Paul Schrimpf. March 22, UBC Vancouver School of Economics 565. Network structure and outcomes. Paul Schrimpf. Introduction. Describing Networks

Transcription

1 s UBC Vancouver School of Economics 565 March 22, 2017

2 References s Overviews: Jackson, Goyal (2012) industries: Economides (1996), Economides and Encaoua (1996)

3 s 1 2 s Lee and Fong (2013)

4 s Section 1

5 I s : nodes & links between them Questions: How does network structure affect behavior? How are networks formed? Focus on networks that are not owned by a single entity i.e. not on network industries where a single firm owns and controls its network (telecom, electricity, airlines, etc) Relatively new area, little empirical work

6 s in IO s R&D collaboration Trade Buyer-supplier Consumer in & targeting

7 s Section 2 s

8 Basic notation s Nodes {1,..., N} = N Adjacency matrix G, N N matrix with g ij representing connection between i and j Graph (N, G) Undirected symmetric G Directed asymmetric G Unweighted (or discrete) g ij {0, 1} Weighted not discrete

9 s Summary statistics I Distance between two nodes = shortest path between them ( if no connected path) Diameter = largest distance between nodes Clustering of graph is portion of j and k connected given j and k both connected to i of node i is the portion of time j and k are connected directly given j and k are connected to i average clustering of graph = average across nodes of node clustering Degree of a node = number of links Directed graphs: in-degree & out-degree Degree centrality = degree N 1 density = fraction of possible links present average degree N 1 = Degree distribution = CDF of node degree

10 Summary statistics II s Centrality measures: Degree, closeness, betweenness, decay Eigenvector, Katz, Bonacich

11 s Section 3

12 s Question: how does network structure affect some outcome? Reduced form work: regress outcome on node or network summary statistics

13 s Example: Gandal (2011) Knowledge spillovers in open-source projects Data: Sourceforge Contributor network: linked if participated in same project Project network: linked if have common contributors Question: how important are project vs contributor spillovers for project success? Project spillover = developers learn from working on a particular project Contributor spillover = developers learn from working with other developers Related paper:

14 Example: Gandal (2011) s

15 s Example: Gandal (2011) Table: The Distribution of Contributors per Project and Projects per Contributor Project Contributor Contributors N Projects Projects N Contributo 1 77, , , , , , , , , Total projects 114,751 Total contributors 160,104

16 s Example: Gandal (2011) Table: Distribution of Component Size Component Size (Contributors) Components (Subnetworks) 55, , , , ,787

17 s Example: Gandal (2011) Table: Distribution of Degree Degree Number of Contributors 0 47, , , , , , , , ,

18 Empirical specification s Degree centrality as measure of direct connections Closeness centrality = C C (i) = j N N 1 d(i,j) conditional on degree measures indirect connections S i = success = number of downloads S i = α + γc c (i)/(n 1) + βdegree i + controls

19 Results - project network s Table: Regression Results: Dependent Variable: ldownloads Regression 1 (All 66,511 Projects) Regression 2 (Giant Component: P Independent variables Coefficient T-Statistic Coefficient T-Statistic Constant lyears_since lcount_topics lcount_trans lcount_aud lcount_op_sy ds_ ds_ ds_ ds_ ds_ ds_ inactive lcpp ldegree giant_comp lgiant_cpp lgiant_degree lcloseness Number of observations 66,511 18,697 Adjusted R

20 Contributor effects s Regress downloads on average contributor degree and average contributor closeness centrality (and controls) Result: Coefficient on log average closeness = 0.12, with t = 1.59 Coefficient on log average degree = 0.019, with t = 0.72 Including both contributor and project measures, project ones significant, contributor ones not

21 Limitations s How to interpret results? structure affects downloads Downloads affect contributions, which affects network structure Why closeness centrality and degree? (they do explore robustness to other measures, but none of them theoretically motivated)

22 Grohsjean (2012) s Developer networks in electronic games Panel data on games & developers Construct network of developers Developers linked in year t if worked together anytime between 1972 and t Look at relationship between revenue (or rating) & degree centrality & closeness centrality

23 Grohsjean (2012) s S igdpt = α i +α d +α p +α t +β 1 D igdpt 1 +β 2 C igdpt 1 +CV igdpt γ+ε igdpt Developer i Game g Developing firm d Publisher p Year t

24 Grohsjean (2012) s

25 Grohsjean (2012) s

26 and Kerr (2016) s Innovation network Directed network of patent citations, Results: stable over time Past innovations (patents) in connected industries predict current patents Impact of innovations are localized

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31 Predicting patents s Predicted patents in industry j from past citations: ˆP j,t = k j 1 a=1 0 Citations j k,a P Patents k,t a k where Citations j k,a = citations of a patent in industry k that is a years old from j Patents k = total patents in k Both estimated using data Predictions for

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34 s Acemoglu, Daron, Ufuk Akcigit, and William R Kerr Innovation network. Proceedings of the National Academy of Sciences : URL http: // Acemoglu, Daron, Vasco M. Carvalho, Asuman Ozdaglar, and Alireza Tahbaz-Salehi The Origins of Aggregate Fluctuations. Econometrica 80 (5): URL Atalay, Enghin, Ali Hortaçsu, James Roberts, and Chad Syverson structure of production. Proceedings of the National Academy of Sciences 108 (13): URL

35 s Balland, Pierre-Alexandre, Mathijs De Vaan, and Ron Boschma The dynamics of interfirm networks along the industry life cycle: The case of the global video game industry, Journal of Economic Geography 13 (5): URL content/13/5/741.abstract. Bramoullé, Yann, Rachel Kranton, and Martin D Amours Strategic Interaction and s. American Economic Review 104 (3): URL aer Chandrasekhar, Arun and Matthew O Jackson Tractable and consistent random graph models. arxiv preprint arxiv: URL

36 s Christakis, Nicholas A., James H. Fowler, Guido W. Imbens, and Karthik Kalyanaraman An Empirical Model for Strategic Formation. Working Paper 16039, National Bureau of Economic Research. URL Claussen, Jörg, Oliver Falck, and Thorsten Grohsjean The strength of direct ties: Evidence from the electronic game industry. International Journal of Industrial Organization 30 (2): URL pii/s x. Economides, Nicholas The economics of networks. International Journal of Industrial Organization 14 (6): URL article/pii/

37 s Economides, Nicholas and David Encaoua Special issue on network economics: Business conduct and market structure. International Journal of Industrial Organization 14 (6): URL pii/ Fafchamps, Marcel and Måns Söderbom Proximity and Business Practices in African Manufacturing. The World Bank Economic Review 28 (1): URL content/28/1/99.abstract. Fershtman, Chaim and Neil Gandal Direct and indirect knowledge spillovers: the social network of open-source projects. The RAND Journal of Economics 42 (1): URL http: //dx.doi.org/ /j x.

38 s Foster, Andrew D. and Mark R. Rosenzweig Learning by Doing and Learning from Others: Human Capital and Technical Change in Agriculture. Journal of Political Economy 103 (6):pp URL Goyal, Sanjeev Connections: an introduction to the economics of networks. Princeton University Press. URL docid= Graham, Bryan S. 2014a. An Empirical Model of Formation: Detecting Homophily When Agents Are Heterogenous. Working Paper 20341, National Bureau of Economic Research. URL b. Methods of Identification in Social s. Working Paper 20414, National Bureau of Economic Research. URL

39 s Hendricks, Kenneth and Robert H. Porter The Timing and Incidence of Exploratory Drilling on Offshore Wildcat Tracts. The American Economic Review 86 (3):pp URL Jackson, Matthew O Social and economic networks. Princeton University Press. König, Michael D, Xiaodong Liu, and Yves Zenou R&D s: Theory, Empirics and Policy Implications. URL files/publications/13-027_2.pdf. Lee, Robin S and Kyna Fong Markov-Perfect Formation An Applied Framework for Bilateral Oligopoly and Bargaining in Buyer-Seller s. Tech. rep. URL papers/mpneformation.pdf.

40 s Leung, Michael Two-step estimation of network- models with incomplete in. Available at SSRN URL zew-docs/veranstaltungen/seek2013/social_ Workshop/SEEK2013_BEN_Leung.pdf. Sheng, Shuyang Identification and estimation of network games. Unpublished Manuscript URL