Land Absorption in U.S. Metropolitan Areas: Estimates and Projections from Regional Adjustment Models
Carruthers, John I., Mulligan, Gordon F., Geographical Analysis
This article adapts a regional adjustment model to estimate and project the spatial outcome of population and employment growth in U.S. metropolitan areas. The three-equation multiplicative model of population change, employment change, and land absorption is estimated using three-stage least squares to account for endogeneity among the dependent variables and contemporaneous correlation across the system of equations. In addition to the core model, alternative specifications are estimated, imposing the initial conditions of size, land availability, and economic structure. The stability of the solutions is then examined using reduced-form equations estimated via the seemingly unrelated regression equations approach. The results reveal substantive evidence that population and employment growth are jointly determined, of how the two affect the outcome of land development, and, perhaps most importantly, stable and fractionally reasonable estimates at projected equilibrium points. Lastly, the adapted model controlling for the initial condition of land availability is used to project patterns of land consumption at equilibrium in 50 rapid-growth metropolitan areas.
This article adapts a regional adjustment model to estimate and project spatially explicit outcomes of population and employment growth in U.S. metropolitan areas. The main idea is that, just as people follow jobs into and/or within regions, jobs follow people. From this point of departure, population (employment) change between two points in time is modeled as a function of employment (population) at the end of the time period, population (employment) at the beginning of the time period, and a set of other relevant exogenous variables. The approach is described as an adjustment model because it portrays population and employment adjusting toward some unknown future state of spatial equilibrium. If this point were ever reached, all individuals and firms would be distributed in such a way that their utility and profits, respectively, were maximized with respect to location. As neither of these conditions presently exists, researchers commonly describe the space economy as being in a state of partial equilibrium, constantly adjusting to an ideal distribution of economic activity.
Regional adjustment models normally portray this process via a system of two simultaneous equations in which population and employment change, the dependent variables, are jointly determined (Steinnes and Fisher 1974; Carlino and Mills 1987; Boarnet 1994a, b; Clark and Murphy 1996). Within this framework, densities instead of levels are used in order to reduce heteroskedasticity introduced by inevitable variation in the size of the spatial units involved, but the denominator often does not accurately describe a geographically relevant area, and, moreover, it usually remains constant through time. The boundaries of the most common units of analysis, including cities, counties, states, and even census tracts, can encompass a vicinity well beyond that which is actually occupied--especially in expansive Western counties and in states with liberal annexation laws, where municipalities may easily extend their jurisdiction outward. Further, due to the fact that the size of most of these units changes only incrementally, if at all, through time, they offer little or no insight into the nature of spatial outcomes associated with the process of regional development.
Responding to these issues, the present analysis alters the traditional regional adjustment model framework in several important ways. First, the model draws on land-use data from the U.S. Department of Agriculture's Natural Resources Inventory to define more precisely the area occupied by economic activity: Counties are the unit of analysis, but only a proportion of their total land area is used as the spatial unit. Second, instead of densities, measured as people (employees) per acre, the analysis is concerned with land absorption, measured as acres per person (employee). …