Dynamic Spatial General Equilibrium

Local shocks to economic activity play out gradually across places over time. One major challenge in studying these gradual responses, however, is developing dynamic spatial models that incorporate forward-looking behavior. To illustrate the effects of a local shock, models must take into account that future investment decisions across locations will depend on economic activity in all locations in all future time periods. 

In this working paper, the authors make important methodological contributions to research on economic geography by developing a framework for studying local shocks that incorporates forward-looking decisions about both capital investments and migration. 

In doing so, they shed new light on how economic activities respond to local shocks over time, and derive closed-form solutions for the entire time path of economic activity across geographic space in response to local shocks to fundamentals such as productivities, amenities, trade costs, and migration costs. The authors then use these closed-form solutions for the economy’s transition path to provide an analytical characterization of the determinants of the economy’s dynamic response to shocks.

Applying the new approach

After developing their model, the authors apply it to the study of the structural shift of economic activity from the “Rust Belt” to the “Sun Belt” between 1965 and 2015. The authors choose this setting because of the availability of data on bilateral shipments of goods, bilateral migration flows, and capital stocks over the long historical time period, and because of the substantial observed changes in the spatial distribution of economic activity over time.

The authors show that the initial distance of a state’s population from its steady-state (to which economic activity converges in the absence of further shocks) has substantial predictive power for subsequent population growth, even after controlling for the initial levels of population and the capital stock and initial population growth.

The exercise shows that local economies converge slowly toward their steady state, with average speeds of around 20 years. This is consistent with previous empirical evidence of the persistent impacts of local shocks. The authors also find substantial differences in how quickly places converge toward their steady state, which is again in line with evidence on the uneven impacts of local shocks. Capital and labor dynamics interact in important ways to shape this speed of convergence, because a high capital stock increases worker productivity, and a high employment increases the incentive to accumulate capital.

This slow convergence toward steady-state also suggests that declines in mobility may not be related to migration barriers. In the authors’ empirical application, actual population shares remain persistently above or below their steady-state values for decades, with actual and steady-state population shares being closer together at the end of the authors’ sample period than at the beginning. This suggests that observed declines in mobility over time could reflect either the size or nature of a shock or that a location is closer to (or farther away from) its steady-state than previously realized.

In a final empirical exercise, the authors extend their analysis to incorporate multiple sectors in U.S. states and foreign countries from 1999-2015. They find more rapid convergence towards steady-state in this multi-sector specification, which reflects greater mobility of labor across sectors within states than across states. 

This implies that the speed with which the economy adjusts to shocks depends crucially on whether the affected industries span locations. Nevertheless, the authors again find substantial variation in economic convergence rates across places, emphasizing that the effects of local shocks are highly sensitive to factors like geography, the affected industries, and the interaction between migration and capital accumulation.