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.     

THE FUTURE OF SPATIAL ECONOMETRICS*

ABSTRACT The purpose of this paper is threefold. First, we give an overview of the general direction the spatial econometrics literature has taken without attempting to provide a representative survey of all interesting work that has appeared. Second, we identify a number of problems in spatial econometrics that are as yet unresolved. Finally, we provide advocacy for the notion that new spatial econometric theory should be inspired by actual empirical applications as opposed to being directed by what appears to be the most obvious extension of what is currently available.     

现代服务业集聚形成机理空间计量分析

在纳入空间效应前提下,构建现代服务业集聚形成机理空间面板计量模型,对我国28个省域相关数据实证研究表明:我国现代服务业集聚在省域之间有较强的空间依赖性和正的空间溢出效应。技术差异在时间维度上对现代服务业集聚促进作用显著,在空间维度上并不显著;交易费用与现代服务业集聚有显著的负相关性;知识溢出、规模经济、政府行为对现代服务业集聚促进作用显著。     

INTRODUCTION: WHITHER SPATIAL ECONOMETRICS?

ABSTRACT Spatial econometrics has become a mainstay for regional scientists aiming to estimate geographic spillovers in regional outcomes. Yet, many remain skeptical, especially urban economists who prefer natural experimental approaches. Their concerns revolve around identification and a general lack of a theoretical foundation in the estimation of spatial econometric models. This theme issue includes three papers from leading regional scientists to appraise the status of spatial econometrics. The outcome is sweeping proposals from (1) abandoning standard spatial econometrics because it cannot identify causality, (2) using nonparametric approaches, and (3) implementing more nuanced changes revolving around better theoretical and empirical modeling.     

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.     

Arms Racing in ‘Space’: Spatial Modelling of Military Spending around the World

This paper builds on previous research into determinants of military spending by examining global and local spatial effects. Other research has examined the effects of regional differences and neighbours' spending levels with standard econometric techniques. This paper uses spatial econometrics to gain a better understanding of the influence of location and distance on levels of defence spending. I find that a spatial lag specification provides much more robust evidence of arms racing and security dilemma dynamics than previous studies. These basic dynamics have been difficult to detect empirically without the context and nuance introduced by spatial modelling. The paper represents a first cut at the topic, but two specific findings emerge. First, globally there is positive spatial correlation (nearby states have similar levels of spending). This conforms to arms racing and security dilemma expectations. And, second, locally there is variation in the patterns of spatial clustering across broad international regions (e.g. Europe, Asia etc.). The second finding supports previous research suggesting important qualitative regional variation in patterns of defence spending and international conflict. The models also confirm the effects of political regime type and interstate war on defence spending, and are robust to the inclusion of a temporally lagged dependent variable.     

TESTING THE SPATIAL SCALE AND THE DYNAMIC STRUCTURE IN REGIONAL MODELS (A CONTRIBUTION TO SPATIAL ECONOMETRIC SPECIFICATION ANALYSIS)*

This article addresses the problem of specification uncertainty in modeling spatial economic theories in stochastic form. It is ascertained that the traditional approach to spatial econometric modeling does not adequately deal with the type and extent of specification uncertainty commonly encountered in spatial economic analyses. Two alternative spatial econometric modeling procedures proposed in the literature are reviewed and shown to be suitable for analyzing systematically two sources of specification uncertainty, viz., the level of aggregation and the spatio-temporal dynamic structure in multiregional econometric models. The usefulness of one of these specification procedures is illustrated by the construction of a simple multiregional model for The Netherlands.     

WHERE IS THE ECONOMICS IN SPATIAL ECONOMETRICS?*

ABSTRACT Spatial econometrics has been criticized by some economists because some model specifications have been driven by data‐analytic considerations rather than having a firm foundation in economic theory. In particular, this applies to the so‐called W matrix, which is integral to the structure of endogenous and exogenous spatial lags, and to spatial error processes, and which are almost the sine qua non of spatial econometrics. Moreover, it has been suggested that the significance of a spatially lagged dependent variable involving W may be misleading, since it may be simply picking up the effects of omitted spatially dependent variables, incorrectly suggesting the existence of a spillover mechanism. In this paper, we review the theoretical and empirical rationale for network dependence and spatial externalities as embodied in spatially lagged variables, arguing that failing to acknowledge their presence at least leads to biased inference, can be a cause of inconsistent estimation, and leads to an incorrect understanding of true causal processes.     

Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models: An Empirical Comparison of Exact Sampling Methods

Spatial econometric specifications pose unique computational challenges to Bayesian analysis, making it difficult to estimate models efficiently. In the literature, the main focus has been on extending Bayesian analysis to increasingly complex spatial models. The stochastic efficiency of commonly used Markov Chain Monte Carlo (MCMC) samplers has received less attention by comparison. Specifically, Bayesian methods to analyze effective sample size and samplers that provide large effective size have not been thoroughly considered in the literature. Thus, we compare three MCMC techniques: the familiar Metropolis‐within‐Gibbs sampling, Slice‐within‐Gibbs sampling, and Hamiltonian Monte Carlo. The latter two methods, while common in other domains, are not as widely encountered in Bayesian spatial econometrics. We assess these methods across four different scenarios in which we estimate the spatial autoregressive parameter in a mixed regressive, spatial autoregressive specification (or, spatial lag model). We find that off‐the‐shelf implementations of the newer high‐yield simulation techniques require significant adaptation to be viable. We further find that the effective sizes are often significantly smaller than nominal sizes. In addition, we find that stopping simulation early may understate posterior credible interval widths when effective sample size is small. More broadly, we suggest that sample information and stopping rules deserve more attention in both applied and basic Bayesian spatial econometric research.     

BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

SPATIAL HEDONIC MODELS OF AIRPORT NOISE,PROXIMITY, AND HOUSING PRICES*

ABSTRACT Despite the refrain that housing prices are determined by “location, location, and location,” few studies of airport noise and housing prices have incorporated spatial econometric techniques. We compare various spatial econometric models and estimation methods in a hedonic price framework to examine the impact of noise on 2003 housing prices near the Atlanta airport. Spatial effects are best captured by a model including both spatial autocorrelation and autoregressive parameters estimated by a generalized moments approach. In our preferred model, houses located in an area in which noise disrupts normal activities (defined by a day–night sound level of 70–75 decibels) sell for 20.8 percent less than houses located where noise does not disrupt normal activities (defined by a day–night sound level below 65 decibels). The inclusion of spatial effects magnifies the negative price impacts of airport noise. Finally, after controlling for noise, houses farther from the airport sell for less; the price elasticity with respect to distance is −0.15, implying that airport proximity is an amenity.     

The Impact of Energy,Transport, and Trade on Air Pollution in China

A team of U.S.- and China-based geographers examines the relationship between China's economic development and its environment by modeling the effects of energy, transport, and trade on local air pollution emissions (sulfur dioxide and soot particulates) using the Environmental Kuznets model. Specifically, the latter model is investigated using spatial econometrics that take into account potential regional spillover effects from high-polluting neighbors. The analysis finds an inverted-U relationship for sulfur dioxide but a U-shaped curve for soot particulates. This suggests that soot particulates such as black carbon may pose a more serious environmental problem in China than sulfur dioxide. Journal of Economic Literature, Classification Numbers: C50, F10, Q43, R40. 4 figures, 3 tables, 47 references.     

Rook or Queen, But How About Some Other Royal Court Suite Members?

The contribution to spatial econometrics of the Cliff–Ord publication is fully recognized, but it is also shown that it should be complemented by some important spatial econometrics features.     

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.     

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。     

Determinants of Variation in Population–Employment Interaction Findings: A Quasi‐Experimental Meta‐Analysis. 人口‐就业相互作用的决定因素研究：一种准实验元分析法

This article reports about a metaregression analysis of empirical results generated using data for the northern Netherlands (1988–2002) in order to investigate the ambiguity in results in the population–employment interaction literature. Specifically, the analysis deals with the issue whether “jobs follow people” or “people follow jobs.” The article starts with introducing the basics of quasi‐experimental meta‐analysis and with identifying some advantages of using quasi‐experimental meta‐analysis as compared with the standard meta‐analysis approach. Two subsequent sections document the selection of the population–employment interaction model and salient characteristics of the data set as well as the setup of the primary analyses. A total of 4,050 quasi‐experimental empirical results for the jobs–people direction of causality are generated using different specifications and estimators for a spatial econometric interaction model. The subsequent metaregression analysis reveals that the empirical results are largely shaped by the spatial, temporal, and employment characteristics of the data sampling. The results also appear much more sensitive to different measurements of the model's key variables when compared with alternative specifications of the spatial weights matrix. The main determinant driving empirical results about jobs–people causality are differences in model specification and estimation, as revealed by an inherent bias in parameter estimates and misguided inferences for some of the commonly used specifications. Finally, suggestions for future research are identified.     

Vector Autoregression (Var) — An Approach to Dynamic analysis of Geographic Processes

Vector autoregression (VAR) is a widely used econometric technique for multivariate time series modelling. This paper shows that with several very attractive features, VAR may also provide a valuable tool for analysing the dynamics among geographic processes and for spatial autoregressive modelling. After a brief discussion of the VAR approach, a VAR model for the dynamics of the US population between 1910 and 1990 is estimated and interpreted to illustrate the techniques. The VAR makes it possible to view the interactions among the four variables used in the model (total population, birth rate, immigration and per capita GNP) more adequately. The paper then discusses recent developments in the VAR methodology such as Bayesian vector autoregression (BVAR), spatial prior for regional modelling and cointegration, as well as the limitations and problems that arise from the application of VARs.     

The Spatiotemporal Evolution of Sydney's Tram Network Using Network Econometrics

This paper examines the evolution of Sydney trams using network econometrics approaches. Network econometrics extends spatial econometrics by developing weight matrices based on the physical structure of the network, allowing for competing and complementary elements to have distinct effects. This research establishes a digitized database of Sydney historical tramway network, providing a complete set of geo-referenced data of the opening and closing year and frequencies by time of day for every line. An autoregressive distributed lag model is specified and reveals that the combination of correlation strength and magnitude of lagged flow change on correlated links is a significant predictor of future tram service. The results indicate that complementary and competitive links play distinct roles in shaping the network structure. A link is more likely to undergo the same structural change highly complementary (upstream or downstream) links underwent previously, where the influence is measured by a combination of correlation strength and link importance, reflected by historical service levels.