How do local housing markets interact across space and time? To answer this question, this paper develops a tractable dynamic spatial equilibrium model with continuous space and time and computable transition dynamics. Our model features fixed housing developers that build housing subject to adjustment costs, and interact in a spatial equilibrium generated by freely mobile households. The spatial equilibrium is key, because it reduces the dimensionality of the problem: rather than solving for the price at every location at every instant (an N x T dimensional problem), we only need to solve for the common household utility at each instant (a T dimensional problem). We show numerically that following a demand shock, housing adjustment paths may be nonmonotonic, as short-run demand increases may induce some developers to overshoot their long-run housing supply. In ongoing work, we apply our model to study how zoning restrictions affect the dynamics following local housing demand shocks in San Francisco. We infer de facto zoning restrictions using bunching in the building height distribution over different zoning classifications, and use our estimates of latent zoning parameters to quantify the model.

Quantifying and projecting climate migration is a critical challenge for policymakers and researchers. While causal inference, agent-based, gravity, and general equilibrium models have been employed to estimate the climate-migration relationship, their results often diverge, and they are typically used in isolation and at different spatio-temporal scales. This paper aims to bridge this gap by introducing a unified conceptual framework, designed to rigorously compare and evaluate the assumptions and outputs of these diverse models at a common scale. We illustrate our comparison using an empirically relevant case study: estimating and projecting the relationship between annual average temperature and internal state-to-state migration in the United States. We show that model results can coincide under certain conditions and illustrate mechanisms through which they can diverge. We conclude by combining insights from each approach, with the aim of improving the quantitative modelling of the climate migration relationship and facilitating future interdisciplinary collaboration.

Uncertainty regarding the rise in global temperatures increases the expected welfare cost of climate change if the welfare function is convex in temperature. We focus on how the geography of the climate shock interacts with geographic adaptation forces (trade and migration) to determine the shape of welfare response to climate change. We demonstrate theoretically that adaptation forces dampen convexity in damage functions, but the strength of these adaptation forces depends on the spatial distribution of the climate shock. Integrating over different climate scenarios, uncertainty amplifies the welfare loss from climate change. The geography of welfare loss, incorporating climate uncertainty, concentrates previously unaccounted for excess losses in the developing world, alongside the United States and some regions in Europe. These excess damages are highly spatially correlated, because adaptation forces through trade and migration display a strong gravity relationship in the data.

Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically show for the case of a symmetric cycle graph that an elementary bifurcation analysis provides insight into the phenomena of clustering. Moreover, for the case of a cycle graph with a hub, we discuss how having a sufficient proportion of zealots in the hub leads to the entire network sharing the opinion of the zealots. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.