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.Community/Rural/Urban Development, Resource /Energy Economics and Policy,

An Agent-Based Model of Exurban Land Development

In contrast to urban areas that are aptly characterized by a large population base and scarce land supply, exurban regions have limited households and plentiful land. This basic difference has far reaching implications for spatial equilibrium in exurban land markets. Rather than bidding their maximum willingness-to-pay and reaching a spatial equilibrium in which households are indifferent to location, as is the central condition of urban economic models, we argue that exurban households will be able to retain some amount of surplus in moving to an exurban location and therefore will choose the location that maximizes this locational surplus. In this paper, we first review the handful of structural spatial models of exurban land development that have been developed. We then develop a structural spatial model of exurban land development that captures these hypothesized features of exurban land markets using an auction model to represent household bidding and adapting the Capooza and Helsley (1990) model to represent landowners’ optimal timing of development. A key innovation of our approach is that, in the absence of full capitalization of land or location differences into land prices, households have preferences for some locations over others and thus it is possible to order household location choices in time and space. This greatly facilitates modeling of land use dynamics by enabling us to model location and land use decisions sequentially in time rather than assuming that all development is instantaneous for given levels of population and income in the region. In addition, the spatial agent-based simulation method that is used to implement the model permits an explicit examination of the implications of exurban land market conditions for the evolution of urban development pattern. Specifically, we ask whether these exurban market conditions explain the emergence and persistence of so-called leapfrog development that is characteristic of exurban regions.Land Economics/Use,

Incorporating Spatial Complexity into Economic Models of Land Markets and Land Use Change

Recent work in regional science, geography, and urban economics has advanced spatial modeling of land markets and land use by incorporating greater spatial complexity, including multiple sources of spatial heterogeneity, multiple spatial scales, and spatial dynamics. Doing so has required a move away from relying solely on analytical models to partial or full reliance on computational methods that can account for these added features of spatial complexity. In the first part of the paper, we review economic models of urban land development that have incorporated greater spatial complexity, focusing on spatial simulation models with spatial endogenous feedbacks and multiple sources of spatial heterogeneity. The second part of the paper presents a spatial simulation model of exurban land development using an auction model to represent household bidding that extends the traditional Capozza and Helsley (1990) model of urban growth to account for spatial dynamics in the form of local land use spillovers and spatially heterogeneous land characteristics.urban growth, urbanization, land development, spatial dynamics, heterogeneity, agent-based models, spatial interactions, Land Economics/Use, Research Methods/ Statistical Methods,

Scale-Invariant Behavior in a Spatial Game of Prisoners’ Dilemma

10.1103/PhysRevE.65.026134Physical Review E - Statistical, Nonlinear, and Soft Matter Physics652026134/1-026134/6PLEE

Application of renormalization-group techniques to random magnetic systems

Renorma1ization-group methods have been applied in the study of quenched random magnetic systems in recent years. We begin with a brief review of second-order phase transitions in pure, homogeneous systems and also of the .. renorma1ization group framework. Then we provide an introduction to quenched random magnetic systems. Next, momentum-space methods and position-space techniques as applied to quenched random magnets are outlined and compared. Grinstein and Luther applied the Wilson-Fisher E-expansion to random n-vector models; Khme1'nitsky discovered that the random Ising model (n = 1) possessed a "random" fixed point of 0(squareroot(e)). This fixed point was found to have one marginal and one irrelevant operator. We have investigated the stability of this fixed point using Ca11an-Symanzik equations and renorma1ized perturbation theory. We find the fixed point stable in the next order; we have also obtained critical exponents to one higher order. Next, position-space techniques are used to study some simple model systems. In addition to critical exponents, global thermodynamic properties are determined. These calculations are based on the Migda1-Kadanoff approximate recursion relations suitably generalized to the inhomogeneous case. Firstly we study the randomly bond-dilute two-dimensional nearest- neighbor Ising model on a square lattice. Calculations give both thermal and magnetic exponents associated with the percolative fixed point. Differential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The critical region of the specific heat becomes unobservably narrow well above the percolation threshold Pc. This provides a possible explanation for the apparent specific-heat rounding in certain experiments. We then study the Edwards-Anderson model of a spin glass. The current theoretical situation, which is far from satisfactory at present, is briefly reviewed. We treat the spin-l/2 Ising model with independently random nearestneighbor interactions in dimensionalities d = 2, 3, and 4. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spinglass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific heat anomaly. Global specific-heat curves are also displayed for d = 2.U of I OnlyThesi

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

An Agent-Based Model of Exurban Land Development

In contrast to urban areas that are aptly characterized by a large population base and scarce land supply, exurban regions have limited households and plentiful land. This basic difference has far reaching implications for spatial equilibrium in exurban land markets. Rather than bidding their maximum willingness-to-pay and reaching a spatial equilibrium in which households are indifferent to location, as is the central condition of urban economic models, we argue that exurban households will be able to retain some amount of surplus in moving to an exurban location and therefore will choose the location that maximizes this locational surplus. In this paper, we first review the handful of structural spatial models of exurban land development that have been developed. We then develop a structural spatial model of exurban land development that captures these hypothesized features of exurban land markets using an auction model to represent household bidding and adapting the Capooza and Helsley (1990) model to represent landowners’ optimal timing of development. A key innovation of our approach is that, in the absence of full capitalization of land or location differences into land prices, households have preferences for some locations over others and thus it is possible to order household location choices in time and space. This greatly facilitates modeling of land use dynamics by enabling us to model location and land use decisions sequentially in time rather than assuming that all development is instantaneous for given levels of population and income in the region. In addition, the spatial agent-based simulation method that is used to implement the model permits an explicit examination of the implications of exurban land market conditions for the evolution of urban development pattern. Specifically, we ask whether these exurban market conditions explain the emergence and persistence of so-called leapfrog development that is characteristic of exurban regions