Luc Anselin

Simple diagnostic tests for spatial dependence

In this paper we propose simple diagnostic tests, based on ordinary least-squares (OLS) residuals, for spatial error autocorrelation in the presence of a spatially lagged dependent variable and for spatial lag dependence in the presence of spatial error autocorrelation, applying the modified Lagrange multiplier (LM) test developed by Bera and Yoon (Econometric Theory, 1993, 9, 649-658). Our new tests may be viewed as computationally simple and robust alternatives to some existing procedures in spatial econometrics. We provide empirical illustrations to demonstrate the usefulness of the proposed tests. The finite sample size and power performance of the tests are also investigated through a Monte Carlo study. The results indicate that the adjusted LM tests have good finite sample properties. In addition, they prove to be more suitable for the identification of the source of dependence (lag or error) than their unadjusted counterparts.

Spatial Externalities, Spatial Multipliers, And Spatial Econometrics

This article outlines a taxonomy of spatial econometric model specifications that incorporate spatial externalities in various ways. The point of departure is a reduced form in which local or global spillovers are expressed as spatial multipliers. From this, a range of familiar and less familiar specifications is derived for the structural form of a spatial regression.

Measuring The Benefits of Air Quality Improvement: A Spatial Hedonic Approach

Abstract The primary objective of this paper is to improve the methodology for estimating hedonic price functions when the data are inherently spatial. A spatial-econometric hedonic housing price model is developed and estimated for the Seoul metropolitan area to measure the marginal value of improvements in sulfur dioxide (SO2) and nitrogen dioxide (NOx) concentrations. Diagnostic testing favored the spatial-lag model over the spatial error model. Results showed that SO2 pollution levels had a significant impact on housing prices while NOx pollution did not. The authors attribute this differential impact to the relatively higher levels of SO2 pollution when compared with pollution standards and the relative recency of the NOx pollution. Marginal WTP for a 4% improvement in mean SO2 concentrations is about

New directions in spatial econometrics.

2333 or 1.4% of mean housing price.

Assessing Spatial Equity: An Evaluation of Measures of Accessibility to Public Playgrounds

1 New Directions in Spatial Econometrics: Introduction.- 1.1 Introduction.- 1.2 Spatial Effects in Regression Models.- 1.2.1 Specification of Spatial Dependence.- 1.2.2 Spatial Data and Model Transformations.- 1.3 Spatial Effects in Limited Dependent Variable Models.- 1.4 Heterogeneity and Dependence in Space-Time Models.- 1.5 Future Directions.- References.- I-A: Spatial Effects in Linear Regression Models Specification of Spatial Dependence.- 2 Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results.- 2.1 Introduction.- 2.2 Tests for Spatial Dependence.- 2.2.1 Null and Alternative Hypotheses.- 2.2.2 Tests for Spatial Error Dependence.- 2.2.3 Tests for Spatial Lag Dependence.- 2.3 Experimental Design.- 2.4 Results of Monte Carlo Experiments.- 2.4.1 Empirical Size of the Tests.- 2.4.2 Power of Tests Against First Order Spatial Error Dependence.- 2.4.3 Power of Tests Against Spatial Autoregressive Lag Dependence.- 2.4.4 Power of Tests Against Second Order Spatial Error Dependence.- 2.4.5 Power of Tests Against a SARMA (1,1) Process.- 2.5 Conclusions.- Acknowledgements.- References.- Appendix 1: Tables.- 3 Spatial Correlation: A Suggested Alternative to the Autoregressive Model.- 3.1 Introduction.- 3.2 The Spatial AR Model of Autocorrelation.- 3.3 The Singularity of (I - pM).- 3.3.1 Theoretical Issues.- 3.3.2 Independent Corroborative Evidence.- 3.4 The Parameter Space.- 3.5 A Suggested Variation of the Spatial AR Model.- 3.5.1 The Suggested Model.- 3.5.2 Some Limiting Correlations.- 3.5.3 A Generalization.- 3.6 Suggestions for Further Work.- Acknowledgements.- References.- Appendix 1: Spatial Weighting Matrices.- 4 Spatial Autoregressive Error Components in Travel Flow Models: An Application to Aggregate Mode Choice.- 4.1 Introduction.- 4.2 The First-Order Spatially Autoregressive Error Components Formulation.- 4.3 Estimation Issues.- 4.4 Empirical Example.- 4.4.1 An Illustration Based on Synthetic Data.- 4.5 Conclusions.- References.- I-B: Spatial Effects in Linear Regression Models Spatial Data and Model Transformations.- 5 The Impacts of Misspecified Spatial Interaction in Linear Regression Models.- 5.1 Introduction.- 5.2 Aggregation and the Identification of Spatial Interaction.- 5.3 Experimental Design.- 5.3.1 Sample Size.- 5.3.2 Spatial Interaction Structures.- 5.3.3 Spatial Models and Parameter Space.- 5.3.4 Test Statistics and Estimators.- 5.3.5 Forms of Misspecification.- 5.4 Empirical Results.- 5.4.1 Size of Tests Under the Null.- 5.4.2 Power of Tests.- 5.4.3 Misspecification Effects on the Power of Tests for Spatial Dependence.- 5.4.4 Sensitivity of Parameter Estimation to Specification of Weight Matrix.- 5.4.5 Impact of Misspecification of Weight Matrix on Estimation.- 5.5 General Inferences References.- 6 Computation of Box-Cox Transform Parameters: A New Method and its Application to Spatial Econometrics.- 6.1 Introduction.- 6.2 The Elasticity Method: Further Elaboration.- 6.2.1 Linearization Bias.- 6.2.2 Discretization Bias.- 6.2.3 Specification Bias.- 6.3 The One Exogenous Variable Test.- 6.4 An Application to Spatial Econometrics.- 6.5 The Multiple Exogenous Variable Computation.- 6.6 Conclusions.- References.- 7 Data Problems in Spatial Econometric Modeling.- 7.1 Introduction.- 7.2 Data for Spatial Econometric Analysis.- 7.3 Data Problems in Spatial Econometrics.- 7.4 Methodologies for Handling Data Problems.- 7.4.1 Influential Cases in the Standard Regression Model.- 7.4.2 Influential Cases in a Spatial Regression Model.- 7.4.3 An Example.- 7.5 Implementing Methodologies.- References.- 8 Spatial Filtering in a Regression Framework: Examples Using Data on Urban Crime, Regional Inequality, and Government Expenditures.- 8.1 Introduction.- 8.2 Rationale for a Spatial Filter.- 8.3 The Gi Statistic.- 8.4 The Filtering Procedure.- 8.5 Filtering Variables: Three Examples.- 8.5.1 Example 1: Urban Crime.- 8.5.2 Example 2: Regional Inequality.- 8.5.3 Example 3: Government Expenditures.- >8.6 Conclusions.- >Acknowledgments.- References.- II: Spatial Effects in Limited Dependent Variable Models.- 9 Spatial Effects in Probit Models: A Monte Carlo Investigation.- 9.1 Introduction.- 9.2 Sources of Heteroscedasticity.- 9.3 Heteroscedastic Probit.- 9.4 Monte Carlo Design.- 9.5 Tests.- 9.6 Monte Carlo Results.- 9.7 Conclusions.- References.- Appendix 1: Monte Carlo Results.- Appendix 2: Heteroscedastic Probit Computer Programs.- Appendix 3: Monte Carlo Computer Programs.- 10 Estimating Logit Models with Spatial Dependence.- 10.1 Introduction.- 10.1.1 Model.- 10.2 Simulation Example.- 10.3 Conclusions.- >References.- Appendix 1: Gauss Program for Finding ML Estimates.- Appendix 2: Gauss Program to Estimate Asymptotic Variances of ML Estimates.- 11 Utility Variability within Aggregate Spatial Units and its Relevance to Discrete Models of Destination Choice.- 11.1 Introduction.- 11.2 Theoretical Background.- 11.3 Estimation of the Maximum Utility Model.- 11.4 Model Specifications and Simulations.- 11.4.1 Specification Issues.- 11.4.2 Description of Simulation Method.- 11.4.3 Results.- 11.5 Conclusions.- Acknowledgement.- References.- III: Heterogeneity and Dependence in Space-Time Models.- 12 The General Linear Model and Spatial Autoregressive Models.- 12.1 Introduction.- 12.2 The GLM.- 12.3 Data Preprocessing.- 12.3.1 Analysis of the 1964 Benchmark Data.- 12.3.2 Evaluation of Missing USDA Values Estimation.- >12.4 Implementation of the Spatial Statistical GLM.- 12.4.1 Preliminary Spatial Analysis of Milk Yields: AR Trend Surface GLMs.- 12.4.2 AR GLM Models for the Repeated Measures Case.- 12.4.3 A Spatially Adjusted Canonical Correlation Analysis of the Milk Production Data.- 12.5 Conclusions.- >References.- >Appendix 1: SAS Computer Code to Compute the Popular Spatial Autocorrelation Indices.- Appendix 2: SAS Code for Estimating Missing Values in the 1969 Data Set.- Appendix 3: SAS Code for 1969 USDA Data Analysis.- 13 Econometric Models and Spatial Parametric Instability: Relevant Concepts and an Instability Index.- 13.1 Introduction.- 13.2 The Expansion Method.- 13.3 Parametric Instability.- 13.3.1 Example.- 13.4 Conclusions.- 13.4.1 Instability Measures: Scope.- 13.4.2 Instability Measures: Significance.- References.- 14 Bayesian Hierarchical Forecasts for Dynamic Systems: Case Study on Backcasting School District Income Tax Revenues.- 14.1 Introduction.- 14.2 Literature Review.- 14.3 The C-MSKF Model: Time Series Prediction with Spatial Adjustments.- 14.3.1 Multi-State Kaiman Filter.- 14.3.2 Spatial Adjustment via Hierarchical Random Effects Model.- 14.3.3 CIHM Method.- 14.3.4 C-MSKF.- 14.4 Case Study and Observational Setting.- 14.4.1 Data.- 14.4.2 Treatments.- 14.5 Results.- >14.6 Conclusions.- >References.- Appendix 1: Poolbayes Program.- 15 A Multiprocess Mixture Model to Estimate Space-Time Dimensions of Weekly Pricing of Certificates of Deposit.- 15.1 Introduction.- 15.2 A Dynamic Targeting Model of CD Rate-Setting Behavior.- 15.2.1 The Model.- 15.2.2 The Decision Rule.- 15.3 The Spatial Econometric Model.- 15.3.1 Spatial Time-Varying Parameters.- 15.3.2 Parameter Estimation.- 15.3.3 Testing Hypotheses with the Model.- 15.4 Implementing the Model.- 15.4.1 The Data.- 15.4.2 Prior Information.- 15.4.3 Empirical Results.- 15.5 Conclusions.- Acknowledgements.- References.- Appendix 1: FORTRAN Program for the Spatial Mixture.- Author Index.- Contributors.

Spatial Panel Econometrics

Geographical and political research on urban service delivery—who benefits and why—has proliferated during the past two decades. Overall, this literature is not characterized by a particular attention to the importance of method in drawing conclusions about spatial equity based on empirical studies. Specifically, there has been scant interest in the effect of geographic methodology on assessing the relationship between access and socioeconomic characteristics that are spatially defined. In this paper we take a spatial analytical perspective to evaluate the importance of methodology in assessing whether or not, or to what degree the distribution of urban public services is equitable. We approach this issue by means of an empirical case study of the spatial distribution of playgrounds in Tulsa, Oklahoma, relative to that of the targeted constituencies (children) and other socioeconomic indicators. In addition to the ‘traditional’ measure (count of facilities in an areal unit), we consider a potential measure (based on the gravity model), average travel distance, and distance to the nearest playground as indicators of accessibility. We find significant differences between the spatial patterns in these measures that are suggested by local indicators of spatial association and other techniques of exploratory spatial data analysis. The choice of access measure not only implies a particular treatment of spatial externalities but also affects conclusions about the existence of spatial mismatch and inequity.

Small sample properties of tests for spatial dependence in regression models : some further results.

Spatial econometrics is a subfield of econometrics that deals with the incorporation of spatial effects in econometric methods (Anselin, 1988a). Spatial effects may result from spatial dependence, a special case of cross-sectional dependence, or from spatial heterogeneity, a special case of cross-sectional heterogeneity. The distinction is that the structure of the dependence can somehow be related to location and distance, both in a geographic space as well as in a more general economic or social network space. Originally, most of the work in spatial econometrics was inspired by research questions arising in regional science and economic geography (early reviews can be found in, among others, Paelinck and Klaassen, 1979, Cliff and Ord, 1981, Upton and Fingleton, 1985, Anselin, 1988a, Haining, 1990, Anselin and Florax, 1995). However, more recently, spatial (and social) interaction has increasingly received more attention in mainstream econometrics as well, both from a theoretical as well as from an applied perspective (see the recent reviews and extensive references in Anselin and Bera, 1998, Anselin, 2001b, Anselin, 2002, Florax and Van Der Vlist, 2003, and Anselin et al., 2004a).

Deforestation and Cattle Ranching in the Brazilian Amazon: External Capital and Household Processes

It has now been more than two decades since Cliff and Ord (1972) and Hordijk (1974) applied the principle of Moran’s Itest for spatial autocorrelation to the residuals of regression models for cross-sectional data. To date, Moran’sIstatistic is still the most widely applied diagnostic for spatial dependence in regression models [e.g., Johnston (1984), King (1987), Case (1991)]. However, in spite of the well known consequences of ignoring spatial dependence for inference and estimation [for a review, see Anselin (1988a)], testing for this type of misspecification remains rare in applied empirical work, as illustrated in the surveys of Anselin and Griffith (1988) and Anselin and Hudak (1992). In part, this may be due to the rather complex expressions for the moments of Moran’s I, and the difficulties encountered in implementing them in econometric Software [for detailed discussion, see Cliff and Ord (1981), Anselin (1992), Tiefelsdorf and Boots (1994)]. Recently, a number of alternatives to Moran’s Ihave been developed, such as the tests of Burridge (1980) and Anselin (1988b, 1994), which are based on the Lagrange Multiplier (LM) principle, and the robust tests of Bera and Yoon (1992) and Kelejian and Robinson (1992). These tests are all asymptotic and distributed as X 2variates. Since they do not require the computation of specific moments of the statistic, they are easy to implement and straightforward to interpret. However, they are all large sample tests and evidence on their finite sample properties is still limited.

The Spatial Patterning of County Homicide Rates: An Application of Exploratory Spatial Data Analysis

This paper decomposes recent deforestation in four study areas in the Brazilian Amazon into components associated with large ranches and small producers. It then assesses in an inferential framework small producer deforestation with respect to the proximate causes of their farming systems, and the household drivers of their farming system choices. It is shown that, for areas with substantial in-migration of small producers, forest clearance at the household level is mainly attributable to the availability of hired labor, and not to household labor force or the physical capital at their disposal. The paper conducts the inferential analysis of small producer deforestation using measures of forest clearance taken from satellite image classification and directly from field surveys. A substantial discrepancy in the measures is identified, which has implications for household level research on land cover change.

Geographic and sectoral characteristics of academic knowledge externalities

The possibility that homicides can spread from one geographic area toanother has been entertained for some time by social scientists, yetsystematic efforts to demonstrate the existence, or estimate the strength,of such a diffusion process are just beginning. This paper uses exploratoryspatial data analysis (ESDA) to examine the distribution of homicides in 78counties in, or around, the St. Louis metropolitan area for two timeperiods: a period of relatively stable homicide (1984–1988) and aperiod of generally increasing homicide (1988–1993). The findingsreveal that homicides are distributed nonrandomly, suggestive of positivespatial autocorrelation. Moreover, changes over time in the distribution ofhomicides suggest the possible diffusion of lethal violence out of onecounty containing a medium-sized city (Macon County) into two nearbycounties (Morgan and Sangamon Counties) located to the west. Althoughtraditional correlates of homicide do not account for its nonrandom spatialdistribution across counties, we find some evidence that more affluentareas, or those more rural or agricultural areas, serve as barriers againstthe diffusion of homicides. The patterns of spatial distribution revealedthrough ESDA provide an empirical foundation for the specification ofmultivariate models which can provide formal tests for diffusion processes.