A Dynamic Model of Household Location, Regional Growth and Endogenous Natural Amenities with Cross-Scale Interactions

We develop a coupled model of regional migration and lake ecology to study the influence of ecological-economic interactions and relative time scales on transient and asymptotic dynamics. Cross-scale interactions fundamentally change system dynamics by eliminating steady states that are present in the decoupled economic model and introduce important time dependence. We find that the relative time scales of interacting variables are a key determinant in system dynamics and resilience and that the system's asymptotic behavior cannot be determined without considering the full dynamics of the system. Other time-dependent effects are found to matter, e.g., when households base their perceptions of environmental amenities on past observation, a path dependence is introduced that can lead to oscillations or decline in transient population. Finally, interactions are found to multiply the costs and benefits of policy by inducing a positive feedback between the ecological and economic components that can reinforce or offset the direct effect of the policy. Such effects imply that the economic and ecological costs of getting the policy wrong can be large. Our findings underscore the critical importance of accounting for multiple time scales and time dependence and suggest that models that ignore such complications can be quite misleading. At best, such models will fail to capture the full dynamics of the system and at worst, could provide a misleading characterization of the basic dynamical structure of these systems.