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  3. American Economic Review: Insights
  4. December 2024
  5. On the Equilibrium Properties of Spatial Models

American Economic Review: Insights

ISSN 2640-205X (Print) | ISSN 2640-2068 (Online)

On the Equilibrium Properties of Spatial Models

  • Treb Allen
  • Costas Arkolakis
  • Xiangliang Li
American Economic Review: Insights
vol. 6, no. 4, December 2024
(pp. 472–89)
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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 one important spatial system: an urban model with spillovers across a large number of different types of agents. An online appendix provides 12 additional examples of both spatial and nonspatial economic frameworks for which our theorem provides new equilibrium characterizations.

Citation

Allen, Treb, Costas Arkolakis, and Xiangliang Li. 2024. "On the Equilibrium Properties of Spatial Models." American Economic Review: Insights, 6 (4): 472–89. DOI: 10.1257/aeri.20230495

Additional Materials

JEL Classification

  • C21 Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
  • R15 General Regional Economics: Econometric and Input-Output Models; Other Models
  • R23 Urban, Rural, Regional, Real Estate, and Transportation Economics: Regional Migration; Regional Labor Markets; Population; Neighborhood Characteristics