ISBN: 354032304x
TITLE: Spatial Econometrics
AUTHOR: Arbia
TOC: 

1 Motivation 3
1.1 Introduction 3
1.2 Theoretical Economic Models Calling for Spatial Econometric Techniques 7
1.2.1 Introduction 7
1.2.2 The ?-convergence Approach 8
1.3 A ?-convergence Analysis of European and Italian Regions 14
1.3.1 Introduction 14
1.3.2 A ?-convergence Analysis of Italian NUTS-3 Provinces (1951-1999) 16
1.3.3 A ?-convergence Analysis of European NUTS-2 Regions (1980-1996) 22
2 Random Fields and Spatial Models 29
2.1 Introduction 29
2.2 The Concept of a Random Field 31
2.2.1 The Nature of the Index S 32
2.2.1.1 Generalities 32
2.2.1.2 The Topology of a Random Field 34
2.2.2 The Dependence Structure of a Random Field 37
2.3 Restrictions on Random Fields 41
2.3.1 Restrictions an the Spatial Heterogeneity of a Random Field 41
2.3.2 Restrictions on The Spatial Dependence of a Random Field 44
2.4 Some Special Random Fields 47
2.4.1 Spatial White Noise 47
2.4.2 Markov Random Fields 47
2.4.2.1 Generalities 47
2.4.2.2 The Hammersley and Clifford Theorem 48
2.4.2.3 Ising's Law 50
2.4.2.4 The Strauss Auto-model 53
2.4.2.5 The Auto-binomial Field 54
2.4.2.6 The Auto-Poisson Model 55
2.4.2.7 The Auto-normal (or CAR) Field 55
2.4.2.8 The Intrinsic Gaussian Field 56
2.4.2.9 The Bivariate Auto-normal Field .57
2.4.2. 10 The Multivariate Auto-normal (or MCAR) Field 58
2.4.3 Non-Markovian Fields 61
2.4.3.1 The Simultaneous Autoregressive Random Field (SAR) 61
2.4.3.2 The Moving Average Random Field 63
2.4.3.3 The Autoregressive Moving Average Random Field 64
2.4.3.4 The Spatial Error Component Random Field 64
2.4.3.5 The Direct Representation of a Random Field 65
2.5 Limiting Theorems for Random Fields 66
2.5.1 Introduction 66
2.5.2 Some Limit Theorems for Random Fields 67
3 Likelihood Function for Spatial Samples 71
3.1 Introduction 71
3.2 Some Approximations for the Likelihood of Random Fields 74
3.2.1 The Coding Technique 74
3.2.2 The Unilateral Approximation 75
3.2.3 The Pseudo-Likelihood  la Besag 77
3.2.4 Computational Aspects 78
3.3 Maximum Likelihood Estimation Properties in Spatial Samples 79
3.4 Tests Based on Likelihood: 79
3.5 Tests Based on Residual Sums of Squares 82
4 The Linear Regression Model with Spatial Data 83
4.1 Introduction 83
4.2 Specification of a Linear Regression Model 83
4.2.1 The Conditional Specification .84
4.2.1.1 Hypotheses on the Probability Model (PM) 84
4.2.1.2 Hypotheses an the Statistical Generating
Mechanism (GM) 85
4.2.1.3 Hypotheses an the Sampling Model (SM) 86
4.2.2 Standard Textbook Specification 86
4.3 Violation of the Hypotheses an the Sampling Model 88
4.3.1 Introduction 88
4.3.2 A General-Purpose Testing Procedure for Spatial Independence 89
4.3.3 The Respecification of the Linear Regression as a Multivariate CAR Field 91
4.3.3.1 Introduction 91
4.3.3.2 Respecification of the PM, GM and SM Hypotheses 92
4.3.3.3 Likelihood of a Bivariate CAR Spatial Linear Regression Model 94
4.3.3.4 Hypothesis Testing in the Bivariate CAR Spatial Linear Regression Model 96
4.3.3.5 Likelihood of a Multivariate CAR Spatial LinearRegression Model 98
4.3.4 The Respecification of the Linear Regression with SAR Residuals (the Spatial Error Model) 98
4.3.4.1 Introduction 98
4.3.4.2 Derivation of the Likelihood 100
4.3.4.3 Equivalence of the Statistical Model Implied by the Bivariate CAR and the SAR Residual 101
4.3.4.4 Hypothesis Testing in the Spatial Error Model 103
4.3.4.5 Generalized Least Squares Estimators 104
4.3.4.6 Approximate Estimation Techniques 106
4.3.5 The Re-specification of the Linear Regression by Adding a Spatial Lag (the Spatial Lag Model) 108
4.3.5.1 Introduction 108
4.3.5.2 Derivation of the Likelihood 108
4.3.5.3 Estimation 111
4.3.5.4 Hypothesis Testing 113
4.3.6 Anselin's General Spatial Model 114
4.4 Violation of the Hypotheses an the Probability Model 118
4.4.1 Introduction 118
4.4.2 Normality 118
4.4.2.1 Generalities 118
4.4.2.2 Testing for Departures from Normality 119
4.4.2.3 Solutions to the Problem of Non-normality 121
4.4.3 Spatial Heteroskedasticity 124
4.4.3.1 Introduction 124
4.4.3.2 Testing for Spatial Heteroskedasticity 126
4.4.3.3 Solution to the Problem of Spatial Heteroskedasticity 129
4.4.4 Spatial Invariante of the Parameters 129
4.4.4.1 Testing Parameters Spatial Invariante 129
4.4.4.2 Estimation in the Presence of Structural Changes 132
5 Italian and European ?-convergence Models Revisited 133
5.1 Introduction 133
5.2 A Spatial Econometric Analysis of the Italian Provinces ?-convergence Model 133
5.2.1 Violation of the Hypotheses an the Sampling Model 133
5.2.2 Violation of the Hypotheses an the Probability Model 136
5.3 A Spatial Econometric Analysis of the European Regions ?-convergence Model 139
5.3.1 Violation of the Hypotheses an the Sampling Model 139
5.3.2 Violation of the Hypotheses an the Probability Model 141
6 Looking Ahead: A Review of More Advanced Topics in Spatial Econometrics 145
6.1 Introduction 145
6.2 Alternative Models 146
6.2.1 Panel Data Models 146
6.2.2 Regional Convergence Models 147
6.2.3 Spate-Time Models 149
6.2.4 Discrete Variables 151
6.2.5 Spatial Externalities 151
6.2.6 Bayesian Models 151
6.2.7 Non-parametric Techniques 152
6.3 Alternative Tests 154
6.4 Alternative Estimation Methods 157
6.5 Exploratory Tools 160
Appendix: A Review of the Available Software for Spatial
Econometric Analysis 161
A.1 Introduction 161
A.2 The SpaceStat Programme 162
A.3 GeoDa 162
A.4 Toolboxes 163
References 165
List of Tables 189
List of Figures 191
Name Index 193
Subject Index 199
END
