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 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.     

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.     

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.     

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.     

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.     

Models for Spatial Weights: A Systematic Look

General properties of spatial weights models, in particular Markovian properties, are systematically investigated. The role of stationary spatial distribution, interpretable as an importance-centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the associated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry, and Dirichlet-Voronoi tessellations illustrate the main concepts, with a particular geometrical emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered from general models.     

A Spatial Prior for Bayesian Vector Autoregressive Models

In this paper we develop a Bayesian prior motivated by cross-sectional spatial autoregressive models for use in time-series vector autoregressive forecasting involving spatial variables. We compare forecast accuracy of the proposed spatial prior to that from a vector autoregressive model relying on the Minnesota prior and find a significant improvement. In addition to a spatially motivated prior variance as in LeSage and Pan (1995) we develop a set of prior means based on spatial contiguity. A Theil-Goldberger estimator may be used for the proposed model making it easy to implement.