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Application of gravity models with a fixed component in the international trade flows of coal, iron ore and crude oil

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Maritime Economics & Logistics Aims and scope


As freight transport flows grow continuously, developing better quantitative models for forecasting future trade flows becomes more important. Trade flows can be estimated by discrete choice theory, leading to gravity models formulations. At a given point in time, trade flows may also be affected by long-term contracts or simply trading habits. This leads to situations where only a fraction of the market is subject to choice. In this article, we extend the traditional gravity model such that a fixed amount is separated from observed trade flows and only residuals are subject to discrete choice. We apply our model on coal, iron ore and oil seaborne trade flows and demonstrate that the proposed construction results in a significantly better fit for the observed data. This observation is important in predicting future trade volumes.

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  1. We have kept the scale as it is reported in Fearnleys Review (in thousand tonnes) although in Andersson et al (2009), the data was converted to million tonnes.


  • Akaike, H. (1998) Information theory and an extension of the maximum likelihood principle. In: E. Parzen, K. Tanabe and G. Kitagawa (eds.) Selected Papers of Hirotugu Akaike. New York: Springer Series in Statistics, pp. 199–213.

    Chapter  Google Scholar 

  • Andersson, J., Jornsten, K., Strandenes, S.P. and Uboe, J. (2009) Modeling freight markets for coal. Maritime Economics and Logistics 11(3): 289–301.

    Article  Google Scholar 

  • Andersson, M. (2007) Disentangling trade flows: Firms, geography and technology. PhD dissertation, No. 36, Jönköping International Business School, Jönköping University, Jönköping, Sweden.

  • Carbone, R. and Armstrong, J.S. (1982) Evaluation of extrapolative forecasting methods: Results of a survey of academicians and practitioners. Journal of Forecasting 1(2): 215–217.

    Article  Google Scholar 

  • Erlander, S. and Stewart, N.F. (1990) The Gravity Model in Transportation Analysis: Theory and Extensions. Utrecht, The Netherlands: VSP.

    Google Scholar 

  • Isard, W. (1960) Methods of Regional Analysis: An Introduction to Regional Science. Cambridge, MA: MIT Press.

    Google Scholar 

  • Knudsen, D.C. and Fotheringham, A.S. (1986) Matrix comparison, goodness-of-fit, and spatial interaction modeling. International Regional Science Review 10(2): 127–147.

    Article  Google Scholar 

  • Leontief, W. and Strout, A. (1963) Multiregional input-output analysis. In: T. Barna (ed.) Structural Interdependence and Economic Development. London: Palgrave Macmillan.

    Google Scholar 

  • Linneman, H. (1966) An Econometric Study of International Trade Flows. Amsterdam, The Netherlands: North Holland.

    Google Scholar 

  • McFadden, D. (1978) Modelling the Choice of Residential Location. In: A. Karlqvist, L. Lundqvist, F. Snickars and J. Weibull (eds.) Spatial Interaction Theory and Planning Models. Amsterdam, The Netherlands: North Holland.

    Google Scholar 

  • Pöyhönen, P. (1963) A tentative model for the volume of trade between countries. Weltwirtschaftliches Archiv: 93–100.

  • Sen, A. and Smith, T.E. (1995) Gravity Models of Spatial Interaction Behavior. Berlin, Germany: Springer-Verlag.

    Book  Google Scholar 

  • Tinbergen, J. (1962) Shaping the World Economy: Suggestions for an International Economic Policy. New York: The 20th Century Fund.

    Google Scholar 

  • Viertel, M. (2013) Determining fixed components in seaborne coal trade, Master thesis, Norwegian School of Economics, Bergen, Norway.

  • Wilson, A.G. (1970) Entropy in Urban and Regional Modelling. London, UK: Pion.

    Google Scholar 

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The authors wish to thank the two anonymous reviewers, whose comments helped them to improve the article.

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Correspondence to Sahar Babri.

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Babri, S., Jørnsten, K. & Viertel, M. Application of gravity models with a fixed component in the international trade flows of coal, iron ore and crude oil. Marit Econ Logist 19, 334–351 (2017).

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