Modeling the International-Trade Network: a gravity approach


We investigate whether the gravity model (GM) can explain the statistical properties of the International Trade Network (ITN). We fit data on trade flows with a GM using alternative estimation techniques and we build GM-based predictions for the weighted topological properties of the ITN, which are then compared to the observed ones. Our exercises show that the GM: (i) may replicate part of the weighted-network structure only if the observed binary architecture is kept fixed; (ii) is not able to explain higher-order statistics that, like clustering, require the knowledge of triadic link-weight topological patterns, even if the binary structure perfectly replicates the observed one; (iii) performs very badly when asked to predict the presence of a link, or the level of the trade flow it carries, whenever the binary structure must be simultaneously estimated.

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  1. 1.

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

  2. 2.

    For example, Abeysinghe and Forbes (2005) show that bilateral trade can only explain a small fraction of the impact that an economic shock originating in a given country can have on another one, which is not among its direct-trade partners. Similarly, Dees and Saint-Guilhem (2011) report that countries that do not trade very much with the US are largely influenced by its dominance over other trade partners linked with the US More generally, (Ward and Ahlquist (2012), p. 2) argue that “as intuition would suggest and recent theoretical advance has formalized, bilateral trade is not independent of the production, consumption, and trading decisions made by firms and consumers in third countries”.

  3. 3.

    See Bhattacharya et al. (2008) and Garlaschelli and Loffredo (2004) for exceptions. See also Squartini et al. (2011a, b) for an alternative approach employing null random models that are able to predict whether observed properties of the ITN are statistically meaningful or simply the result of “constrained” randomness.

  4. 4.

    Defined as the ratio between \(L(t)\) (existing trade partnerships) and \(N(t)\cdot [N(t)-1]\) (all possible trade partnerships).

  5. 5.

    This has led Deardorff (1998) to argue that “just about any plausible model of trade would yield something very like the gravity equation”. See also Evenett and Keller (2002).

  6. 6.

    See Ward and Ahlquist (2012) for an attempt to account for network dependencies in the GM specification.

  7. 7.

    ZINB estimates turn out to be very similar to ZIP ones. No dramatic differences are detected between cross-section and panel-data analyses. Similarly, the introduction of country fixed effects do not alter our results below in any crucial ways. Note also that we employ the same set of regressors in both stages of ZIP and ZINB estimates, as listed in Table 2. Reducing the set of regressors in the first stage does not dramatically change our main results. The whole set of estimation results is available from the authors upon request.

  8. 8.

    Whenever a variable resulted not significant we decided to keep it among the regressors anyway to preserve comparison between estimation techniques.

  9. 9.

    From now on, we suppress time labels for the sake of notational convenience and we refer to a cross-section sequence of estimations.

  10. 10.

    In our simulations, we typically employ samples of 10,000 independent matrix realizations. Our results are robust to different sample sizes.

  11. 11.

    Notice that, in principle, one could have used directly the expected values implied by the fitted model (either PPML or ZIP, see Eqs. 3 and 4) to build a single instance of the predicted ITN and compare its properties with the observed ITN. However, by correctly sampling from the implied distributions, one can have a better idea of the variability of predictions around their expected values.

  12. 12.

    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).

  13. 13.

    In our exercises, we are implicitly assuming that the expected value of any network statistics (given the implied probability distributions of the estimation method employed) can be replaced by the statistic computed on expected values of links and weights, and that expected values of ratios are equal to ratios of expected values. In fact, Squartini et al. (2011a, b) show that such assumptions do not lead to dramatic

    prediction biases, as long as distinct pairs of binary and weighted links are independent, which is indeed the case if we use a well-specified GM.

  14. 14.

    Clustering coefficients are computed without rescaling link weights in the unit interval in order not to bias the analysis with network-dependent rescaling factors (Fagiolo 2007; Saramäki et al. 2007). Therefore, the range of WCC is not within \([0,1]\).

  15. 15.

    Our exercises show that predicted uPPML probabilities for the event that a link is present are all very high and close to unity. Therefore, in the majority of all simulations, the predicted binary structure is close to that of a full graph. Conversely, ITN density ranges from 0.40 to 0.50 (see Table 1), meaning that slightly less than a half of possible trade relationships are present.

  16. 16.

    Among all possible correlations of directed statistics with node in- and out-strength we have selected only those economically more relevant. For example, we have focused on the correlation coefficient between \(ANNS^{out,in}\) and \(NS^{out}\) (and not that between \(ANNS^{out,in}\) and \(NS^{in}\)) because one is much more interested in understanding whether a country that exports more, in turn exports to countries that imports more, rather than knowing whether a country that imports more, in turn exports to countries that imports more.

  17. 17.

    We focus here only on undirected measures. All main results hold also for directed network statistics.

  18. 18.

    KS-tests almost always rejects the null hypothesis that observed and Bernoulli-Logit simulated (total, in and out) degree distributions are the same.


  1. Abbate A, De Benedictis L, Fagiolo G, Tajoli L (2012) The international trade network in space and time. Available at SSRN E-Library

  2. Abeysinghe T, Forbes K (2005) Trade linkages and output-multiplier effects: a structural var approach with a focus on asia. Rev Int Econ 13:356–375

  3. Anderson JE (1979) A theoretical foundation for the gravity equation. Am Econ Rev 69:106–116

  4. Anderson JE, van Wincoop E (2003) Gravity with gravitas: a solution to the border puzzle. Am Econ Rev 93:170–192

  5. Baldwin R, Taglioni D (2006) Gravity for dummies and dummies for gravity equations. NBER working papers 12516. National Bureau of Economic Research, Inc

  6. Barigozzi M, Fagiolo G, Garlaschelli D (2010a) Multinetwork of international trade: a commodity-specific analysis. Phys Rev E 81:046104

  7. Barigozzi M, Fagiolo G, Mangioni G (2010b) Identifying the community structure of the international-trade multi network. Physica A 390:2051–2066

  8. Bergstrand JH (1985) The gravity equation in international trade: some microeconomic foundations and empirical evidence. Rev Econ Stat 67:474–481

  9. Bernard AB, Jensen JB, Redding SJ, Schott PK (2007) Firms in international trade. J Econ Perspect 21:105–130

  10. Bhattacharya K, Mukherjee G, Manna S (2007) The international trade network. In: Chatterjee A, Chakrabarti B (eds) Econophysics of markets and business networks. Springer, Milan

  11. Bhattacharya K, Mukherjee G, Sarämaki J, Kaski K, Manna S (2008) The international trade network: weighted network analysis and modeling. J Stat Mech Theory Exp A 2:P02002

  12. Burger M, Oort Fv, Linders G (2009) On the specification of the gravity model of trade: Zeros, excess zeros and zero-inflated estimation. Research paper ERS-2009-003-ORG revision. Erasmus Research Institute of Management (ERIM)

  13. De Benedictis L, Taglioni D (2011) The gravity model in international trade. In: De Benedictis L, Salvatici L (eds) The trade impact of European Union preferential policies. Springer, Milan

  14. De Benedictis L, Tajoli L (2011) The world trade network. World Econ 34:1417–1454

  15. Deardorff A (1998) Determinants of bilateral trade: Does gravity work in a neoclassical world? In: The regionalization of the world economy. National Bureau of Economic Research, Inc, pp 7–32

  16. Dees S, Saint-Guilhem A (2011) The role of the united states in the global economy and its evolution over time. Empir Econ 41:573–591

  17. Eaton J, Kortum SS, Sotelo S (2012) International trade: linking micro and macro. Working paper 17864. National Bureau of Economic Research

  18. Evenett SJ, Keller W (2002) On theories explaining the success of the gravity equation. J Political Econ 110:281–316

  19. Fagiolo G (2007) Clustering in complex directed networks. Phys Rev E 76:026107

  20. Fagiolo G (2010) The international-trade network: gravity equations and topological properties. J Econ Interact Coord 5:1–25

  21. Fagiolo G, Schiavo S, Reyes J (2008) On the topological properties of the world trade web: a weighted network analysis. Physica A 387:3868–3873

  22. Fagiolo G, Schiavo S, Reyes J (2009) World-trade web: topological properties, dynamics, and evolution. Phys Rev E 79:036115

  23. Fagiolo G, Schiavo S, Reyes J (2010) The evolution of the world trade web: a weighted-network approach. J Evol Econ 20:479–514

  24. Felbermayr GJ, Kohler W (2006) Exploring the intensive and extensive margins of world trade. Rev World Econ (Weltwirtschaftliches Archiv) 142:642–674

  25. Forbes K (2002) Are trade linkages important determinants of country vulnerability to crises? In: Sebastian E, Jeffrey F (eds) Preventing currency crises in emerging markets. University of Chicago Press, Chicago

  26. Fratianni M (2009) The gravity model in international trade. In: Rugman AM (ed) The Oxford handbook of international business. Oxford University Press, Oxford

  27. Galvandatilde AB, Artis M, Marcellino M (2007) The transmission mechanism in a changing world. J Appl Econ 22:39–61

  28. Garlaschelli D, Di Matteo T, Aste T, Caldarelli G, Loffredo M (2007) Interplay between topology and dynamics in the world trade web. Eur Phys J B 57:1434–6028

  29. Garlaschelli D, Loffredo M (2004) Fitness-dependent topological properties of the world trade web. Phys Rev Lett 93:188701

  30. Garlaschelli D, Loffredo M (2005) Structure and evolution of the world trade network. Physica A 355:138–144

  31. Glick R, Rose AK (2001) Does a currency union affect trade? the time series evidence. NBER working papers 8396. National Bureau of Economic Research, Inc

  32. Helliwell JF, Padmore T (1985) Empirical studies of macroeconomic interdependence. In: Jones R, Kenen P (eds) Handbook of international economies. Elsevier Science Publishers B.V, Amsterdam

  33. Kali R, Mendez F, Reyes J (2007) Trade structure and economic growth. J Int Trade Econ Dev 16:245–269

  34. Kali R, Reyes J (2010) Financial contagion on the international trade network. Econ Inq 48:1072–1101

  35. Krugman P (1995) Growing world trade: causes and consequences. Brookings papers on economic activity 26:327–377

  36. Li X, Jin YY, Chen G (2003) Complexity and synchronization of the world trade web. Physica A Stat Mech Appl 328:287–296

  37. Linders G-JM, de Groot HL (2006) Estimation of the gravity equation in the presence of zero flows. Tinbergen Institute discussion papers 06–072/3. Tinbergen Institute

  38. Long J (1997) Regression models for categorical and limited dependent variables. Advanced quantitative techniques in the social sciences. Sage Publications, London

  39. Melitz MJ (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71:1695–1725

  40. Pöyhönen P (1963) A tentative model for the volume of trade between countries. Weltwirtschaftliches Archiv 90:93–99

  41. Reyes J, Schiavo S, Fagiolo G (2008) Assessing the evolution of international economic integration using random-walk betweenness centrality: the cases of East Asia and Latin America. Adv Complex Syst 11:685–702

  42. Reyes J, Schiavo S, Fagiolo G (2010) Using complex networks analysis to assess the evolution of international economic integration: the cases of East Asia and Latin America. J Int Trade Econ Dev 19:215–239

  43. Riccaboni M, Schiavo S (2010) Structure and growth of weighted networks. New J Phys 12:023003

  44. Rose AK, Spiegel MM (2002) A gravity model of sovereign lending: trade, default and credit. Working papers in applied economic theory 2002–09. Federal Reserve Bank of San Francisco

  45. Santos Silva JMC, Tenreyro S (2006) The log of gravity. Rev Econ Stat 88:641–658

  46. Saramäki J, Kivelä M, Onnela J-P, Kaski K, Kertész J (2007) Generalizations of the clustering coefficient to weighted complex networks. Phys Rev E 75:027105

  47. Serrano A (2003) Topology of the world trade web. Phys Rev E 68:015101(R)

  48. Serrano A, Boguñá M, Vespignani A (2007) Patterns of dominant flows in the world trade web. J Econ Interact Coord 2:111–124

  49. Snijders TAB (2005) Models for longitudinal network data. In: Carrington P, Scott J, Wasserman S (eds) Models and methods in social network analysis. Cambridge University Press, Cambridge, pp 215–247

  50. Squartini T, Fagiolo G, Garlaschelli D (2011a) Randomizing world trade. I. A binary network analysis. Phys Rev E 84:046117

  51. Squartini T, Fagiolo G, Garlaschelli D (2011) Randomizing world trade. II. A weighted network analysis. Phys Rev E 84:046118

  52. Squartini T, Fagiolo G, Garlaschelli D (2012) Null models of economic networks: the case of the world trade web. J Econ Interact Coord (forthcoming)

  53. Subramanian A, Wei S-J (2003) The wto promotes trade, strongly but unevenly. Working paper 10024. National Bureau of Economic Research

  54. Tinbergen J (1962) Shaping the world economy: suggestions for an international economic policy. New York

  55. van Bergeijk P, Brakman S (eds) (2010) The gravity model in international trade. Cambridge University Press, Cambridge

  56. Ward MD, Ahlquist JS (2012) Gravity’s rainbow: modeling the world trade network. Working paper. APSA 2011 annual meeting paper

  57. Winkelmann R (2008) Econometric analysis of count data. Springer, New York

  58. Wooldridge JM (2001) Econometric analysis of cross section and panel data. The MIT Press, Boston

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The Authors gratefully acknowledge financial support received by the research project “The international trade network: empirical analyses and theoretical models” ( funded by the Italian Ministry of Education, University and Research (Scientific Research Programs of National Relevance 2009).

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Correspondence to Marco Dueñas.

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Dueñas, M., Fagiolo, G. Modeling the International-Trade Network: a gravity approach. J Econ Interact Coord 8, 155–178 (2013).

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  • International Trade Network
  • Gravity equation
  • Weighted network analysis
  • Topological properties
  • Econophysics

JEL Classification

  • F10
  • D85