ADDITIVE-INTERACTION MODELS OF SPATIAL AGGLOMERATION*

A wide variety of existing models of spatial agglomeration postulate additive-interaction effects among agents. In this paper, a synthesis of such models is achieved by establishing certain mathematical equivalences between them. In particular, it is shown that Rockafellar's conjugacy theory of concave functions yields a symmetric one-to-one correspondence between three classes of existing models, here designated as spatial-accessibility models, endogenous-contact models, and fixed-contact models. These correspondences not only allow the transference of results between models, but also suggest new economic interpretations of each model in terms of its conjugate model. A series of examples are drawn from the literature to illustrate these results.     

PRICE AND LOCATION CONJECTURES IN MEDIUM- AND LONG-RUN SPATIAL COMPETITION MODELS*

ABSTRACT. This paper examines medium-run and long-run equilibria in unbounded (circular) and bounded (linear) one-dimensional multifirm markets. A price-location adjustment model is outlined that dows simulation of the spatial equilibrium when these firms anticipate reactions from their nearest spatial rivals. Thus, the market equilibrium is derived from the interdependent but atomistic decisions of the competing firms and is not imposed by some outside observer or agency. Ail conjectures are exogenous; the three well-known price conjectures (Greenhut-Ohta, Hotelling-Smithies, and Losch) are highlighted; and the relevant comparative statics are provided.     

POISSON GRAVITY MODELS OF SPATIAL FLOWS*

ABSTRACT The purpose of this paper is to bring together a number of results on spatial flow models, and to reformulate them within a unified probability framework based on Poisson frequencies. To do so, a class of discrete stochastic processes, designated as independent flow processes, is developed which not only yields a complete characterization of Poisson flow frequencies, but also allows a wide range of gravity-type flow models to be formulated within this distributional framework. In particular, a hierarchical classification of 12 model types is developed, and each model type is shown to be characterizable directly in terms of behavioral axioms on independent flow processes.     

DISCRETE SPATIAL CHOICE MODELS FOR AGGREGATE DESTINATIONS*

ABSTRACT. In problems of spatial choice, the choice set is typically more aggregated than the one considered by decision-makers, often because choice data are available only at the aggregate level. These aggregate choice units will exhibit heterogeneity in utility and in size. To be consistent with utility maximization, a choice model must estimate choice probabilities on the basis of the maximum utility within heterogeneous aggregates. The ordinary multinomial logit model applied to aggregate choice units fails this criterion as it is estimated on the basis of average utility. In this paper, we derive and discuss a model which utilizes the theory underlying the nested logit model to estimate the appropriate maximum utilities of aggregates. We also demonstrate that the aggregate alternative error terms are asymptotically Gumbel, thereby relaxing the assumption of extreme value distributed error terms. This is accomplished with help from the asymptotic theory of extremes.     

SPATIAL HETEROGENEITY AND THE WAGE CURVE REVISITED*

ABSTRACT Most “wage curve” studies ignore the geography of local labor markets. However, when a local labor market is in close proximity of other labor markets, a local shock that increases unemployment may not lead to lower pay rates if employers fear outward migration of their workers. Hence, the unemployment elasticity of pay will be greater, the more isolated the local labor market is. Wages are also expected to be higher in regions that interact strongly with other regions. These hypotheses are confirmed by means of an estimation of wage curves with data for 327 regions of western Germany over the period 1990–1997.     

SPATIAL HEDONIC MODELS OF AIRPORT NOISE,PROXIMITY, AND HOUSING PRICES*

ABSTRACT Despite the refrain that housing prices are determined by “location, location, and location,” few studies of airport noise and housing prices have incorporated spatial econometric techniques. We compare various spatial econometric models and estimation methods in a hedonic price framework to examine the impact of noise on 2003 housing prices near the Atlanta airport. Spatial effects are best captured by a model including both spatial autocorrelation and autoregressive parameters estimated by a generalized moments approach. In our preferred model, houses located in an area in which noise disrupts normal activities (defined by a day–night sound level of 70–75 decibels) sell for 20.8 percent less than houses located where noise does not disrupt normal activities (defined by a day–night sound level below 65 decibels). The inclusion of spatial effects magnifies the negative price impacts of airport noise. Finally, after controlling for noise, houses farther from the airport sell for less; the price elasticity with respect to distance is −0.15, implying that airport proximity is an amenity.     

ON THE SHAPE OF MARKET AREAS IN LÖSCHIAN SPATIAL MODELS*

ABSTRACT. The paper analyzes the lattice shape of equilibrium configurations of firms in spatial models. Lösch's assertion that free entry will result in hexagonal market areas is proved for a variety of assumptions about the nature of the market equilibrium, and about the preferences of customers. All the models considered, however, incorporate rational entry behavior and identify the stable lattice as an entry deterring equilibrium. A simple proof is presented of the optimality of hexagonal market areas, at least among regular space-filling configurations.     

MODELING SPATIAL AUTOCORRELATION IN SPATIAL INTERACTION DATA: AN APPLICATION TO PATENT CITATION DATA IN THE EUROPEAN UNION*

ABSTRACT Spatial interaction models of the gravity type are widely used to model origin–destination flows. They draw attention to three types of variables to explain variation in spatial interactions across geographic space: variables that characterize an origin region of a flow, variables that characterize a destination region of a flow, and finally variables that measure the separation between origin and destination regions. This paper outlines and compares two approaches, the spatial econometric and the eigenfunction‐based spatial filtering approach, to deal with the issue of spatial autocorrelation among flow residuals. An example using patent citation data that capture knowledge flows across 112 European regions serves to illustrate the application and the comparison of the two approaches.     

SPATIAL COMPETITION AND THE JOINT CONSUMPTION OF SERVICES*

In Hotelling location models, an implicit assumption has been made that a customer uses the service provided by the firm, independent of other customers. However, for firms that supply meeting rooms, wedding halls, tennis courts, and golf links it is essential to incorporate the fact that the customer only uses the service in conjunction with other customers. The objective of this paper is to formulate the Hotelling location model n consideration of the interdependence among customers in one-dimensional space, and to characterize the state of equilibrium. In our model, each group of members within a given distance enjoys a fixed amount of service of the firms, under the assumption that the travel cost incurred by each group is defined as the travel cost of the farthest customer in the group.