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The evolution of the world trade web: a weighted-network analysis

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Abstract

This paper employs a weighted network approach to study the empirical properties of the web of trade relationships among world countries, and its evolution over time. We show that most countries are characterized by weak trade links; yet, there exists a group of countries featuring a large number of strong relationships, thus hinting to a core-periphery structure. Also, better-connected countries tend to trade with poorly-connected ones, but are also involved in highly-interconnected trade clusters. Furthermore, rich countries display more intense trade links and are more clustered. Finally, all network properties are remarkably stable across the years and do not depend on the weighting procedure.

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Notes

  1. A survey of this enormous literature is beyond the scope of this paper. The interested reader is referred to Scott (2000), Barabási (2003), Watts (2003), Carrington et al. (2005), among others.

  2. Well-known examples of such studies include networks of friendship and social acquaintances (Rapoport and Horvath 1961; Milgram 1967), marriages (Padgett and Ansell 1993), and job-market interactions (Granovetter 1974).

  3. See Jackson (2004) for an introduction.

  4. The analysis of weighted networks was introduced in Barrat et al. (2004, 2005), Barthélemy et al. (2005), and further developed in Dall’Asta et al. (2006), Saramaki et al. (2007), Onnela et al. (2005), DeMontis et al. (2005).

  5. Cf. also Fagiolo et al. (2009), where links are weighted using trade flows only.

  6. We refer the reader to Fagiolo et al. (2007) for more formal definitions and notation.

  7. Self-loops, i.e. links connecting i with itself are not typically considered. This means that a ii  = 0, for all i.

  8. For example in random networks where each link is in place with a certain given probability, independently on all the others (i.e., according the simplest Erdös-Renyi random-graph model: see e.g. Bollobás 1985). In what follows, we employ the term “random network” as a synonym for the Erdös-Renyi random-graph model.

  9. Network clustering is a well-known concept in sociology, where notions such as “cliques” and “transitive triads” have been widely employed (Wasserman and Faust 1994; Scott 2000). For example, friendship networks are typically highly clustered (i.e. they display high cliquishness) because any two friends of a person are very likely to be friends.

  10. See Herfindahl (1959) and Hirschman (1964). For early applications of the disparity index to networks, see Almaas et al. (2004) and Barthélemy et al. (2005).

  11. That is (a ij ,w ij ) are replaced by (max{a ij ,a ji },0.5(w ij  + w ji )), see De Nooy et al. (2005).

  12. Sacks et al. (2001) build a measure of country position in the network based on the concept of “structural autonomy” and show that it has a positive effect on country’s per capita GDP.

  13. Very similar results are obtained by Mahutga (2006), who shows that the globalization process has induced structural heterogeneity and thus inequality.

  14. There is no agreement whatsoever on the way this threshold should be chosen. For example, Kim and Shin (2002) use cutoff values of US$ 1 million and 10 million. Kastelle et al. (2005) endogenously set a cutoff so as to have, in each year, a connected graph. Kali and Reyes (2009) experiment with different lower thresholds defined as shares of country’s total exports. On the contrary, other papers (Serrano and Boguñá 2003; Garlaschelli and Loffredo 2004a, 2005; Kali and Reyes 2007) straightforwardly define a link whenever a non-zero trade flow occurs.

  15. That is, they weight each link by the difference between exports and imports. Notice that, as happens also in Bhattacharya et al. (2007a, b), their across-year comparison may be biased by the fact that trade flows are expressed in current U.S. dollars and do not appear to be properly deflated.

  16. See Fagiolo et al. (2007) for technical details. Note that the corresponding standardized index takes values at least 10 standard deviations below zero.

  17. Due to the extreme symmetry of the network, results do not change if one symmetrizes the export matrix first and then divides by the GDP of the exporting country.

  18. As the right panel of Fig. 5 shows, there seems to be a subset of countries featuring low ND and relatively high strength.

  19. As discussed in Section 5.7, this holds true even if one replaces the baseline weighting procedure with a few, economically meaningful, alternative schemes.

  20. The key assumptions are that the benefits from connections exhibit decreasing returns, and that they depend negatively on distance. Contrary to the predictions of the model, the WTW does not display a single country as its center. This is due to the fact that in the (real) world of international trade, the benefit from connecting to a country is not monotonically increasing in the number of its trading partners. This suffices for a network to display more that one hub.

  21. This interpretation is further corroborated by the fact that geographically-structured networks are typically highly clustered, with short-distance links counting more than long-distance ones.

  22. Indeed, the weighted version of the CC, albeit quite stable over time, is significantly smaller (from a statistical point of view) than its expected value in a random network. Indeed, average clustering ranges from 3.8776×10 − 4 (in 1994) to 5.5106×10 − 4 (in 1982) whereas the expected value of weighted clustering in random networks goes in the same years from 0.2272 to 0.2717—that is, \(\frac{27}{64}\) times network density (see Fagiolo et al. 2007 for details).

  23. To do so, for each year we generated a sample of 10000 random networks whose adjacency matrices have been kept fixed and equal to the observed one, whereas observed link weights have been randomly reshuffled across the links.

  24. Also the shape of the underlying relation is different. While degree seems to be linearly related to pcGDP, a log-log relation holds between strength and pcGDP. This means that pcGDP influences more heavily node strength than node degree.

  25. The correlation between the two indicators is not statistically different from 1.

  26. A very similar result is obtained if one attributes the core status to those countries displaying values of RWBC above the mean plus one standard deviation.

  27. This is expected since one of the interpretations of node strength is related to the degree of influence that a given node has on the network or to what extent other nodes depend on a given node; also, the correlation between RWBC and NS is very high.

  28. As mentioned, we have also experimented with another weighting scheme where we have symmetrized the graph before dividing by exporter (or importer) GDP. All these alternatives did not result in any significant change of our main findings.

  29. This counter-intuitive result depends on the fact that the index computed controls for magnitude effects. Therefore, GDP scaling may enhance differences between imports and exports rather than balancing them.

  30. More detailed results are available from the authors upon request.

  31. In this respect, an interesting exercise would imply to find (if any) a proper rescaling or manipulation of original trade flows that makes weighted and binary undirected network results looking the same.

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Acknowledgements

Thanks to Marc Barthélemy, Diego Garlaschelli, and to an anonymous referee for their useful and insightful comments. All usual disclaimers apply.

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Authors and Affiliations

  1. Sant’Anna School of Advanced Studies, Piazza Martiri della Libertà 33, 56127, Pisa, Italy

    Giorgio Fagiolo

  2. Department of Economics, Sam M. Walton College of Business, University of Arkansas, Fayetteville, AR, USA

    Javier Reyes

  3. Department of Economics, University of Trento, Trento, Italy

    Stefano Schiavo

  4. OFCE, Paris, France

    Stefano Schiavo

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  1. Giorgio Fagiolo
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  2. Javier Reyes
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  3. Stefano Schiavo
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Correspondence to Giorgio Fagiolo.

Appendix A: Countries in the balanced panel (1981–2000)

Appendix A: Countries in the balanced panel (1981–2000)

The dataset provided by Gleditsch (2002) includes 196 countries for which there are data on trade flows from 1948 to 2000. However, trade data contain many missing (or badly reported) values before 1970. In addition, there are some countries with zero total exports in some years.

Notice also that our analysis requires to match trade data with real GDP (both in levels and per capita). This is because: (i) weights are defined as exports divided by GDP; (ii) one wants to cross-sectionally correlate network measures with country-specific variables like per-capita GDP.

We have therefore selected countries in such a way to have: (i) a time horizon and a country sample size as long as possible; (ii) no missing values in trade data and GDP (both in levels and per capita); (iii) non-zero total exports.

By applying conditions (i) and (ii) we get only 83 countries from 1960–2000. This number becomes 138 for the period 1970–2000; 152 for the period 1970–2000; 163 for the period 1981–2000; and 168 for the period 1990–2000. We thus decided to select the time interval 1981-2000 using 163 countries. However, 4 of them (San Marino, Andorra, Liechtenstein, Monaco) have total exports equal to zero in some years. This leaves us with N = 159 countries, whose list is in Table 2.

Table 2 List of countries in the balanced panel
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Fagiolo, G., Reyes, J. & Schiavo, S. The evolution of the world trade web: a weighted-network analysis. J Evol Econ 20, 479–514 (2010). https://doi.org/10.1007/s00191-009-0160-x

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