Working Paper: NBER ID: w27837
Authors: 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.
Keywords: Spatial Models; Equilibrium; Heterogeneous Agents; Elasticity; Urban Economics
JEL Codes: C6; D85; E23; F4; O18; R13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| spectral radius of the elasticity matrix (C49) | unique equilibrium exists (C62) |
| spectral radius of the elasticity matrix (C49) | at most one equilibrium exists (C62) |
| spectral radius of the elasticity matrix (C49) | multiple equilibria assured (D50) |