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Journal of Economic Interaction and Coordination

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01.04.2013 | Regular Article

Null models of economic networks: the case of the world trade web

verfasst von: Giorgio Fagiolo, Tiziano Squartini, Diego Garlaschelli

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 1/2013

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Abstract

In all empirical-network studies, the observed properties of economic networks are informative only if compared with a well-defined null model that can quantitatively predict the behavior of such properties in constrained graphs. However, predictions of the available null-model methods can be derived analytically only under assumptions (e.g., sparseness of the network) that are unrealistic for most economic networks like the world trade web (WTW). In this paper we study the evolution of the WTW using a recently-proposed family of null network models. The method allows to analytically obtain the expected value of any network statistic across the ensemble of networks that preserve on average some local properties, and are otherwise fully random. We compare expected and observed properties of the WTW in the period 1950–2000, when either the expected number of trade partners or total country trade is kept fixed and equal to observed quantities. We show that, in the binary WTW, node-degree sequences are sufficient to explain higher-order network properties such as disassortativity and clustering-degree correlation, especially in the last part of the sample. Conversely, in the weighted WTW, the observed sequence of total country imports and exports are not sufficient to predict higher-order patterns of the WTW. We discuss some important implications of these findings for international-trade models.

Vorheriger Artikel On the distributional properties of size, profit and growth of Icelandic firms

Nächster Artikel Diffusion of competing innovations in influence networks

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In economics the use of purely-random models is not new. Examples range from industrial agglomeration (Ellison and Glaeser 1997; Rysman and Greenstein 2005 to international trade Armenter and Koren 2010).

See for example Katz and Powell (1957), Holland and Leinhardt (1976), Snijders (1991), Rao et al. (1996), Kannan et al. (1999); Roberts (2000), Newman et al. (2001), Shen-Orr et al. (2002), Maslov et al. (2004), Ansmann and Lehnertz (2011), Bargigli and Gallegati (2011).

In what follows, given a statistic \(X\) computed on the \(N\) nodes of graph, we call “sequence” of \(X\) the collection \(\{x_i\}_{i=1}^{N}\). The degree of a node is defined as the number of links of a node. The strength of a node is the sum of all weights of the links of a given node. See Tables 1 and 2 for formal definitions.

See for example Li et al. (2003), Serrano and Boguñá (2003), Garlaschelli and Loffredo (2004a, 2005); Garlaschelli et al. (2007), Serrano et al. (2007), Bhattacharya et al. (2008, 2007), Fagiolo et al. (2008, 2009), Reyes et al. (2008, 2010), Barigozzi et al. (2010a), Fagiolo (2010, 2010b), De Benedictis and Tajoli (2011).

Cf., among others, Snyder and Kick (1979), Nemeth and Smith (1985), Sacks et al. (2001), Breiger (1981), Smith and White (1992), Kim and Shin (2002).

There is no agreement whatsoever on the way this threshold should be chosen (see for example Kim and Shin 2002; Serrano and Boguñá 2003; Garlaschelli and Loffredo 2004a, 2005). In what follows, in line with much of the existing literature, we straightforwardly define a link whenever a non-zero trade flow occurs.

The work-horse model in international trade is the so-called gravity equation. Fagiolo (2010) shows that a gravity model can explain a great deal of WTW architecture, but that a still relevant amount of information is left in the weighted network built using the residuals of gravity-equation estimation.

See for example Katz and Powell (1957), Holland and Leinhardt (1976), Snijders (1991), Rao et al. (1996), Kannan et al. (1999), Roberts (2000), Newman et al. (2001), Shen-Orr et al. (2002), Maslov et al. (2004), Ansmann and Lehnertz (2011), Bargigli and Gallegati (2011).

See Serrano et al. (2007), Opsahl et al. (2008) for extensions of this method that control for average vertex strengths in undirected and directed networks. Note that by controlling for either degree or strength sequences, one automatically fixes the “volume” of the network, in terms of either the total number of links or the sum of link weights. Conversely, controlling for the volume only, means assuming equi-probability among links and weights. This typically destroys the topology of the underlying network and thus turns out to be a bad null model for most observed networks.

This method has been applied to several networks, including the Internet and protein networks (Maslov and Sneppen 2002; Maslov et al. 2004). Different webs have been found to be affected in very different ways by local constraints, making the problem interesting and not solvable a priori.

It must be noted that the WTW is a very dense network. Density in the aggregate directed network indeed oscillates in the range \([0.32,0.56]\). As a result, in the case of the WTW, applying a local rewiring algorithm would be rather expensive.

See Tables 1 and 2 for a detailed account of the expressions for the randomized properties appearing in the following analysis. Cf. Squartini and Garlaschelli (2011) for a discussion on how standard deviations of topological properties under the random null model are obtained.

Data are freely available at http://privatewww.essex.ac.uk/~ksg/data.html.

This is a well-known issue in international trade statistics. Most of the literature on gravity has indeed tried to estimate models where one accounts for the large number of zero entries, see for example Santos Silva and Tenreyro (2006). Nevertheless, only a few papers have addressed the problem of discriminating between sheer zeros and missing valus, cf. Baranga (2009) for some progress in this direction.

These are labelled cycle (if \(i\) exports to \(j\), who exports to \(h\), who exports to \(i\)), in (if both \(j\) and \(h\), who are trade partners, exports to \(i\)), out (if both \(j\) and \(h\), who are trade partners, imports from \(i\)) and mid (if \(i\) imports from \(h\) and exports to \(j\), and \(j\) and \(h\) are trade partners).

Note that these quantities are trivially reproduced by our null models where, by definition, \(\langle k_i^{out}\rangle =k_i^{out}(A)\), \(\langle k_i^{in}\rangle =k_i^{in}(A)\), \(\langle s_i^{out}\rangle =s_i^{out}(W)\) and \(\langle s_i^{in}\rangle =s_i^{in}(W)\).

Note that the null model misses not only the scale of disassortativity in the network, but also the scale of ANNS levels associated to every observed NS. Indeed, the blue line in Fig. 13, which describes expected ANNS, appears flat only because it attains values in a very narrow ANNS range, and not because the ANNS-NS correlation is close to zero.

An earlier attempt to go in this direction has been recently made by Helpman et al. (2008), Eaton et al. (2012), who develop international-trade models with heterogeneous firms that are consistent with a number of data facts, including the number of zeros (i.e., network density). However, they fall short of providing explanations of where exactly these zeros are, i.e. why some potential trade-link actually turns on.

For example, existing databases differ in the way trade flows are reported according to the reporter (importer or exporter), whether zeroes are all considered as missing trade, etc.

See Bhattacharya et al. (2008) for an attempt in this direction.

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Titel: Null models of economic networks: the case of the world trade web
verfasst von: Giorgio Fagiolo
Tiziano Squartini
Diego Garlaschelli
Publikationsdatum: 01.04.2013
Verlag: Springer-Verlag
Erschienen in: Journal of Economic Interaction and Coordination / Ausgabe 1/2013
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-012-0104-7

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