IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v132y2022icp133-165.html
   My bibliography  Save this article

A dynamic theory of spatial externalities

Author

Listed:
  • Boucekkine, Raouf
  • Fabbri, Giorgio
  • Federico, Salvatore
  • Gozzi, Fausto

Abstract

We characterize the shape of spatial externalities in a continuous time and space differential game with transboundary pollution. We posit a realistic spatiotemporal law of motion for pollution (diffusion and advection), and tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. We allow for a rich set of geographic heterogeneities across states. We solve analytically the induced non-cooperative differential game and characterize its long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the affine feedbacks. We further provide with a full exploration of the free riding problem and the associated border effect.

Suggested Citation

  • Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:133-165
    DOI: 10.1016/j.geb.2021.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825621001639
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2021.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    3. Duvivier, Chloé & Xiong, Hang, 2013. "Transboundary pollution in China: a study of polluting firms' location choices in Hebei province," Environment and Development Economics, Cambridge University Press, vol. 18(4), pages 459-483, August.
    4. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2018. "Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case," Working Papers halshs-01792440, HAL.
    5. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    6. Molly Lipscomb & Ahmed Mushfiq Mobarak, 2017. "Decentralization and Pollution Spillovers: Evidence from the Re-drawing of County Borders in Brazil," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(1), pages 464-502.
    7. Fernando Alvarez & David Argente, 2020. "A Simple Planning Problem for COVID-19 Lockdown," Working Papers 2020-34, Becker Friedman Institute for Research In Economics.
    8. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial effects and strategic behavior in a multiregional transboundary pollution dynamic game," Journal of Environmental Economics and Management, Elsevier, vol. 97(C), pages 182-207.
    9. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    10. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    11. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    12. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    13. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    14. Silva, Emilson C. D. & Caplan, Arthur J., 1997. "Transboundary Pollution Control in Federal Systems," Journal of Environmental Economics and Management, Elsevier, vol. 34(2), pages 173-186, October.
    15. James E. Monogan & David M. Konisky & Neal D. Woods, 2017. "Gone with the Wind: Federalism and the Strategic Location of Air Polluters," American Journal of Political Science, John Wiley & Sons, vol. 61(2), pages 257-270, April.
    16. Volker Beckmann & Justus Wesseler, 2007. "Spatial Dimension of Externalities and the Coase Theorem: Implications for Co-existence of Transgenic Crops," Springer Books, in: Wim Heijman (ed.), Regional Externalities, chapter 11, pages 223-242, Springer.
    17. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    18. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Hutchinson, Emma & Kennedy, Peter W., 2008. "State enforcement of federal standards: Implications for interstate pollution," Resource and Energy Economics, Elsevier, vol. 30(3), pages 316-344, August.
    20. Helland, Eric & Whitford, Andrew B., 2003. "Pollution incidence and political jurisdiction: evidence from the TRI," Journal of Environmental Economics and Management, Elsevier, vol. 46(3), pages 403-424, November.
    21. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    22. Sigman, Hilary, 2005. "Transboundary spillovers and decentralization of environmental policies," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 82-101, July.
    23. Hilary Sigman, 2002. "International Spillovers and Water Quality in Rivers: Do Countries Free Ride?," American Economic Review, American Economic Association, vol. 92(4), pages 1152-1159, September.
    24. Matthew E. Kahn & Pei Li & Daxuan Zhao, 2015. "Water Pollution Progress at Borders: The Role of Changes in China's Political Promotion Incentives," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 223-242, November.
    25. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    26. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    27. Raouf Boucekkine & Jacek Krawczyk & Thomas Vallée, 2011. "Environmental quality versus economic performance: A dynamic game approach," Post-Print hal-03193660, HAL.
    28. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    29. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    30. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    31. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    32. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    33. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    34. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    35. repec:oup:restud:v:84:y::i:1:p:464-502. is not listed on IDEAS
    36. Carmen Camacho & Agustin Perez Barahona, 2015. "Land Use Dynamics and the Environment," Post-Print hal-01161661, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boucekkine, Raouf & Ruan, Weihua & Zou, Benteng, 2023. "The irreversible pollution game," Journal of Environmental Economics and Management, Elsevier, vol. 120(C).
    2. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. Jacek Rothert, 2021. "Optimal federal transfers during uncoordinated response to a pandemic," GRAPE Working Papers 58, GRAPE Group for Research in Applied Economics.
    4. Jacek Rothert, 2022. "Optimal federal transfers during uncoordinated response to a pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1124-1153, October.
    5. Rabah Amir & Raouf Boucekkine, 2022. "Introduction to the special issue on new insights into economic epidemiology: Theory and policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 861-872, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "A dynamic theory of spatial externalities," Working Papers halshs-02613177, HAL.
    2. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    4. Boucekkine, Raouf & Ruan, Weihua & Zou, Benteng, 2023. "The irreversible pollution game," Journal of Environmental Economics and Management, Elsevier, vol. 120(C).
    5. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    6. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "A Spatiotemporal Framework for the Analytical Study of Optimal Growth Under Transboundary Pollution," Department of Economics University of Siena 813, Department of Economics, University of Siena.
    7. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.
    8. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    9. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    10. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
    11. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    12. Boucekkine, R. & Fabbri, G. & Federico, S. & Gozzi, F., 2020. "Control theory in infinite dimension for the optimal location of economic activity: The role of social welfare function," Working Papers 2020-02, Grenoble Applied Economics Laboratory (GAEL).
    13. Pan, Dan & Chen, Huan, 2021. "Border pollution reduction in China: The role of livestock environmental regulations," China Economic Review, Elsevier, vol. 69(C).
    14. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    15. Zhonghao Zhang & Tiantian Nie & Yingtao Wu & Jiahui Ling & Danhuang Huang, 2022. "The Temporal and Spatial Distributions and Influencing Factors of Transboundary Pollution in China," IJERPH, MDPI, vol. 19(8), pages 1-15, April.
    16. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    17. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    18. James E. Monogan & David M. Konisky & Neal D. Woods, 2017. "Gone with the Wind: Federalism and the Strategic Location of Air Polluters," American Journal of Political Science, John Wiley & Sons, vol. 61(2), pages 257-270, April.
    19. Alessandro Calvia & Fausto Gozzi & Marta Leocata & Georgios I. Papayiannis & Anastasios Xepapadeas & Athanasios N. Yannacopoulos, 2023. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Papers 2304.11568, arXiv.org.
    20. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.

    More about this item

    Keywords

    Spatial externalities; Spatial diffusion; Differential games in continuous time and space; Infinite dimensional optimal control problems; Environmental federalism;
    All these keywords.

    JEL classification:

    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:133-165. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.