attributional and relational determinants of both the probability to publish of an economist and his/her scientific productivity have been already presented in Cainelli et al. (2012), this paper focuses on the positional determinants by exploiting the SNA indexes computed in section “Relational structure of co-authorships” and using them as regressors in the econometric analysis.

The determinants of the probability to publish

To identify the attributional determinants of the probability to publish, we estimate a maximum-likelihood probit model as follows:³¹

$$ Pr\left( {publish_{i} = 1|X} \right) = \varPhi \left( {X_{i}^{\prime } \beta } \right) $$

(10)

where Φ is the cumulative distribution function of the standard normal distribution, publish _i is a dummy variable that is equal to 1 if the economist has at least published one (column [1.] of Table 5), two, (column [2.] of Table 5) three (column [3.] of Table 5) or four (column [4.] of Table 5) journal articles (JA) in Econlit in the period 1969–2006, and 0 otherwise, and X indicates the regressors. These variables, constituted by a set of attributional dummy variables, are added stepwise in the econometric specifications, and are available for all the economists in our 2006 population. They include: (1) five geographic dummies (North West, North East, Centre,³² Islands and South) describing the location of the economist’s institution; (2) a dummy indicating whether the economist works in a Faculty of Economics and 0 otherwise (Fac_economics); (3) four dummies for economist’s disciplinary groups (Economics, Public Economics, Econometrics, and Others ³³); (4) a dummy for gender (Gender) equals to 1 if the academic is male and 0 otherwise; (5) a dummy (Tenured) if the economist has a tenured academic position; (6) a dummy (NTLecturer), that is equal to 1 if the economist is a non-tenured lecturer and 0 otherwise has been introduced in order to take into account the “beginning of career” effect.

Table 5 reports the main findings of the analysis. The results suggest that the probability that an economist will publish an Econlit JA is positively influenced by gender, geographic location of the university, and scientific sub-sector. In particular, these findings shows that men tend to be more productive than women and economists working in Northern universities have a higher probability to publish than those located in Sothern universities. This result can be explained on the basis of the traditional socio-economic dualism characterising the Italian economic system. Dualism which is the result of differences in the social capital endowment and in the cultural and historical traditions. Finally, tenure has a negative impact on the probability to publish, while the dummy indicating the position of “untenured lecturer” is negative and statistically significant. This is because the youngest member of the Italian academic community may be will awaiting publication for already submitted papers. In this first econometric exercise, this variable is the only one that allows us to control for the “age” of an individual economist.

In order to check the robustness of these results, we replicate our analysis by taking into account different values of the cut-off. In other words, we consider not only the probability of publishing at least one Econlit JA, but also that of publishing at least two, three or four Econlit JA. The main findings of this analysis are reported in columns [2.], [3.] and [4.] of Table 5. The sign and the statistical significance of the main explanatory variables do not tend to change. What it emerges is that only the marginal effects of some variables change. For example, our evidence shows that the probability to publish more than one journal article increases for econometricians. For this group of academics, the marginal effects go from 0.092 for just one Econlit JA to 0.238 for four Econlit JA. Finally, it is interesting to note that the marginal effect of tenure does not change.

The determinants of the scientific productivity

In this section firstly we focus on the roles of the relational and then on the positional variables in the scientific productivity of Italian economists. In both cases, an economist’s scientific productivity³⁴—the dependent variable in these models—is measured as the total number of Econlit JA divided by his/her “seniority”. Since we do not have information on the biogical age of the economists in our sample, we use the proxy variable of “seniority”, computed as the difference between the year of his/her first Econlit publication and 2006.³⁵

In order to fully exploit the use of SNA indexes, the econometric analysis is conducted on both the full sample and the MC of the co-authorship network (i.e. the largest group of economists which are connected by collaboration ties), which accounts for 70 % of the whole sample.

Role of the relational variables in scientific productivity: full sample

In terms of relational driving forces, Italian economist’s individual productivity is explained by two types of variables: (1) propensity to co-author and (2) propensity to cooperate with “foreign” researchers. The propensity to co-author (prop_coauth) is measured as the proportion of co-authored articles on the total number of articles in the Econlit database. This variable ranges between 0 and 1, where 0 is no collaboration and 1 indicates that all papers are co-authored.

Foreign measures the proportion of collaboration with foreign economists, i.e. set F, and is a proxy for the economist’s level of “external” connections. For this reason, Foreign is calculated as the proportion of foreign economists in total co-authors.³⁶

We control for attributional variables shown to be significant in the previous econometric exercise (i.e. gender, tenure, geographical location, see Table 5). We control also for age class. Since the 1970s, the university system in Italy has experienced major changes to the career advancement system, research assessment, propensity for internationalization, etc. we try to capture these institutional changes through four time dummies to indicate the date of the first Econlit JA (1997–2006; 1987–1996; 1977–1986 and 1969–1976): Age97_06, Age87_96, Age77_86, and Age69_76. These dummies control for the different “publication regimes” applying to the economists in our sample.

The econometric analysis involves two econometric problems: (1) sample selection and (2) endogeneity. To address these simultaneously, we estimate a two-stage model. In the first stage, we eliminate the selection bias problem. Selection bias may occur because the average characteristics of the economists in the sample of publishing authors differ from those of the whole population. Without addressing this selection effect, the statistical association between scientific productivity and co-authorship will be inferred incorrectly because the impact of cooperation might be confounded with the coefficients determining the selection. To model the selection mechanism to enable adjustment of the parameter estimations in the structural equation, we adopt a Heckman (1979) procedure. This method uses all the available observations to estimate a probit model of the selection indicator. The residuals of this regression are then used to construct a selection bias control factor λ _i : the inverse Mill’s ratio which, for each individual, can be computed as:

$$ \lambda_{i} = \frac{{\varphi_{i} \left( X \right)}}{{\varPhi_{i} \left( X \right)}} $$

(11)

where X denotes the covariates used in the selection process, φ _i is the density probability function, and Φ _i is the cumulative probability function. This factor, which accounts for the effects of all the unmeasured characteristics related to the selection variable, is then introduced into the structural equation as an extra explanatory variable. Operationally, we estimate the inverse Mill’s ratio from the fourth specification reported in Table 6.

At the second stage, we estimate a structural equation given by:

$$ prod_{i} = \alpha_{o} + \alpha_{1} prop\_coauth_{i} + \alpha_{2} foreign_{i} + X_{i}^{\prime } \beta + \theta \lambda_{i} + \upsilon_{i} $$

(12)

where prod _i is the scientific productivity of each economist i, prop_coauth _i and foreign _i denote the respective propensity to co-author and to cooperate with foreign researchers; λ _i is the inverse Mill’s ratio computed from the previous selection equation and is used to control for selection bias; X indicates other covariates such as Gender, Tenured, and controls such as North West, North East, Centre, South, Islands, Age97_06, Age87_96, Age77_86, Age69_76. Finally, υ _i is the error term with the usual statistical properties.

The direction of causality is an important issue in analysing the relationship between scientific productivity and co-authorship. While it has been shown that cooperation affects productivity, it may well be the case, as suggested by anecdotal evidence, that productivity might affect cooperation: i.e., very productive economists are seen as potentially better co-authors, thus generating a classic reverse causality problem. Also, the presence of endogeneity—i.e., one or more explanatory variables correlated to the true (but unobserved) error term—can generate biased and inconsistent OLS estimates of the coefficient under investigation. We deal with this problem by adopting an IV strategy. The variable that satisfies these conditions is the number of CVA—i.e. chapters in edited books—authored by each economist. CVA are used as an instrument for the propensity for co-authorship because the most recent literature and university policy recommendations assume CVA are the effect of personal connections and relational attitudes that, while not comparable in quality with JA, may reflect alternative use of a researcher’s time. If a researcher is contributing to a collected volume, this leaves less time to write JAs. Thus CVA may measure the propensity to cooperate and interact with the wider scientific community irrespective of the impact in terms of the most known bibliometric indexes of scientific productivity.

Under the null hypothesis that the model is appropriately specified with all explanatory variables exogenous, both Hausman tests reject the null hypothesis of exogeneity of the co-authorship propensity variable, which suggests that IV method is the most appropriate method to estimate our model (see the p value of the Hausman test in Table 6).

Note that the inverse Mill’s ratio variable is always negative³⁷ and often statistically significant. This suggests that correcting for sample selection is the right choice.

Table 6 reports the main results. The findings suggest that co-authorship is a significant determinant of scientific productivity. In fact, the coefficient of the variable prop_coath is positive and statistically significant. This means that economists that are more collaborative are also more productive in JA terms. The results underline another positive role of networking outside the national borders. Collaboration with foreign economists has a positive impact on scientific productivity. Belonging to an international network can thus be interpreted as “signalling” the intrinsic “quality” of the economist and his/her positive political and social attitudes to forging scientific relationships with foreign groups.³⁸ Tenure, Age and geographical dummies are in general, not significantly different from zero, with the exception of North East.

The role of positional variables in scientific productivity: main component only

Finally, we test for the role of some positional variables characterizing the MC, in explaining the scientific productivity of Italian economists, defined as before. The idea behind the choice of this “biased” sub-sample is to analyse the complex relationships existing between collaborative behaviours and productivity by focussing on the most connected community of economists (i.e. those who are in the “thick of things”) so to avoid the misleading influences of “lone wolves” (people writing alone) and of isolated and marginal couplets or triplets (peripheral cliques).

The variables added to the econometric analysis, derived from the SNA exercise presented in section “Relational structure of co-authorships”,³⁹ are:

• 1. the betweenness centrality index (Betweennees), which measures the strategic influence of an author with special reference to his “bridging role” in relation to different academic groups;

• 2. the closeness centrality index (Closeness), which measures the global centrality of a researcher, i.e. his/her capacity to reach all other researcher through the lowest number of co-authors;

• 3. the clustering coefficient⁴⁰ (CC), which measures the proportion of researcher’s co-authors who also co-author with one another;⁴¹

• 4. a measure for the stability of the scientific cooperation (Stability) which ranges between 0, if all co-authors are different, and 1, if all co-authors are the same.

We also introduce the set of covariates defined previously.⁴²

We adopt the econometric approach described in Eq. 12 with the only difference that in this case the estimator is OLS. This choice is justified by the fact that here endogeneity is less a problem because all network indexes refer to second order network features, which are not easily observable by the individual author when deciding on his/her co-authorship strategy.⁴³ The main findings of our analysis are presented in Table 7.

Table 7 Determinants of scientific productivity (MC)

The variables Foreign and Stability have sign, size and significance similar to those recorded in Table 5, thus signaling the robustness of our result to the use of different estimation methods.

Both variables referring to the individual economist’s centrality (Closeness and Betweenness) are positive and statistically significant. Centrality, however defined, in the co-authorship network boosts scientific productivity. However, if scientific productivity is the researcher’s main goal, then acting as a “bridge” between different scientific sub-sectors and/or different “schools” and academic groups (as measured by betweenness centrality index) is more beneficial than being globally central (as measured by closeness centrality index). Our results are thus in line with a large stream of literature (Burt 1992 and 2004; Fleming et al. 2007) suggesting that network brokers, that span structural holes, enjoy larger than average benefits with respect to other network members since they act as an intermediary between otherwise unconnected sub-groups.

Clustering is negative and, in most cases, statistically significant, thus signalling the interests of “star” authors in hindering the interactions among their co-authors in order to preserve a hierarchical and productive “hub and spoke” co-authorship structure. This result indirectly confirms the results obtained by Goyal et al. (2006) when looking at the world population of economists,⁴⁴ thus showing that, at least in this aspect, the Italian community of economists does not behave differently from other nationality.

Although there are plenty of theoretical reasons for and against frequent changes of co-authors (based on the trust-building vs intellectual novelty trade-off), our econometric results shows that, at least for Italian economists, Stability pays. Keeping the same group of authors for successive JA is the best strategy to improve scientific productivity, suggesting that the reduction in transaction costs and the incremental trust building, achieved by repeated interaction prevails over the diversification advantages derived from writing papers with new co-authors.

Conclusions

This paper analyses the effects of the collaborative behaviour (co-authorship) of Italian academic economists on their scientific productivity. To achieve this aim we built an original database by merging the CINECA-MIUR personnel dataset with the Econlit bibliographic dataset. SNA techniques allowed us to study the structure and evolution of co-authorship among Italian economists and to derive positional and relational data for each scientist, exploited in several econometric exercises to explain the scientific productivity (measured by number of journal articles published per year) of this community.

Collaborative behaviour has become more and more frequent within this scientific community as time passed. The resulting network of collaboration is complex (composed of many subnets) and characterized by low density. It is interesting to note that the percentage of foreign economists is higher in the MC than in the whole network, which may signal a correlation between the propensity to co-authorship and the international openness of the Italian academic economist. There are several criteria that might explain the structure and composition of specific sub-networks (such as scientific discipline, geographical location, schools of thought), but the overall structure of the MC displays a small world structure, and the evolution of the network through time is guided by a (non linear) preferential attachment mechanism.

The econometric analysis shows that ‘attributional’ (age, gender, academic position, tenure, scientific sub-discipline, geographical location), ‘relational’ (propensity to cooperate and stability of cooperation patterns) and ‘positional’ (betweenness and closeness centrality indexes and clustering coefficient) variables influence the individual researcher’s scientific productivity. It is interesting to note that the econometric results show that the individual productivity of an Italian economist depends (among other factors) on his/her propensity to collaborate, his/her ‘international’ connections and the stability of his/her collaborative behaviour.

Further, we found that the position of an individual economist in the co-authorship networks affects his/her scientific productivity. Being ‘central’ increases the number of scientific publications per unit of time, but being a ‘bridge’ (i.e. connecting two almost separated parts of a network) is even more beneficial.

Finally we showed that stable partnership with other fellows economists, belonging to different cliques (these being geographically, ideologically or subject based), spurs the individual productivity as well as a crafted strategy of co-authorship.

In conclusion our analysis shed some lights on the determinants of the individual scientist productivity as being the results of a number of different individual, institutional and social characteristics.

Future extensions of the paper will use a “quality adjusted” output measures (i.e. numbers of published papers weighted by their impact factors); extend the full sample to “foreign affiliated” Italian academics which, in this case, have been considered only as co-authors; focus on the determinants of co-authorships of a given couplet of researchers.

This paper was originated by pure scientific curiosity and the desire to contribute to the public debate on the university reform process in Italy. Our results suggest that policy makers should be very careful in designing and implementing an explicit incentives system (via a research assessment exercise mainly based on quantitative bibliometric indexes) since the performance of an individual scientist may be influenced by a number of exogenous factors which are beyond his/her control.

Appendix

See Tables 8 and 9.

Table 8 Academic position, scientific sector and gender of Italian Economist as at December the 31st 2006

Table 9 Descriptive statistics of dependent variables and regressors