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On the Equilibrium Properties of Network Models with Heterogeneous Agents

Author

Listed:
  • Treb Allen
  • Costas Arkolakis
  • Xiangliang Li

Abstract

We consider a broad class of spatial models where there are many types of interactions across a large number of locations. We provide a new theorem that offers an iterative algorithm for calculating an equilibrium and sufficient and “globally necessary” conditions under which the equilibrium is unique. We show how this theorem enables the characterization of equilibrium properties for two important spatial systems: an urban model with spillovers across a large number of different types of agents and a dynamic migration model with forward looking agents. An Online Appendix provides eleven additional examples of both spatial and non-spatial economic frameworks for which our theorem provides new equilibrium characterizations.

Suggested Citation

  • Treb Allen & Costas Arkolakis & Xiangliang Li, 2020. "On the Equilibrium Properties of Network Models with Heterogeneous Agents," NBER Working Papers 27837, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:27837
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    Cited by:

    1. Bruno Conte & Klaus Desmet & Dávid Krisztián Nagy & Esteban Rossi-Hansberg, 2021. "Local sectoral specialization in a warming world," Journal of Economic Geography, Oxford University Press, vol. 21(4), pages 493-530.
    2. Xavier Giroud & Simone Lenzu & Quinn Maingi & Holger Mueller, 2021. "Propagation and Amplification of Local Productivity Spillovers," NBER Working Papers 29084, National Bureau of Economic Research, Inc.
    3. Benny Kleinman & Ernest Liu & Stephen J. Redding, 2023. "Dynamic Spatial General Equilibrium," Econometrica, Econometric Society, vol. 91(2), pages 385-424, March.
    4. Costas Arkolakis & Federico Huneeus & Yuhei Miyauchi, 2023. "Spatial Production Networks," Working Papers Central Bank of Chile 971, Central Bank of Chile.
    5. Luke Heath Milsom, 2023. "Moving OpportunityLocal Connectivity and Spatial Inequality," CEPREMAP Working Papers (Docweb) 2303, CEPREMAP.
    6. Ishan Nath, 2021. "Climate Change, The Food Problem, and the Challenge of Adaptation through Sectoral Reallocation," Working Papers 21-29, Center for Economic Studies, U.S. Census Bureau.
    7. Stephan Heblich & David Krisztián Nagy & Alex Trew & Yanos Zylberberg, 2023. "The death and life of great British cities," Economics Working Papers 1867, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Piyush Panigrahi, 2021. "Endogenous Spatial Production Networks: Quantitative Implications for Trade and Productivity," CESifo Working Paper Series 9466, CESifo.
    9. Nagy, Dávid Krisztián, 2022. "Quantitative economic geography meets history: Questions, answers and challenges," Regional Science and Urban Economics, Elsevier, vol. 94(C).
    10. Jonathan I. Dingel & Felix Tintelnot, 2020. "Spatial Economics for Granular Settings," NBER Working Papers 27287, National Bureau of Economic Research, Inc.
    11. Kokovin, Sergey & Molchanov, Pavel & Bykadorov, Igor, 2022. "Increasing returns, monopolistic competition, and international trade: Revisiting gains from trade," Journal of International Economics, Elsevier, vol. 137(C).
    12. Krebs, Oliver & Pflüger, Michael P., 2019. "On the Road (Again): Commuting and Local Employment Elasticities in Germany," IZA Discussion Papers 12257, Institute of Labor Economics (IZA).
    13. David Krisztián Nagy, 2020. "Quantitative economic geography meets history: Questions, answers and challenges," Economics Working Papers 1774, Department of Economics and Business, Universitat Pompeu Fabra, revised Mar 2021.
    14. Parkhomenko, Andrii & Delventhal, Matthew J, 2023. "Spatial Implications of Telecommuting in the United States," Institute of Transportation Studies, Working Paper Series qt97q6c2rg, Institute of Transportation Studies, UC Davis.
    15. Allen, Treb & Donaldson, Dave, 2022. "Persistence and path dependence: A primer," Regional Science and Urban Economics, Elsevier, vol. 94(C).
    16. Dávid Krisztián Nagy, 2021. "Quantitative Economic Geography Meets History: Questions, Answers and Challenges," Working Papers 1249, Barcelona School of Economics.
    17. Nath, Ishan, 2022. "Climate Change, The Food Problem, and the Challenge of Adaptation through Sectoral Reallocation," Conference papers 333404, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    18. Krebs, Oliver & Pflüger, Michael, 2023. "On the road (again): Commuting and local employment elasticities in Germany," Regional Science and Urban Economics, Elsevier, vol. 99(C).
    19. Piyush Panigrahi, 2021. "Endogenous Spatial Production Networks: Quantitative Implications for Trade & Productivity," Cowles Foundation Discussion Papers 2314, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • F4 - International Economics - - Macroeconomic Aspects of International Trade and Finance
    • O18 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Urban, Rural, Regional, and Transportation Analysis; Housing; Infrastructure
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies

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