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Gravitational Analysis in Regional Science and Spatial Economics: A Vector Gradient Approach to Trade


  • Peter Nijkamp
  • Waldemar Ratajczak


For decades, gravitational analysis has been a key instrument in analyzing spatial flows. Time and again, it has prompted new and challenging research questions. This paper provides a concise overview of the foundation, the conceptualization and empirical relevance of gravitational principles in regional science and spatial economics. Attention is also given to general “social physics†interpretations of gravity in spatial interaction models and to the impact of intangible distance frictions. The main emphasis in the study is placed on the significance of spatial impedance functions and gravity potential analysis. In particular, the paper focuses on cross-border trade and has three main goals: (i) to address the robustness of distance friction parameters related to trade borders, employing, inter alia, quantitative results from meta-analyses on trade models in spatial economics; (ii) to present a promising methodology based on gravity potential and the related gravitational gradient models that include directional intensities of flows; (iii) to test the validity of the latter approach on the basis of a vector gradient analysis of export patterns of the Netherlands. The paper argues that—despite the space-reducing impact of the modern digital technologies—gravitational principles still have an uncontested relevance in an analysis of spatial flows in regional science.

Suggested Citation

  • Peter Nijkamp & Waldemar Ratajczak, 2021. "Gravitational Analysis in Regional Science and Spatial Economics: A Vector Gradient Approach to Trade," International Regional Science Review, , vol. 44(3-4), pages 400-431, May.
  • Handle: RePEc:sae:inrsre:v:44:y:2021:i:3-4:p:400-431
    DOI: 10.1177/0160017620980519

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    2. L. V. Melnikova, 2022. "Efficiency and Equality: Twenty Years of Discussion on Spatial Development," Regional Research of Russia, Springer, vol. 12(4), pages 439-450, December.
    3. Mikrajuddin Abdullah, 2023. "A New Approach to Overcoming Zero Trade in Gravity Models to Avoid Indefinite Values in Linear Logarithmic Equations and Parameter Verification Using Machine Learning," Papers 2308.06303,
    4. Luigi Capoani, 2023. "Theory of Commercial Gravitational Fields in Economics: The Case of Europe," Networks and Spatial Economics, Springer, vol. 23(4), pages 845-884, December.
    5. Šveda, Martin & Madajová, Michala Sládeková, 2023. "Estimating distance decay of intra-urban trips using mobile phone data: The case of Bratislava, Slovakia," Journal of Transport Geography, Elsevier, vol. 107(C).
    6. Peng Peng & Jessie P. H. Poon & Xiaowei Xie, 2024. "COVID-19 Medical Trade: Multilayer Network Analysis and Network Determinants," Networks and Spatial Economics, Springer, vol. 24(1), pages 27-48, March.
    7. Héctor Romero-Ramírez, 2023. "The trade dependence of Mexico and Canada towards the USA: An input-output approach (1965-1990)/La dependencia comercial de México y Canadá hacia los Estados Unidos: un enfoque de insumo-producto," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 38(2), pages 293-316.
    8. Mikrajuddin Abdullah, 2024. "Theoretical Foundation for the Pareto Distribution of International Trade Strength and Introduction of an Equation for International Trade Forecasting," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 52(1), pages 17-29, March.

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