Estimating the turning points of nonlinear response functions is central to empirical economics and beyond. We show that the standard turning point estimator suffers from the same pathologies as weak-instrument IV: it is a ratio estimator with a fat-tailed sampling distribution and severe median bias. Standard inference can be misleading, and point estimates are drawn toward the regressor mean. We develop robust sign-restricted confidence sets and shrinkage estimators that pool information across units to stabilise inference. In temperature-GDP and temperature-mortality applications, standard confidence intervals understate uncertainty, and patterns interpreted as climate adaptation are spurious and reflect a statistical artifact.

To combat global warming, climate policies like carbon taxes, renewable subsidies, and carbon tariffs must be implemented to phase out fossil fuel consumption and lower emissions. Who are the winners and losers of such policies? Through a simple Integrated Assessment Model with heterogeneous countries and international trade in goods and energy, we study both the costs of implementing these policies unilaterally, and the local costs and global gains of international policy cooperation. To do so, we express and decompose welfare changes under different policy regimes to the first order as a function of sufficient statistics that depend on observables and identifiable elasticities like nations' energy mix, energy rents, trade shares, energy supply and demand elasticities, and damage parameters. We show that climate change has non-trivial reallocation effects through international trade in goods and energy. Pursuing unilateral policies generates strong leakage effects, primarily through energy trade. Global climate policy cooperation mitigates leakage, but not all countries have an incentive to participate. Regional climate clubs operate differently: an EU-wide club reduces global emissions but creates internal winners and losers, while an ASEAN climate club achieves smaller global gains but delivers welfare increases for member nations.

One rationale for place-based policy is that local development produces positive productivity spillovers. We examine the employment spillovers from a large local development project: opening a casino. Comparing employment in neighborhoods that won a casino license to runner-up neighborhoods that narrowly lost, we find that casinos create jobs in their immediate vicinity. However, we estimate net job losses overall when considering the broader neighborhood. Employment gains concentrate in the leisure and hospitality industry, suggesting spillovers are industry-specific or are driven by demand-side forces like trip-chaining. We develop theory to show that our estimates imply a rapid spatial decay of productivity spillovers.

Cities are engines of economic development, but the world economy's ability to reap the benefits of urbanization is limited by the costs of urban scale. Urban costs depend on commuting costs and the city's capacity to expand up and out. These three dimensions of cities' urban costs combine to form a city's urban cost elasticity, which measures how urban costs scale with population size. Using a structural model and geospatial data on over 10,000 cities, I measure urban costs globally. Cities in developing countries grow by building out, rather than up, even though residents face higher transportation costs. Compared to cities in the developed world, developing nations' cities have urban cost elasticities that are 35% higher. Embedding my estimates of urban costs in a quantitative spatial model featuring a system of cities and rural-to-urban migration, I find that high urban costs have large implications. Lowering urban cost elasticities to the average level observed in the United States would raise welfare in developing nations by 66%, six times the gains in the rich world. One third of the gains in the developing world are driven by general equilibrium responses, as workers both move out of agriculture and reallocate to more productive cities. To examine how policy might achieve these gains, I focus on urban road paving, which I find to be a cost-effective way to reduce urban costs in developing economies. Additionally, high urban costs not only affect economic development, but also hinder the efficacy of urbanization as a climate change adaptation strategy.

We document that women's earnings are closer to parity with men's in larger cities in the United States. This female-specific city-size earnings premium is nearly 50% larger than men's city-size premium, is driven by non-college-educated women, and cannot be explained by occupational sorting, commuting, or differences in labor supply. We develop a quantitative spatial model with local frictional marriage markets to explain why large gender-specific earnings differentials can coexist with balanced gender ratios in spatial equilibrium: the marriage market acts as an endogenous amenity, generating gender-specific congestion elasticities. Counterfactual analysis suggests eliminating the female city-size premium would increase the aggregate gender wage gap by 7%.

Projected temperature changes are variable in both their magnitude and geography. This paper studies how nonlinear damages and general equilibrium forces filter this climate risk across time and space. To do so, we build a tractable dynamic spatial model linking countries through trade and migration, and derive analytical first- and second-order welfare approximations that decompose the mean and variance of welfare changes into damage function, trade, and migration components. Using an ensemble of temperature projections from CMIP-6 and an empirically estimated damage function, we show that climate change-induced welfare risk is large. The standard deviation of country-level projected welfare loss across temperature projections is on average over 8% -- compared to an average welfare loss of 13% -- and is spatially unequal. Climate risk inequality is half as large as global income inequality. We show that spatial linkages reshape not only the level of climate damages, but also the spatial distribution of climate risk: accounting for trade and migration can reduce the standard deviation of welfare changes by up to 40% in low-income, internationally integrated nations that can diversify their exposure to local shocks.

This paper was previously circulated as "Geography, uncertainty, and the cost of climate change"

A firm’s residual demand elasticity takes into account both the household's demand elasticity and the equilibrium response of competitors, and therefore measures its market power. We measure over 9 million of these residual demand elasticities for over 100,000 products in different regions and years using retail scanner data. We find the distribution of these elasticities is stationary over time, suggesting any conclusions that markups are rising in retail markets must be driven by assumptions on conduct. We document substantial spatial heterogeneity in residual demand elasticity estimates, implying the toughness of competition varies considerably more across markets than across time.

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.

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’.