Superstar Economists: Coauthorship networks and research output - PowerPoint PPT Presentation

Superstar Economists: Coauthorship networks and research output Chih-Sheng Hsieh 1 , Michael D. König 2 , Xiaodong Liu 3 , and Christian Zimmermann 4 Department of Economics Hong Kong Baptist University 1 Department of Economics, Chinese University of Hong Kong. 2 Department of Economics, University of Zurich. 3 Department of Economics, University of Colorado Boulder. 4 Department of Economic Research, Federal Reserve Bank of St. Louis. 1/47 14 th November 2017

Scientific Collaborations in Economics from 24.7% during 1970’s to 50% to 2000’s, and to 62.7% in 2011 (Laband and Tollison, 2000; Ductor, 2014). The network distance among authors has declined signifjcantly due to emergence of interlinked star economists (Goyal, van der Leji, and Moraga-Gonzalez, 2001). increase: greater gains from specialization and labor division (McDowell and Melvin, 1983), falling communication cost (Hudson, 1996), a greater pressure to publish (Barnett et al., 1988), increasing uncertainty in the editorial review process (Barnett et al., 1988), and the possible increase in productivity through collaboration (Laband and Tollison, 2000), among others. 2/47 ◮ The proportion of economic papers written by multiple authors rose ◮ The literature has provided some explanations on why collaborations

Scientific Collaborations in Economics leads to better scientifjc outputs may trigger debates on the free-rider efgect (negative externality) (Jackson and Wolinsky, 1996). spillover efgect (positive externality) and negative congestion research projects that he/she participates in a network game. model is that individual researcher chooses endogenous efgort on which collaborations afgect projects’ outputs. The key feature of our problem, shirking on efgort, cronyism, etc. Ductor, 2014). might afgect individual productivity (see Laband and Tollison, 2000; particularly, very few papers discuss which channels that collaboration Jones, and Uzzi, 2007; Laband and Tollison, 2000; Ductor, 2014); and academic productivity or not (Chung et al., 2009; Hollis, 2001; Wuchty, 3/47 ◮ However, there is no agreement on whether coauthorship can increase ◮ Without discussing the channel, showing that having more co-authors ◮ In this paper, we propose a structural model to study the channel in ◮ Collaborations in our model bring in two possible efgects: positive

Our Approach: Model co-authorship networks. Cabrales et al., 2011; Jackson and Wolinsky, 1996), we are able to in multiple, possibly overlapping projects, and there are interaction efgects in the cost of efgort. efgorts, but also efgorts of their co-authors on their co-authored projects; meanwhile, decreasing coauthors’ efgorts on projects other than their co-authored ones. 4/47 ◮ We build a micro-founded model for the output produced in scientifjc ◮ Difgerent from previous works on network games (Ballester et al., 2006; characterize the interior equilibrium when multiple agents spend efgort ◮ Our model implies that authors’ abilities raise not only their own

Our Approach: Empirics agents can contribute to many potentially overlapping projects in the Nash equilibrium, and the participation is endogenously modelled. matching process that depends on both, the authors’ and projects’ characteristics. coauthorships between economists registered in the Research Papers in Economics (RePEc) author service. 5 negative congestion efgect. The spillover efgects are even stronger if we divide the payofg by the number of co-authors or we weight the collaboration spillover by skill similarity. 5 http://repec.org/ 5/47 ◮ We propose an estimation framework for our theoretical model in which ◮ The allocation of agents into difgerent projects is determined by a ◮ We estimate this model using data for the network of scientifjc ◮ From the empirical result, we obtain a positive spillover efgect and a

Our Approach: Policy departments) that quantifjes the endogenous decline in research output due to the removal of an economist from the network (“key players”, “superstar” economists) (Azoulay, 2010; Waldinger, 2012; Zenou, 2015). with the largest number of citations, or coincide with other ranking measures used in the literature. typically not derived from microeconomic foundations, and do not take into account the spillover efgects generated in scientifjc knowledge production networks. 6/47 ◮ We develop a novel ranking measure (for economists and their ◮ We fjnd that the highest ranked authors are not necessarily the ones ◮ However, this discrepancy is not surprising, as traditional rankings are

Production Function 2 between the research efgorts of collaborating agents, and project s ), (1) 7/47 ◮ Assume that there are s ∈ P = { 1 , . . . , p } research projects (papers) and i ∈ N = { 1 , . . . , n } researchers (authors). ◮ Let the production function for project s be given by α i e is + λ ∑ ∑ ∑ Y s = Y s ( G ) = f ij e is e js , i ∈N i ∈N j ∈N \{ i } ◮ where Y s is the research output of project s , e is is the research efgort that agent i spent in project s ( e is = 0 if agent i does not participate in ◮ α i captures the productivity of agent i , ◮ f ij ∈ ( 0 , 1 ] measures the (skill) similarity between agents i and j , ◮ the spillover-efgect parameter λ > 0 represents complementarity ◮ G represents the bipartite network of authors and projects.

Example e 12 projects, where round circles represent authors and squares represent projects. 2 1 e 32 2 3 0 1 2 8/47 1 2 e 32 e 12 e 21 e 11 1 2 3 ( e 21 ) ( e 11 ) ( 0 ) Figure: (Left panel) The bipartite collaboration network G of authors and (Right panel) The projection of the bipartite network G on the set of coauthors.

Utility 2 participating in project s . efgorts of the same agent in difgerent projects. (2) cost e is e it e 2 9/47 payofg ◮ The utility of agent i is then given by   ∑ ∑ ∑ ∑ U i = U i ( G ) = g is δ s Y s − 1 is + ϕ ,  s ∈P s ∈P s ∈P t ∈P\{ s } � �� � � �� � ◮ where g is ∈ { 0 , 1 } indicates whether agent i participates in project s , δ s ∈ ( 0 , 1 ] is a discount factor, 6 and ◮ the parameter ϕ > 0 represents substitutability between the research 6 If δ s = 1, then individual payofg from research output Y s is not discounted. If δ s = 1 / ∑ i ∈N g is , then individual payofg is discounted by the number of agents (coauthors)

Equilibrium Characterization (3) ones. being f ij , and 10/47 and ◮ Let W = G ( diag p s = 1 { δ s } ⊗ F ) G , M = G ( J p ⊗ I n ) G , where ⊗ denotes Kronecker product, G is an np -dimentional diagonal matrix given by G = diag p s = 1 { diag n i = 1 { g is }} , ◮ F is an n × n zero-diagonal matrix with the ( i , j ) -th ( i ̸ = j ) element ◮ J p is an p × p zero-diagonal matrix with ofg-diagonal elements being ◮ Further, let ρ max ( A ) denote the spectral radius of a square matrix A .

(4) and (5) 11/47 ◮ Proposition: Suppose the production function for each project s ∈ P is given by Equation (1) and the utility function for each agent i ∈ N is given by Equation (2). Given the bipartite network G , if | ϕ | < 1 /ρ max (( I np − λ W ) − 1 M ) , | λ | < 1 /ρ max ( W ) then the equilibrium efgort portfolio is given by e ∗ = ( I np − L λ,ϕ ) − 1 G ( δ ⊗ α ) , where L λ,ϕ = λ W − ϕ M , δ = [ δ 1 , · · · , δ p ] ′ and α = [ α 1 , · · · , α n ] ′ .

Example – continued 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 and, hence, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 12/47 0 0 0 0 0 0 0 1 0 and ◮ Following Equation (3),                 W = M = ,                   λ − ϕ λ     L λ,ϕ = λ W − ϕ M =   .   − ϕ λ       λ

Example – continued 11 0 0 1 32 22 12 31 21 13/47 ◮ The suffjcient condition for the existence of a unique equilibrium given by (4) holds if | λ | < 1 and | ϕ | < 1 − λ 2 . ◮ From Equation (5) the equilibrium efgort portfolio is   e ∗ e ∗     e ∗ e ∗ =   = ( I np − L λ,ϕ ) − 1 G ( I np ⊗ α )   e ∗     e ∗   e ∗ ( 1 − λ 2 − ϕ ) α 1 + λ ( 1 − λ 2 ) α 2 − λϕα 3   λ ( 1 − λ 2 − ϕ ) α 1 + ( 1 − λ 2 − ϕ 2 ) α 2 − λ 2 ϕα 3       = .  ( 1 − λ 2 − ϕ ) α 1 − λϕα 2 + λ ( 1 − λ 2 ) α 3  ( 1 − λ 2 ) 2 − ϕ 2       λ ( 1 − λ 2 − ϕ ) α 1 − λ 2 ϕα 2 + ( 1 − λ 2 − ϕ 2 ) α 3