Spatial Econometrics,9783540323044

Spatial Econometrics

by
ISBN13: 9783540323044
ISBN10: 354032304X
Format: Hardcover
Pub. Date: 2006-05-15
Publisher(s): Springer Verlag
List Price: $178.49

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Summary

The new economic geography and the debate on regional economic convergence have drawn increasingly the interest of economists in the empirical analysis of regional and spatial data. However, even if the methodology for the econometric treatment of spatial data is well developed, there does not exist a book without strong pre-requisites that is easily accessible to economists. This book bridges the gap between economic theory and spatial econometric techniques. It is easy accessible to people with only basic statistical background and no prior knowledge of spatial econometric methods. It provides a comprehensive treatment of the topic by motivating the reader with examples and real data analysis. The volume provides a rigorous treatment, founded on stochastic fields theory, of the basic spatial linear model, and discusses the violations of the classical regression assumptions that occur when dealing with spatial data.

Table of Contents

1 Motivation 3(28)
1.1 Introduction
3(4)
1.2 Theoretical Economic Models Calling for Spatial Econometric Techniques
7(7)
1.2.1 Introduction
7(1)
1.2.2 The β-convergence Approach
8(6)
1.3 A β-convergence Analysis of European and Italian Regions
14(13)
1.3.1 Introduction
14(2)
1.3.2 A β-convergence Analysis of Italian NUTS-3 Provinces (1951-1999)
16(6)
1.3.3 A β-convergence Analysis of European NUTS-2 Regions (1980-1996)
22(5)
1.4 A list of Omitted Topics and an Outline of the Book
27(4)
2 Random Fields and Spatial Models 31(42)
2.1 Introduction
31(2)
2.2 The Concept of a Random Field
33(10)
2.2.1 The Nature of the Index S
34(5)
2.2.1.1 Generalities
34(2)
2.2.1.2 The Topology of a Random Field
36(3)
2.2.2 The Dependence Structure of a Random Field
39(4)
2.3 Restrictions on Random Fields
43(6)
2.3.1 Restrictions on the Spatial Heterogeneity of a Random Field
43(3)
2.3.2 Restrictions on The Spatial Dependence of a Random Field
46(3)
2.4 Some Special Random Fields
49(19)
2.4.1 Spatial White Noise
49(1)
2.4.2 Markov Random Fields
49(14)
2.4.2.1 Generalities
49(1)
2.4.2.2 The Hammersley and Clifford Theorem
50(2)
2.4.2.3 Ising's Law
52(3)
2.4.2.4 The Strauss Auto-model
55(1)
2.4.2.5 The Auto-binomial Field
56(1)
2.4.2.6 The Auto-Poisson Model
57(1)
2.4.2.7 The Auto-normal (or CAR) Field
57(1)
2.4.2.8 The Intrinsic Gaussian Field
58(1)
2.4.2.9 The Bivariate Auto-normal Field
59(1)
2.4.2.10 The Multivariate Auto-normal (or MCAR) Field
60(3)
2.4.3 Non-Markovian Fields
63(5)
2.4.3.1 The Simultaneous Autoregressive Random Field (SAR)
63(2)
2.4.3.2 The Moving Average Random Field
65(1)
2.4.3.3 The Autoregressive Moving Average Random Field
66(1)
2.4.3.4 The Spatial Error Component Random Field
66(1)
2.4.3.5 The Direct Representation of a Random Field
67(1)
2.5 Limiting Theorems for Random Fields
68(5)
2.5.1 Introduction
68(1)
2.5.2 Some Limit Theorems for Random Fields
69(4)
3 Likelihood Function for Spatial Samples 73(12)
3.1 Introduction
73(3)
3.2 Some Approximations for the Likelihood of Random Fields
76(5)
3.2.1 The Coding Technique
76(1)
3.2.2 The Unilateral Approximaticn
77(2)
3.2.3 The Pseudo-Likelihood à la Besag
79(1)
3.2.4 Computational Aspects
80(1)
3.3 Maximum Likelihood Estimation Properties in Spatial Samples
81(1)
3.4 Tests Based on Likelihood
81(3)
3.5 Tests Based on Residual Sums of Squares
84(1)
4 The Linear Regression Model with Spatial Data 85(50)
4.1 Introduction
85(1)
4.2 Specification of a Linear Regression Model
85(5)
4.2.1 The Conditional Specification
86(2)
4.2.1.1 Hypotheses on the Probability Model (PM)
86(1)
4.2.1.2 Hypotheses on the Statistical Generating Mechanism (GM)
87(1)
4.2.1.3 Hypotheses on the Sampling Model (SM)
88(1)
4.2.2 Standard Textbook Specification
88(2)
4.3 Violation of the Hypotheses on the Sampling Model
90(30)
4.3.1 Introduction
90(1)
4.3.2 A General-Purpose Testing Procedure for Spatial Independence
91(2)
4.3.3 The Respecification of the Linear Regression as a Multivariate CAR Field
93(7)
4.3.3.1 Introduction
93(1)
4.3.3.2 Respecification of the PM, GM and SM Hypotheses
94(2)
4.3.3.3 Likelihood of a Bivariate CAR Spatial Linear Regression Model
96(2)
4.3.3.4 Hypothesis Testing in the Bivariate CAR Spatial Linear Regression Model
98(2)
4.3.3.5 Likelihood of a Multivariate CAR Spatial Linear Regression Model
100(1)
4.3.4 The Respecification of the Linear Regression with SAR Residuals (the Spatial Error Model)
100(10)
4.3.4.1 Introduction
100(2)
4.3.4.2 Derivation of the Likelihood
102(1)
4.3.4.3 Equivalence of the Statistical Model Implied by the Bivariate CAR and the SAR Residual
103(2)
4.3.4.4 Hypothesis Testing in the Spatial Error Model
105(1)
4.3.4.5 Generalized Least Squares Estimators
106(2)
4.3.4.6 Approximate Estimation Techniques
108(2)
4.3.5 The Re-specification of the Linear Regression by Adding a Spatial Lag (the Spatial Lag Model)
110(6)
4.3.5.1 Introduction
110(1)
4.3.5.2 Derivation of the Likelihood
110(3)
4.3.5.3 Estimation
113(2)
4.3.5.4 Hypothesis Testing
115(1)
4.3.6 Anselin's General Spatial Model
116(4)
4.4 Violation of the Hypotheses on the Probability Model
120(15)
4.4.1 Introduction
120(1)
4.4.2 Normality
120(6)
4.4.2.1 Generalities
120(1)
4.4.2.2 Testing for Departures from Normality
121(2)
4.4.2.3 Solutions to the Problem of Non-normality
123(3)
4.4.3 Spatial Heteroskedasticity
126(5)
4.4.3.1 Introduction
126(2)
4.4.3.2 Testing for Spatial Heteroskedasticity
128(3)
4.4.3.3 Solution to the Problem of Spatial Heteroskedasticity
131(1)
4.4.4 Spatial Invariance of the Parameters
131(4)
4.4.4.1 Testing Parameters' Spatial Invariance
131(3)
4.4.4.2 Estimation in the Presence of Structural Changes
134(1)
5 Italian and European β-convergence Models Revisited 135(12)
5.1 Introduction
135(1)
5.2 A Spatial Econometric Analysis of the Italian Provinces β-convergence Model
135(6)
5.2.1 Violation of the Hypotheses on the Sampling Model
135(3)
5.2.2 Violation of the Hypotheses on the Probabiiity Model
138(3)
5.3 A Spatial Econometric Analysis of the European Regions β-convergence Model
141(6)
5.3.1 Violation of the Hypotheses on the Sampling Model
141(2)
5.3.2 Violation of the Hypotheses on the Probability Model
143(4)
6 Looking Ahead: A Review of More Advanced Topics in Spatial Econometrics 147(16)
6.1 Introduction
147(1)
6.2 Alternative Models
148(8)
6.2.1 Panel Data Models
148(1)
6.2.2 Regional Convergence Models
149(2)
6.2.3 Space-Time Models
151(2)
6.2.4 Discrete Variables
153(1)
6.2.5 Spatial Externalities
153(1)
6.2.6 Bayesian Models
153(1)
6.2.7 Non-parametric Techniques
154(2)
6.3 Alternative Tests
156(3)
6.4 Alternative Estimation Methods
159(3)
6.5 Exploratory Tools
162(1)
Appendix: A Review of the Available Software for Spatial Econometric Analysis 163(4)
A.1 Introduction
163(1)
A.2 The SpaceStat Programme
164(1)
A.3 GeoDa
164(1)
A.4 Toolboxes
165(2)
References 167(24)
List of Tables 191(2)
List of Figures 193(2)
Name Index 195(6)
Subject Index 201

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