Description
Spatial Econometrics provides a modern, powerful and flexible skillset to early career researchers interested in entering this rapidly expanding discipline. It articulates the principles and current practice of modern spatial econometrics and spatial statistics, combining rigorous depth of presentation with unusual depth of coverage.
Introducing and formalizing the principles of, and ‘need’ for, models which define spatial interactions, the book provides a comprehensive framework for almost every major facet of modern science. Subjects covered at length include spatial regression models, weighting matrices, estimation procedures and the complications associated with their use. The work particularly focuses on models of uncertainty and estimation under various complications relating to model specifications, data problems, tests of hypotheses, along with systems and panel data extensions which are covered in exhaustive detail.
Extensions discussing pre-test procedures and Bayesian methodologies are provided at length. Throughout, direct applications of spatial models are described in detail, with copious illustrative empirical examples demonstrating how readers might implement spatial analysis in research projects.
Designed as a textbook and reference companion, every chapter concludes with a set of questions for formal or self--study. Finally, the book includes extensive supplementing information in a large sample theory in the R programming l
Chapter
1 Spatial Models: Basic Issues
1.1 Illustrations Involving Spatial Interactions
1.2 Concept of a Neighbor and the Weighting Matrix
1.3 Some Different Ways to Specify Spatial Weighting Matrices
1.4 Typical Weighting Matrices in Computer Studies
2 Specification and Estimation
2.1.2 Geršgorin's Theorem and Weighting Matrices
2.1.3 Normalization to Ensure a Continuous Parameter Space
2.1.4 An Important Condition in Large Sample Analysis
2.2 Estimation: Various Special Cases
2.2.1 Estimation When ρ1=ρ2=0
2.2.2 Estimation When ρ1=0 and ρ2<>0
2.2.2.1 Maximum Likelihood Estimation: ρ1=0, ρ2<>0
2.2.3 Assumptions of the General Model
2.2.4 A Generalized Moments Estimator of ρ2
2.3 IV Estimation of the General Model
2.4 Maximum Likelihood Estimation of the General Model
2.5 An Identification Fallacy
2.6 Time Series Procedures Do Not Always Carry Over
Appendix A2 Proofs for Chapter 2
3 Spillover Effects in Spatial Models
3.1 Effects Emanating From a Given Unit
3.2 Emanating Effects of a Uniform Worsening of Fundamentals
3.3 Vulnerability of a Given Unit to Spillovers
4 Predictors in Spatial Models
4.1 Preliminaries on Expectations
4.2 Information Sets and Predictors of the Dependent Variable
4.3 Mean Squared Errors of the Predictors
5 Problems in Estimating Weighting Matrices
5.2 Shortcomings of Selection Based on R2
5.3 An Extension to Nonlinear Spatial Models
5.4 R2 Selection in the Multiple Panel Case
6 Additional Endogenous Variables: Possible Nonlinearities
6.1 Introductory Comments
6.2 Identification and Estimation: A Linear System
6.3 A Corresponding Nonlinear Model
6.4 Estimation in the Nonlinear Model
6.5 Large Sample and Related Issues
6.6 Generalizations and Special Points to Note
6.7 Applications to Spatial Models
7.1 Introductory Comments
7.2 Fundamentals of the Bayesian Approach
7.3 Learning and Prejudgment Issues
7.4 Comments on Uninformed Priors
7.5 Applications and Limiting Cases
7.6 Properties of the Multivariate t
7.7 Useful Sampling Procedures in Bayesian Analysis
7.8 The Spatial Lag Model and Gibbs Sampling
7.9 Bayesian Posterior Odds and Model Selection
7.10 Problems With the Bayesian Approach
8 Pretest and Sample Selection Issues in Spatial Analysis
8.1 Introductory Comments
8.5 Pretesting in Spatial Models: Large Sample Issues
8.6 Final Comments on Pretesting
8.7 A Related Issue: Data Selection
8.8 Endogenous Data Selection Issues
8.9 Exogenous Data Selection Issues
9 HAC Estimation of VC Matrices
9.1 Introductory Comments on Heteroskedasticity
9.2 Spatially Correlated Errors: Illustrations
9.3 Assumptions and HAC Estimation
9.4 Kernel Functions That Satisfy Assumption 9.8
9.5 HAC Estimation With Multiple Distances
9.6 Nonparametric Error Terms and Maximum Likelihood: Serious Problems
10 Missing Data and Edge Issues
10.1 Introductory Comments
10.2 A Simple Model and Limits of Information
10.3 Incomplete Samples and External Data
10.4 The Spatial Error Model: IV and ML With Missing Data
10.5 A More General Spatial Model
10.6 Spatial Error Models: Be Careful What You Do
Appendix A10 Proofs for Chapter 10
11 Tests for Spatial Correlation
11.1 Introductory Comments: Occam's Razor
11.2 Some Preliminary Issues on a Quadratic Form
11.3 The Moran I Test: A Basic Model
11.4 An Important Independence Result
11.5 Application: The Moments of the Moran I
11.6 Generalized Moran I Tests: Qualitative Models and Spatially Lagged Dependent Variable Models
11.7 Lagrangian Multiplier Tests
11.9 Spatial Correlation Tests: Comments and Caveats
12 Nonnested Models and the J-Test
12.1 Introductory Comments
12.2 The Null Model: Nonparametric Error Terms
12.3 The Alternative Models
12.5 The Augmented Equation and the J-Test
12.6 The J-Test: SAR Error Terms
12.7 J-Test and Nonlinear Alternatives
13 Endogenous Weighting Matrices: Specifications and Estimation
13.1 Introductory Comments
13.3 Issues Concerning Error Term Specification
13.4 Further Specifications
13.5 The Instrument Matrix
13.6 Estimation and Inference
14 Systems of Spatial Equations
14.1 Introductory Comments
14.2 An Illustrative Two-Equations Model
14.3 The Model With Nonparametric Error Terms
14.4 Assumptions of the Model
14.5 Interpretation of the Assumptions
14.6 Estimation and Inference
14.7 The Model With SAR Error Terms
14.8 Estimation and Inference: GS3SLS
15.1 Introductory Comments
15.2 Some Important Preliminaries
15.3 The Random Effects Model
15.4 A Generalization of the Random Effects Model
15.5 The Fixed Effects Model
15.6 A Generalization of the Fixed Effects Model
15.7 Tests of Panel Models: The J-Test
A Introduction to Large Sample Theory
A.1 An Intuitive Introduction
A.2 Application of the Large Sample Result in (A.1.6)
A.3 More Formalism: Convergence in Probability
A.5 An Important Property of Convergence in Probability
A.6 A Matrix Illustration of Consistency
A.7 Generalizations of Slutsky-Type Results
A.8 A Note on the Least Squares Model
A.9 Convergence in Distribution
A.10 Results on Convergence in Distribution
A.11 Convergence in Distribution: Slutsky-Type Results
A.12 Constructing Finite Sample Approximations
A.13 A Result Relating to Nonlinear Functions of Estimators
A.14 Orders in Probability
A.15 Triangular Arrays: A Central Limit Theorem
B.3 Reading Data and Creating Weights
B.4 Estimating Spatial Models
Spatial Econometrics
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