The World Wine Web: The Structure of the Global Wine Trade Kym Anderson Wine Economics Research Centre University of Adelaide Joe Francois World Trade Institute University of Bern Doug Nelson Murphy Institute Tulane University Glyn Wittwer Centre for Policy Studies Victoria University

What we do in this paper Briefly discuss what network analysis does Briefly review some basic tools of network analysis Apply these tools to the global wine trade

What are networks? Any collection of objects in which some pairs of these objects are connected by links. The objects are generically called nodes; and The links are generically called edges. In this paper, The nodes are countries (national economies); and The edges are annual exports of wine Thus, the edges are weighted; and Since we are using exports, our edges are directed That is, the edge from France to Germans will have a different value than the edge from Germany to France.

Analyzing networks: graphs Graph theory provides a natural language and set of tools for the analysis of networks. For relatively small networks, pictures do a great job of illustrating the main elements of the network. Consider the 15 top exporters and 15 top importers of wine.

Wine export links among 15 largest exporters

Wine import links among 15 largest importers

Analyzing networks: graphs Graph theory provides a natural language and set of tools for the analysis of networks. For relatively small networks, pictures do a great job of illustrating the main elements of the network. Consider the 15 top exporters and 15 top importers of wine. Unfortunately, for large networks this doesn’t work so well. Consider the entire WWW for 2009-2013.

Analyzing Networks: Simple Statistics A number of simple statistics characterize the structure of the network and can be used to analyze the evolution of the network over time. In particular, we are interested in: Size of network Symmetry or asymmetry of network participants Centralization and density

Analyzing Networks: Simple Statistics Size is easy. We consider Number of countries Number of bilateral links between countries Total trade volume The WWW has grown dramatically since the mid 1960s. 1964-68 1969-73 1974-78 1979-83 1984-88 1989-93 1994-98 1999-03 2004-08 2009-13 # of Countries 165 194 199 198 226 228 231 236 # of Links 1946 2527 3081 3218 3264 4269 4945 6664 7807 8191 Total Trade 595825 1199123 2366399 4105618 5192202 8307726 11711724 15204269 25278382 31567495

Analyzing Networks: Simple Statistics Symmetry/Asymmetry of Nodes A simple approach is to compare the number of links (“degree”) or the size of trade (“weighted degree”) of the largest exporter (outdegree) or importer (indegree) to the mean and median of these measures. 1964-68 1969-73 1974-78 1979-83 1984-88 1989-93 1994-98 1999-03 2004-08 2009-13 Max out degree 155 175 183 184 198 201 203 205 210 Median out degree 2 1 3 5 9 12 Max weighted out degree 186341 426262 883433 1627690 2604111 4039201 4938656 5531519 8610675 10107513 Median weighted out degree 10 14 25 49 101 134 159 213 Mean degree 13 15 16 19 22 29 34 35 Mean weighted degree 3611 6181 11891 20735 26091 36760 51367 65819 109430 133761 Max in degree 60 58 77 78 90 93 140 114 127 Median in degree 11 17 24 Max weighted in degree 141902 182757 355994 817930 1074401 1576075 2253532 3669508 5584330 5108323 Median weighted in degree 168 308 422 588 764 1324 1551 1669 3305 4760

Analyzing Networks: Simple Statistics Degree distribution Instead of a normal distribution, the degree distributions of many social networks are characterized by a power law. That is, degree, say k, obeys a power law if the probability of a node having degree k, P(k), is drawn from a distribution 𝑃 𝑘 ∝ 𝑘 −𝛾 , γ is a constant parameter of the distribution called the scaling parameter. This parameter typically lies in the range 2 < γ < 3. Such a distribution is called “scale free” (i.e. scaling k by a constant, c, simply multiplies the original power law relation by c-γ).

Analyzing Networks: Simple Statistics Thus, the degree distribution is approximated by a straight line log 𝑃 𝑘 ~−𝛾 log 𝑘 . Note that, if this fits the data, the slope of the line is an estimate of the scaling parameter. That is, there are “fat tails”—i.e. there are more instances of nodes with many links than would be predicted by a normal distribution. Many social phenomena are characterized by power law distributions Firm size City size Income distributions We have not tested for this, but will for the final version of the paper.

Analyzing Networks: Simple Statistics Density The basic statistics suggest that the WWW should have been growing progressively denser. The standard measure of density is the number of (unweigted) links observed in the data as a proportion of possible links. The number of possible links is just [n(n – 1)] Thus, we divide # of links from the first table, by this number. So density has increased systematically 1964-68 1969-73 1974-78 1979-83 1984-88 1989-93 1994-98 1999-03 2004-08 2009-13 Density 0.037 0.067 0.078 0.083 0.084 0.096 0.125 0.147 0.148

Analyzing Networks: Simple Statistics Centralization Centralization is the extent to which a single node dominates all links. A maximally centralized network is a star (i.e. a network in which each node has degree 1 [or 2 for directed networks], and the center has degree n – 1). Thus, we calculate the extent to which the WWW deviates from the star network. That is, we use UCINET to calculate the sum of the differences between the degree of the most central node and all other nodes, as a fraction of the maximum sum of differences

Analyzing Networks: Simple Statistics 1964-68 1969-73 1974-78 1979-83 1984-88 1989-93 1994-98 1999-03 2004-08 2009-13 Out centralization 0.879 0.844 0.85 0.86 0.8 0.75 In centralization 0.296 0.234 0.312 0.315 0.374 0.331 0.316 0.48 0.35 0.39 Not surprisingly, centralization is rather low. Our centralization declines modestly, but steadily, over this period. In centralization rises up to the mid-1980s and then stabilizes (with 1999-03 something of an outlier).