SPATIAL AUTOCORRELATION IN BRITISH UNEMPLOYMENT

ABSTRACT. The recent literature on local unemployment in Britain and the U.S. is reviewed, and a model estimated for Britain which is consistent with the findings of that literature. Spatial econometric techniques are applied to test and elaborate on that model. The results indmte the presence of significant spillovers in adjustments to local demand shocks. These spillovers occur over a wide spatial field and are strongest after a lag, suggesting that they reflect migration behavior. In addition, highly localized spatial interactions are found, consistent with commuting adjustments in response to shocks. Incorporating these effects eliminates spatial autocorrelation from the residuals. A simulation exercise is undertaken to demonstrate the effects of supply- and demand-side shocks on the model solution.     

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 WITH CONSISTENT CONJECTURES*

ABSTRACT Equilibrium in spatial models invariably depends on firms' conjectures about how competitors will react to their price changes. This paper analyzes spatial price and location equilibrium when firms hold consistent (i.e. correct) conjectures. Most spatial models assume an exogenous conjecture. Consistent conjectures are one method, albeit a controversial one, for endogenizing the conjecture. We show that the consistent conjecture about a competitor's reaction to a price change in the simplest case is 1/3. When demand is elastic the consistent conjecture is a decreasing function of the radius. It is always below 1/3 and can be negative. In the third model, we show that the consistent conjecture declines as the number of dimensions and the number of competitors increases.     

SPATIAL COMPETITION WITH LOCATION-DEPENDENT COSTS*

This paper investigates the behavior of spatially-competitive firms whose costs depend on their locations. Necessary and sufficient conditions for optimum locations are derived. Comparative-statistics analysis of the equilibrium shows that the responses of firms to changes in input and output transport rates depend on the properties of consumer demand curves or are ambiguous in sign.     

SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS*

ABSTRACT. We determine the location equilibria in a duopoly model under a novel solution concept. Typically, spatial equilibrium is described as either a simultaneous price and location game, or else as a two-stage location-then-price game. We introduce a new alternative, a two-stage price-then-location game. It is well known that no (pure strategy) equilibrium usually exists under the two standard solution concepts when products are homogeneous. We show this is also true for the new concept. We then provide numerical results for a specific functional form (the logit model) which introduces product heterogeneity into the standard framework, restoring equilibrium when the degree of substitutability between products is not too small.     

MILL PRICING AND SPATIAL PRICE DISCRIMINATION MONOPOLY PERFORMANCE AND LOCATION WITH SPATIAL RETAIL MARKETS*

ABSTRACT. Most of the monopoly spatial price discrimination literature explicitly assumes uniform population density over space. It also implicitly assumes that firms (plants) are spatially isolated from each other with production and retail points that coincide in location. While departures from these assumptions have been explored separately in the literature, it remains to examine performance and location when these assumptions are relaxed simultaneously. What emerges in this paper is a model where density functions approximate a pair of cities isolated from other cities. Each city has its own retail market, while the location of a single production or wholesale point is determined by characteristics of the two markets. Comparisons of mill pricing and spatial price discrimination found in the spatial monopoly literature can be interpreted as special cases of the more general framework provided here.     

PRICING POLICY REACTIONS TO AGGLOMERATION IN A MARKET WITH SPATIAL SEARCH*

ABSTRACT. Price dispersion (variation) and agglomeration are common characteristics of spatial markets, in particular, markets with imperfect consumer information and search. However, pricing and location strategies in these markets are not well analyzed since spatial search is difficult to model without restricting the spatial dimension of the problem. This paper analyzes pricing and location strategies in a market with spatid search using a probabilistic modeling strategy that does not restrict search patterns in the plane. Specifically, the analysis considers the pricing strategy of an isolated firm in response to the agglomeration of competing firms. Results indicate that spatial and temporal price dispersion are effective responses to competitors'agglomeration. However, the relative effectiveness of these strategies varies with market conditions. In addition, agglomeration can have some counterintuitive effects. This paper also provides insights into existing theories of spatial search and spatial competition in spatially-restricted (linear and circular) markets.     

INTERDEPENDENT BEHAVIOR WITH RELOCATION COSTS: THE COMPARATIVE STATICS OF SPATIAL HISTORY*

Relocation costs are a form of sunk costs because they are relevant to new entrants, not to agents at their existing locations. With sufficiently high relocation costs, initial (historically given) locations and other conditions determine the equilibrium assignment of agents to locations. Comparative static results depend on initial conditions, i.e., history matters and historical persistence can be characterized. The model suggests empirically-relevant results which can be tested by collecting data on relocation and transportation costs. For example, appropriate levels of these costs imply that suburbanization always occurs with the entry of new firms. Sequential entry strategies may be adopted by existing firms which earn pure profits. This may be contrasted with traditional NUE models which predict changes in the boundaries of central zones.     

SPATIAL DISEQUILIBRIUM

ABSTRACT. The well-known extremal principle for the solution of spatial equilibrium for a single commodity [Samuelson (1952)] is extended to deal with the case of disequilibrium caused by rigid prices and/or price controls. Both disequilibrium in consumer markets and in factor markets is covered.
The study of disequilibrium is well known in general interdependent economic systems (the so-called fixed-price model of interdependent systems). The present work extends this approach to the spatial dimension, and shows how it is possible to represent and solve disequilibrium models by mathematical programming rather than by fixed-point techniques.     

SPATIAL PRICE COMPETITION WITH CONSUIMERS ON A PLANE,AT INTERSECTIONS,AND ALONG MAIN ROADWAYS*

ABSTRACT. This paper examines two-dimensional price competition on a plane, with a block metric and a square grid of main roadways. One store is located at each intersection of main roadways. Consumer locations include a uniform distribution over the plane, linear concentrations along main roadways, and point concentrations at intersections. Bertrmd-Nash mill price competition is examined first. The equilibrium price depends on the relative numbers of consumers in the three types of locations (and on travel costs per mile and the spacing between stores). If too many consumers are in each point concentration, then the price equilibrium is undermined by a high-price strategy or by mill-price undercutting. Spatial competition with price discrimination is examined next, and compared to Bertrand-Nash mill price competition.     

SPATIAL DEPENDENCE AND SPATIAL STRUCTURAL INSTABILITY IN APPLIED REGRESSION ANALYSIS*

The stability of regression coefficients over the observation set (“regional homogeneity”) is typically assessed by means of a Chow test or within a seemingly unrelated regression (SUR) framework. When spatial error autocorrelation is present in cross-sectional equations the traditional tests are no longer applicable. I evaluate this both in formal terms as well as empirically. I introduce a taxonomy of spatial effects in models for structural instability, and discuss its implication for testing. I compare the performance of traditional tests, robust approaches, maximum-likelihood procedures and pretest techniques by means of a series of simple Monte Carlo experiments.     

DEREGULATING THE DISTRIBUTION OF ELECTRICITY: PRICE AND WELFARE CONSEQUENCES OF SPATIAL OLIGOPOLY WITH UNIFORM DELIVERED PRICES*

ABSTRACT. Theoretical, spatial oligopoly models are developed and calibrated to simulate the price and welfare consequences of deregulating the retail price of electricity (the distribution function), assuming competing sources of generation supply are available. Two types of distribution competition are considered, retaining the currently used uniform delivered pricing structure: competition for customers at neighboring utilities’ borders and franchise competition. Because duplicate facilities are required for borderline competition, short-run price increases ranging between 14 and 37 percent over existing regulated prices are estimated for upstate New York, largely because deregulated prices reflect replacement, not historic, costs of facilities.