An Approach for Empirical Work in Spatial Dynamics

Abstract

This paper illustrates how to incorporate forward-looking behavior into empirical spatial equilibrium models with locational heterogeneity. The main insight is that the standard spatial equilibrium already embeds a natural starting point for dynamics: the presence of spatial indifference conditions can dramatically simplify the state space of forward-looking agents. One needs to know how utility evolves with the variables in the system, but not every individual state, effectively side-stepping the curse of dimensionality. Standard numerical rational expectations methods can be applied to derive approximate solutions to the full dynamic specification. The paper uses an example model of landowners exercising real options in construction of housing to show how the approximation's errors are negligibly small, and importantly, much smaller than the differences between dynamic and myopic specifications of the same model.

The Role of Housing in Carbon Emissions

“…The previous subsection described the equilibrium conditional on housing stock. This subsection describes how the builder supplies the housing stock, borrowing heavily from Mangum (2017). Each location consists of one agent responsible for housing supply.…”

“…Differences between locations in costs and/or function parameters will yield differences in structure density, motivated by Table 1. Differences in the shadow cost of land can be one component of this, as Mangum (2017) describes. The factor demand condition (9) allows for the re-expression of (7) as a continuous choice of a single input.…”

“…These issues are discussed at length in Mangum (2017), which proposes a method for solving the dynamic equilibrium. The main argument, in brief, is to leverage the no-arbitrage spatial equilibrium condition to yield a feasible approximation to the full solution.…”

“…Still, this can be hard to characterize, so a numerical approximation a la Krusell and Smith (1998) is employed, whereby a function S is iterated upon until behavior is consistent with a rational expectations equilibrium. More details and the computational method are available in Mangum (2017).…”

“…A land development problem in a large equilibrium model imposes a challenging dynamic problem, so this paper relies on techniques developed in Mangum (2017) to solve and estimate the model. Estimation is facilitated by a rich dataset describing the living area and land intensity of housing stocks and flows in all large U.S. metro areas over a three-decade period.…”