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.     

ON FRONTIER SPECIFICATIONS FOR DISCRETE BINARY CHOICE ANALYSIS

ABSTRACT. In estimating a discrete choice model one is actually estimating the parameters of a conditional indirect utility function. I explore the consequences of recognizing that this function is a maximum-value (frontier) function. I formulate several frontier choice models and, using a pilot empirical study of transportation mode choice, compare the resulting estimates with those of the conventional logit specification. Most strikingly, it appears that the values of time implied by the frontier models are substantially below those of the logit model. This implies that policies designed to improve travel times may be of less value to consumers than is conventionally believed.     

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.     

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.     

DIAGNOSTICS FOR REGRESSION MODELING IN SPATIAL ECONOMETRICS*

ABSTRACT. This paper describes statistics for model criticism in spatial econometrics. The purpose of these statistics is to evaluate how well a chosen model fits the data and to identify influential cases and how they affect the aggregate picture. The paper reviews results in Martin (1992) for the regression model with correlated errors where the coefficients of the variance matrix are assumed either known or fixed. The problems of applying the statistics in spatial econometric modeling are discussed. An application is reported which considers diagnostics for the mean function and highlights cases that might influence estimates of the parameter of the error model. Different ways of assessing the influence of cases are also described.     

ALTERNATIVE MODELS FOR ORGANIZATION OF STATE COURT SYSTEMS*

The dominant theme in court reorganization has been to state judiciaries by consolidating trial courts and centralizing their administration in a state level office. This article suggests that the debate over the relative merits of a centralized vs. a decentralized (or fragmented) court system ignores the rich variety of organizational structures used in other fields. The potential judicial implications of three models-franchise, corporate, and federal-are examined in detail. Their underlying assumptions are compared with those of the centralization approach. The argument is made that none of the models is appropriate for all circumstances. Each approach to court organization emphasizes a particular set of objectives at the expense of another set. An effort is made to identify what each approach has to offer.     

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 RESIDENTIAL CHOICE*

ABSTRACT. This paper presents a new approach in the modeling of residential choices for simulation purpose. The originality of the approach resides in the way recent developments in stochastic choice models are combined with deterministic mathematical programming which allows to define an equilibration process for simulation. In that respect, ex ante probabilities of housing choice based on random utility maximization under perceived constraints are distinguished from ex post probabilities of choice that respect supply constraints. The proposed model is tested on the Montreal Metropolitan Region, and a few simulation results based on a scenario of population aging and decrease in household size are analyzed.     

MODELING SPATIAL STRUCTURES THROUGH EQUILIBRIUM STATES FOR TRANSITION MATRICES*

ABSTRACT. In this paper we present a model for spatial interaction within a network of towns. This interaction is modeled through equilibrium states for certain Markov chains where, in particular, explicit formulas for these states are given. Our model exploits and intertwines ideas from gravity models, the competing destinations model and the intervening opportunities model. The central idea in the paper is to capture the effect of spatial structure in a framework where interaction is determined by the global network configuration.