Estimating Spatial Models Within A Disequilibrium Framework

Modeling demand in a spatial context requires careful handling of regional interactions. In situations where there are constraints in some markets that lead to spillovers to others it is useful to build this explicitly into the model. In this paper I present a theoretical model that is related to the disequilibrium and the spatial econometric literature. Under certain conditions the model may be estimable and an appropriate estimation technique that uses the EM algorithm, is put forward. A data set from the U.K. market for secondary school places provides a test for the procedure.     

Spatial Autoregressive Models for Geographically Hierarchical Data Structures

This article discusses how standard spatial autoregressive models and their estimation can be extended to accommodate geographically hierarchical data structures. Whereas standard spatial econometric models normally operate at a single geographical scale, many geographical data sets are hierarchical in nature—for example, information about houses nested into data about the census tracts in which those houses are found. Here we outline four model specifications by combining different formulations of the spatial weight matrix W and of ways of modeling regional effects. These are (1) groupwise W and fixed regional effects; (2) groupwise W and random regional effects; (3) proximity‐based W and fixed regional effects; and (4) proximity‐based W and random regional effects. We discuss each of these model specifications and their associated estimation methods, giving particular attention to the fourth. We describe this as a hierarchical spatial autoregressive model. We view it as having the most potential to extend spatial econometrics to accommodate geographically hierarchical data structures and as offering the greatest coming together of spatial econometric and multilevel modeling approaches. Subsequently, we provide Bayesian Markov Chain Monte Carlo algorithms for implementing the model. We demonstrate its application using a two‐level land price data set where land parcels nest into districts in Beijing, China, finding significant spatial dependence at both the land parcel level and the district level.     

Spatial Inequality Between and Within Urban Areas: The Case of Israeli Cities

Central areas enjoy greater efficiency in the production of goods and services than do outlying areas. Because of the inherent advantages of central areas over outlying areas, disparities among regions do not vanish over time. On the contrary, centripetal forces increase inequalities across space. The phenomena of increased globalization, trade liberalization and treaties among countries not only enable the flow of labour, products (export) and foreign direct investment but also help reduce spatial inequality between countries. These phenomena also induce greater spatial economic concentration within a country. Thus, although disparities among countries decrease, a widening gap is observed between regions within countries and within large urban areas. In the empirical part, we analyse the general patterns of spatial inequality found among 55 localities in Israel with population size over 20,000. Looking at the spatial inequality relationship, both within and between cities in Israel, we show how all economic indicators measured, including inequality, decrease with distance from the core. Localities in the periphery that experience greater equality also experience lower average income, lower education, less self-employment and more unemployment.     

Spatial Models of Spread-Backwash Processes

Spread-backwash processes are central elements in regional development thought. This article argues that the main spread-backwash processes produce developmental change that has a general spatial form. Straightforward models of the processes of government incomes and expenditure flows, private capital flows, intraregional trade, migration-commuting, and the diffusion of innovations provide the rationale for the general distance decay form of developmental impact. Each model is supported by evidence from the relevant literature. It is argued that there is not a dichotomous set of spread versus backwash processes, but rather that the same set of processes yields differential spatial impacts.     

Income Diffusion and Spatial Econometric Models

This paper considers the development of linked small-area spatial econometric models in which income flows between the areas constitute an important part of model specification. The attributes of income diffusion processes are considered in detail. Both static models and temporal income diffusion models are discussed. The spatial and spatial-temporal autocorrelation functions are derived which provide a measure of the spatial distribution of income. The Green function is also derived as a measure of income impulses through the system of regions. An important aspect of the paper is to relate properties of these functions to key economic parameters in particular propensities to spend locally and to spend nonlocally.     

Models of Space Searching in Urban Areas

City dwellers occasionally must seek jobs, dwellings, or particular services or goods. Two very different ways exist by which the individual may conduct such a search. Lacking prior information, the person may elect to visit perceived possible locations until an appropriate one is found. Alternatively, an address may first be ascertained and then visited by finding a path to it. Clearly, there is a substantial difference between these two methods in terms of the amount of spatial movement they require in order to satisfy the searcher's needs. In this paper, this difference is modeled for situations that vary in terms of the density of acceptable end points of the search, as well as in characteristics of the signs of these end points, their patterns, and the level of information with which the searcher may begin.     

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC ³ by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.     

Symptoms of Instability in Models of Spatial Dependence

In recent years, there has been a growing interest in the problems caused by the existence of instability in cross-sectional regressions. The results about local autocorrelation measures are part of this debate, as are the proposals concerning the concept of geographically weighted regressions. This article also deals with the problem of stability (or the lack thereof), but focusing the discussion on the supposition of constancy in the parameter of spatial dependence. In most cases, this assumption is treated, with the risks that this involves, as a maintained hypothesis, which should be ascertained before continuing with the modeling exercise. In the article, we present a simple heterogeneity test for this type of parameters, based on the Lagrange Multiplier principle. To illustrate its use, we take the distribution of per capita income among the European regions as our discussion case. According to our results, there are clear signs of structural breaks in the spatial distribution of this variable and the scale factor and the autocorrelation coefficient appear to be principal actors.     

Building Spatial Choice Models from Aggregate Data

Abstract Choice model construction is usually based on information about a number of separate choice situations, for which all relevant quantities are known. This paper concerns the case where only higher level, aggregate information is available about the choice results and the prevailing conditions. We demonstrate the applicability of a generic inverse parameter estimation method in estimating a model for grocery store choice. We also propose some enhancements to standard spatial choice models and demonstrate their applicability.     

Single and Multiscale Models of Process Spatial Heterogeneity

Recent work in local spatial modeling has affirmed and broadened interest in multivariate local spatial analysis. Two broad approaches have emerged: Geographically Weighted Regression (GWR) which follows a frequentist perspective and Bayesian Spatially Varying Coefficients models. Although several comparisons between the two approaches exist, recent developments, particularly in GWR, mean that these are incomplete and missing some important axes of comparison. Consequently, there is a need for a more thorough comparison of the two families of local estimators, including recent developments in multiscale variants and their relative performance under controlled conditions. We find that while both types of local models generally perform similarly on a series of criteria, some interesting and important differences exist.     

Congestion Tolling and Urban Spatial Structure

According to the standard model of urban traffic congestion and urbanspatial structure, congestion tolling results in a more concentrated city. In recent years, a new model of rush-hour urban auto congestion has been developed that incorporates trip-timing decisions—the bottleneck model. In the simplest bottleneck model optimal congestion tolling without toll-revenue redistribution has no effect on trip price because the efficiency gainsexactly equal the toll revenue collected. Optimal congestion tolling then has no effect on urban spatial structure. This paper formalizes and extends this result.