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Spatial regression-based model specifications for exogenous and endogenous spatial interaction

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  • Manfred M Fischer
  • James P. LeSage

Abstract

Spatial interaction models represent a class of models that are used for modelling origin-destination flow data. The focus of this paper is on the log-normal version of the model. In this context, we consider spatial econometric specifications that can be used to accommodate two types of dependence scenarios, one involving endogenous interaction and the other exogenous interaction. These model specifications replace the conventional assumption of independence between origin-destination flows with formal approaches that allow for two different types of spatial dependence in magnitudes. Endogenous interaction reflects situations where there is a reaction to feedback regarding flow magnitudes from regions neighbouring origin and destination regions. This type of interaction can be modelled using specifications proposed by LeSage and Pace (2008) who use spatial lags of the dependent variable to quantify the magnitude and extent of the feedback effects, hence the term endogenous interaction. Exogenous interaction represents a situation where spillovers arise from nearby (or perhaps even distant) regions, and these need to be taken into account when modelling observed variations in flows across the network of regions. In contrast to endogenous interaction, these contextual effects do not generate reactions to the spillovers, leading to a model specification that can be interpreted without considering changes in the long-run equilibrium state of the system of flows. As in the case of social networks, contextual effects are modelled using spatial lags of the explanatory variables that represent characteristics of neighbouring (or more generally connected) regions, but not spatial lags of the dependent variable, hence the term exogenous interaction. In addition to setting forth expressions for the true partial derivatives of non-spatial and endogenous spatial interaction models and associated scalar summary measures from Thomas-Agnan and LeSage (2014), we propose new scalar summary measures for the exogenous spatial interaction specification introduced here. An illustration applies the exogenous spatial interaction model to a flow matrix of teacher movements between 67 school districts in the state of Florida.

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  • Manfred M Fischer & James P. LeSage, 2014. "Spatial regression-based model specifications for exogenous and endogenous spatial interaction," ERSA conference papers ersa14p716, European Regional Science Association.
    • Handle: RePEc:wiw:wiwrsa:ersa14p716
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    References listed on IDEAS

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    5. Manfred M. Fischer & Jinfeng Wang, 2011. "Spatial Data Analysis," SpringerBriefs in Regional Science, Springer, number 978-3-642-21720-3, April.
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    13. Manfred M. Fischer & Peter Nijkamp (ed.), 2014. "Handbook of Regional Science," Springer Books, Springer, edition 127, number 978-3-642-23430-9, June.
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    Cited by:

    1. Sardadvar, Sascha & Vakulenko, Elena, 2020. "Estimating and interpreting internal migration flows in Russia by accounting for network effects," Socio-Economic Planning Sciences, Elsevier, vol. 69(C).
    2. Rodolfo Metulini & Paolo Sgrignoli & Stefano Schiavo & Massimo Riccaboni, 2018. "The network of migrants and international trade," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 35(3), pages 763-787, December.
    3. Thomas-Agnan, Christine & Margaretic, Paula & Laurent, Thibault, 2022. "Generalizing impact computations for the autoregressive spatial interaction model," TSE Working Papers 22-1357, Toulouse School of Economics (TSE), revised Feb 2023.
    4. James Paul LeSage & Manfred M. Fischer, 2020. "Cross-sectional dependence model specifications in a static trade panel data setting," Journal of Geographical Systems, Springer, vol. 22(1), pages 5-46, January.
    5. Morton, Craig & Mattioli, Giulio, 2023. "Competition in Multi-Airport Regions: Measuring airport catchments through spatial interaction models," Journal of Air Transport Management, Elsevier, vol. 112(C).
    6. Manfred M. Fischer & James P. LeSage, 2020. "Network dependence in multi-indexed data on international trade flows," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-26, December.
    7. Laurent, Thibault & Margaretic, Paula & Thomas-Agnan, Christine, 2021. "Do neighboring countries matter when explaining bilateral remittances?," TSE Working Papers 21-1221, Toulouse School of Economics (TSE).
    8. Yufei Lin & Yingxia Pu & Xinyi Zhao & Guangqing Chi & Cui Ye, 2023. "The Spatiotemporal Elasticity of Age Structure in China’s Interprovincial Migration System," Sustainability, MDPI, vol. 15(10), pages 1-18, May.
    9. Rodolfo Metulini & Roberto Patuelli & Daniel A. Griffith, 2018. "A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade," Econometrics, MDPI, vol. 6(1), pages 1-15, February.
    10. Oshan, Taylor M., 2020. "The spatial structure debate in spatial interaction modeling: 50 years on," OSF Preprints 42vxn, Center for Open Science.
    11. Fischer, Manfred M. & LeSage, James P., 2018. "The role of socio-cultural factors in static trade panel models," Working Papers in Regional Science 2018/04, WU Vienna University of Economics and Business.
    12. Martina Neuländtner & Thomas Scherngell, 2020. "Geographical or relational: What drives technology-specific R&D collaboration networks?," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 65(3), pages 743-773, December.
    13. Yingxia Pu & Xinyi Zhao & Guangqing Chi & Jin Zhao & Fanhua Kong, 2019. "A spatial dynamic panel approach to modelling the space-time dynamics of interprovincial migration flows in China," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 41(31), pages 913-948.
    14. Moura, Ticiana Grecco Zanon & Chen, Zhangliang & Garcia-Alonso, Lorena, 2019. "Spatial interaction effects on inland distribution of maritime flows," Transportation Research Part A: Policy and Practice, Elsevier, vol. 128(C), pages 1-10.

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