EFFICIENT ALGORITHMS FOR CONSTRUCTING PROPER HIGHER ORDER SPATIAL LAG OPERATORS*

ABSTRACT. This paper extends the work of Blommestein and Koper (1992)–BK–on the construction of higher-order spatial lag operators without redundant and circular paths. For the case most relevant in spatial econometrics and spatial statistics, i.e., when contiguity between two observations (locations) is defined in a simple binary fashion, some deficiencies of the BK algorithms are outlined, corrected and an improvement suggested. In addition, three new algorithms are introduced and compared in terms of performance for a number of empirical contiguity structures. Particular attention is paid to a graph theoretic perspective on spatial lag operators and to the most efficient data structures for the storage and manipulation of spatial lags. The new forward iterative algorithm which uses a list form rather than a matrix to store the spatial lag information is shown to be several orders of magnitude faster than the BK solution. This allows the computation of proper higher-order spatial lags “on the fly” for even moderately large data sets such as 3,111 contiguous U. S. counties, which is not practical with the other algorithms.     

An Anisotropic Model for Spatial Processes

One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model.     

Fluvial spatial taphonomy: a new method for the study of post-depositional processes

Traditional taphonomic analyses do not consider the emergent properties resulting from the relationship of variables. Several of these emergent properties are expressed spatially. Here, we present a spatial taphonomic approach to the understanding of post-depositional processes affecting experimental assemblages modified by fluvial currents. Spatial statistical methods are a great tool to understand how different taphonomic variables relate at a spatial scale. The results of the application of this method to bone assemblages affected by low- and high-energy flows show the loss or modification of most of the original spatial taphonomic relationships. It also shows the degree of bone loss according to element, anatomical section and bone structure, and shape types. Anisotropy is identified in both experimental contexts. These results add new criteria to assess the impact of water flows in bone assemblages and contribute to define the properties of lag assemblages.     

Properties of Tests for Spatial Dependence in Linear Regression Models

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).     

Noninferior Bandwidth Line Simplification: Algorithm and Structural Analysis

Digital line simplification operators are an important preprocessing component of a spatial data handling system. Simplification operators are used to generalize digital line files because these files are encoded at one scale but the objects they represent can be displayed at many other scales. Most line simplification algorithms are heuristics that caricaturize lines by eliminating points representing redundant data or conversely retaining the characteristic points of a line that have a high informational content. This paper presents a noninferior simplification algorithm that produces an optimal caricature of an encoded line with respect to the bandwidth criterion that all deleted points must be within a prespecified distance of the simplified line. Results show that it is a practical alternative to existing bandwidth heuristics.     

SPATIAL HEDONICS AND THE WILLINGNESS TO PAY FOR RESIDENTIAL AMENITIES*

ABSTRACT We investigate the role of spatial multipliers when using spatial‐lag hedonic models to measure the benefits of residential amenity improvements. Such benefits are commonly measured using the product of the coefficient of the amenity in question and a spatial multiplier. We show this is correct only when the spatial spillovers transmitted through the multiplier are strictly technological. If they are instead strictly pecuniary, then benefits are fully measured using the coefficient with no spatial multiplier. In either case, or in intermediate cases where both types of spillovers exist, a spatial‐lag specification is required to obtain valid benefits measures.     

Principal Component Regression in Spatial Lag Model: Teen Employment in the City of Rosario,Argentina

Teen employment is a very important socioeconomic phenomenon because of its consequences on human capital formation. We assess the relation between teen employment and poverty, education, and unemployment in the city of Rosario, using information from the 2010 Argentina Census disaggregated at census block level. We use two different spatial models: The spatial lag model (SLM) and a linear regression model with the spatial component filtered (filtering model, FM). Given the nature of the variables employed, multicollinearity is an issue. One of the techniques proposed in the literature to deal with multicollinearity problems is principal component regression (PCR). We develop an adaptation of such methodology to be used in the SLM. Both models are estimated using their traditional methodologies (instrumental variables for the SLM and OLS for the FM) and using PCR. Although results are similar between the two models, depending on the methodology used in the estimations they differ greatly. Under traditional methodologies estimations show high variability, instability, and contradictory outcomes, but under PCR, results behave according to the literature.     

A Genetic Approach to Detecting Clusters in Point Data Sets

Spatial analysis techniques are widely used throughout geography. However, as the size of geographic data sets increases exponentially, limitations to the traditional methods of spatial analysis become apparent. To overcome some of these limitations, many algorithms for exploratory spatial analysis have been developed. This article presents both a new cluster detection method based on a genetic algorithm, and Programs for Cluster Detection, a toolkit application containing the new method as well as implementations of three established methods: Openshaw's Geographical Analysis Machine (GAM), case point-centered searching (proposed by Besag and Newell), and randomized GAM (proposed by Fotheringham and Zhan). We compare the effectiveness of cluster detection and the runtime performance of these four methods and Kulldorf's spatial scan statistic on a synthetic point data set simulating incidence of a rare disease among a spatially variable background population. The proposed method has faster average running times than the other methods and significantly reduces overreporting of the underlying clusters, thus reducing the user's postprocessing burden. Therefore, the proposed method improves upon previous methods for automated cluster detection. The results of our method are also compared with those of Map Explorer (MAPEX), a previous attempt to develop a genetic algorithm for cluster detection. The results of these comparisons indicate that our method overcomes many of the problems faced by MAPEX, thus, we believe, establishing that genetic algorithms can indeed offer a viable approach to cluster detection.     

江苏省县域经济集聚和收敛的空间计量分析

通过探索性空间数据分析和空间计量分析方法,以实际人均GDP为测度指标,对江苏省65个县市的经济空间集聚、增长收敛性以及收敛机制进行讨论。研究发现1993-2009年实际人均GDP显示出越来越高的全局正相关,局部空间相关性也有增强的趋势。空间计量分析结果表明江苏省县域经济存在着β收敛,分时段研究为不同研究时段选择恰当的空间收敛模型后,收敛速度加快。技术扩散收敛机制和资本收敛机制分别在研究区间的前期和后期占主导作用,收敛机制的转变与江苏省在20世纪90年代末开始实行的区域协调发展政策密切相关。     

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.     

AGGLOMERATION,CONGESTION, AND U.S. REGIONAL DISPARITIES IN EMPLOYMENT GROWTH

Wide regional disparities exist in U.S. employment growth. To identify the causes of this disparities, we assess the relative contribution of locational characteristics to regional employment growth in the United States from 2001 to 2010 by estimating an employment growth model with the spatial‐lag effect. Results show that, at the margin, congestion effects dominate localized scale externalities in urban counties. A diverse industrial structure and rich human capital are the main factors that contribute to regional disparities in employment growth. Significant spatial‐lag effects indicate that spatial targeting and regional coordination are necessary to maximize the effectiveness of employment growth policies.     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

An Axiomatic Approach to Geographical Space

Geographical space is a major concept in spatial analysis. Curiously enough, no attempt has so far been made to provide a general and rigorous presentation. In this paper, a formal definition of the basic geographical components is given. For that purpose, topology and measure theory are used. A general definition of geographical space is then proposed and some properties are examined. Finally, the relations between the proposed definition and the particular representations used in spatial analysis are discussed.     

Estimation Bias in Spatial Models with Strongly Connected Weight Matrices

This article shows that, for both spatial lag and spatial error models with strongly connected weight matrices, maximum likelihood estimates of the spatial dependence parameter are necessarily biased downward . In addition, this bias is shown to be present in general Moran tests of spatial dependency. Thus, positive dependencies may often fail to be detected when weight matrices are strongly connected. The analysis begins with a detailed examination of downward bias for the extreme case of maximally connected weight matrices. Results for this case are then extended by continuity to a broader range of (appropriately defined) strongly connected matrices. Finally, a simulated numerical example is presented to illustrate some of the practical consequences of these biases.     

Measuring Spatial Autocorrelation of Vectors

This article introduces measures to quantify spatial autocorrelation for vectors. In contrast to scalar variables, spatial autocorrelation for vectors involves an assessment of both direction and magnitude in space. Extending conventional approaches, measures of global and local spatial associations for vectors are proposed, and the associated statistical properties and significance testing are discussed. The new measures are applied to study the spatial association of taxi movements in the city of Shanghai. Complications due to the edge effect are also examined.     

SPATIAL MULTIPLIERS IN HEDONIC ANALYSIS: A COMMENT ON “SPATIAL HEDONIC MODELS OF AIRPORT NOISE,PROXIMITY, AND HOUSING PRICES”*

ABSTRACT This note draws upon the spatial‐hedonic analysis of Cohen and Coughlin to clarify the role of spatial multipliers in regression specification and benefits measurement, and to demonstrate the appropriate calculation of these benefits from dummy‐variable coefficients in semi‐logarithmic spatial‐lag models.     

ISSUES IN SPATIAL DATA ANALYSIS

ABSTRACT.  Misspecified functional forms tend to produce biased estimates and spatially correlated errors. Imposing less structure than standard spatial lag models while being more amenable to large datasets, nonparametric and semiparametric methods offer significant advantages for spatial modeling. Fixed effect estimators have significant advantages when spatial effects are constant within well-defined zones, but their flexibility can produce variable, inefficient estimates while failing to account adequately for smooth spatial trends. Though estimators that are designed to measure treatment effects can potentially control for unobserved variables while eliminating the need to specify a functional form, they may be biased if the variables are not constant within discrete zones.     

A Structural Equation Approach to Models with Spatial Dependence

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it possible to obtain a closer correspondence between theory and empirics, to explicitly account for measurement errors, and to reduce multicollinearity. We extend the standard SEM maximum likelihood estimator to allow for spatial dependence and propose easily accessible SEM software like LISREL 8 and Mx. We present an illustration based on Anselin's Columbus, OH, crime data set. Furthermore, we combine the spatial lag model with the latent multiple-indicators–multiple-causes model and discuss estimation of this latent spatial lag model. We present an illustration based on the Anselin crime data set again.     

THE SPATIAL MONOPSONY: A THEORETICAL ANALYSIS*

ABSTRACT. In this paper some of the most important properties of the behavior of a spatial monopsonist are derived. Many results are mirror images of corresponding results for the spatial monopolist. A few results are, however, genuinely new. A lot of effort is spent in comparing the properties of the profit function under three different pricing policies, f.o.b. (mill)-pricing, uniform delivered pricing, and spatial price discrimination. It is shown, for example, how the profitability and welfare consequences of the different policies are related to the shapes of the supply and demand functions. It is argued that the theory may have important applications in economic analyses of renewable natural resources such as forests, where total transportation costs are nonnegligible.     

Elementary Spatial Systems of Industrial Production

An elementary spatial system of industrial production is conceptualized as the primary geographical formation in industry. Such an elementary production system (EPS) is viewed as consisting of raw-material and consumption nodes connected by lines of movement with a single production node. Besides the measures proposed by Kansky (University of Chicago, Research Paper 84, 1963), such a system, represented in the form of a connected, directed graph, can be described by measures of material and spatial transformation and by indices of dispersion of aggregate nodes. Characteristic properties of EPS are the spatial attraction between nodes and the spatial coincidence and intersection of common nodes of two or more systems. The usual Weberian movement-minimization approach to the building of a model of such an elementary production system is judged to be inadequate because it ignores local differences in production costs, and a “field of potential costs” is proposed instead to take account of the total cost picture.