| Motivation | p. 3 |
| Introduction | p. 3 |
| Theoretical Economic Models Calling for Spatial Econometric Techniques | p. 7 |
| Introduction | p. 7 |
| The ß-convergence Approach | p. 8 |
| A ß-convergence Analysis of European and Italian Regions | p. 14 |
| Introduction | p. 14 |
| A ß-convergence Analysis of Italian NUTS-3 Provinces (1951-1999) | p. 16 |
| A ß-convergence Analysis of European NUTS-2 Regions (1980-1996) | p. 22 |
| Random Fields and Spatial Models | p. 29 |
| Introduction | p. 29 |
| The Concept of a Random Field | p. 31 |
| The Nature of the Index <$>\cal {S}<$> | p. 32 |
| Generalities | p. 32 |
| The Topology of a Random Field | p. 34 |
| The Dependence Structure of a Random Field | p. 37 |
| Restrictions on Random Fields | p. 41 |
| Restrictions on the Spatial Heterogeneity of a Random Field | p. 41 |
| Restrictions on The Spatial Dependence of a Random Field | p. 44 |
| Some Special Random Fields | p. 47 |
| Spatial White Noise | p. 47 |
| Markov Random Fields | p. 47 |
| Generalities | p. 47 |
| The Flammersley and Clifford Theorem | p. 48 |
| Ising's Law | p. 50 |
| The Strauss Auto-model | p. 53 |
| The Auto-binomial Field | p. 54 |
| The Auto-Poisson Model | p. 55 |
| The Auto-normal (or CAR) Field | p. 55 |
| The Intrinsic Gaussian Field | p. 56 |
| The Bivariate Auto-normal Field | p. 57 |
| To he Multivariate Auto-normal (or MCAR) Field | p. 58 |
| Non-Markovian Fields | p. 61 |
| The Simultaneous Autoregressive Random Field (SAR) | p. 61 |
| The Moving Average Random Field | p. 63 |
| The Autoregressive Moving Average Random Field | p. 64 |
| The Spatial Error Component Random Field | p. 64 |
| The Direct Representation of a Random Field | p. 65 |
| Limiting Theorems for Random Fields | p. 66 |
| Introduction | p. 66 |
| Some Limit Theorems for Random Fields | p. 67 |
| Likelihood Function for Spatial Samples | p. 71 |
| Introduction | p. 71 |
| Some Approximations for the Likelihood of Random Fields | p. 74 |
| The Coding Technique | p. 74 |
| The Unilateral Approximation | p. 75 |
| The Pseudo-Likelihood à la Besag | p. 77 |
| Computational Aspects | p. 78 |
| Maximum Likelihood Estimation Properties in Spatial Samples | p. 79 |
| Tests Based on Likelihood | p. 79 |
| Tests Based on Residual Sums of Squares | p. 82 |
| The Linear Regression Model with Spatial Data | p. 83 |
| Introduction | p. 83 |
| Specification of a Linear Regression Model | p. 83 |
| The Conditional Specification | p. 84 |
| Hypotheses on the Probability Model (PM) | p. 84 |
| Hypotheses on the Statistical Generating Mechanism (GM) | p. 85 |
| Hypotheses on the Sampling Model (SM) | p. 86 |
| Standard Textbook Specification | p. 86 |
| Violation of the Hypotheses on the Sampling Model | p. 88 |
| Introduction | p. 88 |
| A General-Purpose Testing Procedure for Spatial Independence | p. 89 |
| The Respecification of the Linear Regression as a Multivariate CAR Field | p. 91 |
| Introduction | p. 91 |
| Respecification of the PM, GM and SM Hypotheses | p. 92 |
| Likelihood of a Bivariate CAR Spatial Linear Regression Model | p. 94 |
| Hypothesis Testing in the Bivariate CAR Spatial Linear Regression Model | p. 96 |
| Likelihood of a Multivariate CAR Spatial Linear Regression Model | p. 98 |
| The Respecification of the Linear Regression with SAR Residuals (the Spatial Error Model) | p. 98 |
| Introduction | p. 98 |
| Derivation of the Likelihood | p. 100 |
| Equivalence of the Statistical Model Implied by the Bivariate CAR and the SAR Residual | p. 101 |
| Flypothesis Testing in the Spatial Error Model | p. 103 |
| Generalized Least Squares Estimators | p. 104 |
| Approximate Estimation Techniques | p. 106 |
| The Re-specification of the Linear Regression by Adding a Spatial Lag (the Spatial Lag Model) | p. 108 |
| Introduction | p. 108 |
| Derivation of the Likelihood | p. 108 |
| Estimation | p. 111 |
| Hypothesis Testing | p. 113 |
| Anselin's General Spatial Model | p. 114 |
| Violation of the Hypotheses on the Probability Model | p. 118 |
| Introduction | p. 118 |
| Normality | p. 118 |
| Generalities | p. 118 |
| Testing for Departures from Normality | p. 119 |
| Solutions to the Problem of Non-normality | p. 121 |
| Spatial Heteroskedasticity | p. 124 |
| Introduction | p. 124 |
| Testing for Spatial Heteroskedasticity | p. 126 |
| Solution to the Problem of Spatial Heteroskedasticity | p. 129 |
| Spatial Invariance of the Parameters | p. 129 |
| Testing Parameters' Spatial Invariance | p. 129 |
| Estimation in the Presence of Structural Changes | p. 132 |
| Italian and European ß-convergence Models Revisited | p. 133 |
| Introduction | p. 133 |
| A Spatial Econometric Analysis of the Italian Provinces ß-convergence Model | p. 133 |
| Violation of the Hypotheses on the Sampling Model | p. 133 |
| Violation of the Hypotheses on the Probability Model | p. 136 |
| A Spatial Econometric Analysis of the European Regions ß-convergence Model | p. 139 |
| Violation of the Hypotheses on the Sampling Model | p. 139 |
| Violation of the Hypotheses on the Probability Model | p. 141 |
| Looking Ahead: A Review of More Advanced Topics in Spatial Econometrics | p. 145 |
| Introduction | p. 145 |
| Alternative Models | p. 146 |
| Panel Data Models | p. 146 |
| Regional Convergence Models | p. 147 |
| Space-Time Models | p. 149 |
| Discrete Variables | p. 151 |
| Spatial Externalities | p. 151 |
| Bayesian Models | p. 151 |
| Non-parametric Techniques | p. 152 |
| Alternative Tests | p. 154 |
| Alternative Estimation Methods | p. 157 |
| Exploratory Tools | p. 160 |
| Appendix: A Review of the Available Software for Spatial Econometric Analysis | p. 161 |
| Introduction | p. 161 |
| The Space Stat Programme | p. 162 |
| Geo Da | p. 162 |
| Toolboxes | p. 163 |
| References | p. 165 |
| List of Tables | p. 189 |
| List of Figures | p. 191 |
| Name Index | p. 193 |
| Subject Index | p. 199 |
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