Spatial Interaction Models: A Broad Historical Perspective

  • Johannes BröckerEmail author
Living reference work entry


More than a century ago the Austrian railway engineer Eduard Lill stated for the first time an empirical regularity in mathematical form that today is known as the gravity model of spatial interaction. This chapter reviews five, partly overlapping, waves of literature aiming at a theoretical underpinning of the most simple and of more sophisticated forms of the gravity equation: (1) the Social Physics analogy, (2) the maximum entropy approach, (3) the maximum (deterministic) utility model, (4) the random choice model, and (5) the microeconomic general equilibrium model. The chapter shows that, from different angles, isomorphic formal structures have emerged from the different schools of thought, though recent trade research applying gravity models as its work horse is not fully aware of this isomorphism. The chapter furthermore emphasizes that theoretical progress did not only deliver a theoretical underpinning of what empiricists did anyway, but contributed to progress in two more ways: it transformed the simple model treating individual origin-destination flows in isolation to a system model accounting for the general interdependence of flows between all origins and all destinations, and it allowed to extend the field of applications from measurement and analysis to policy evaluation.


Gravity model Spatial interaction Maximum entropy Random choice Trade model Social physics General equilibrium Consumer’s surplus 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Faculty of Business, Economics and Social Sciences, Institute for Environmental, Resource and Regional EconomicsCAU Kiel UniversityKielGermany

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