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| Introduction | |
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| Spatial dependence | |
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| The spatial autoregressive process | |
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| Spatial autoregressive data generating process | |
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| An illustration of spatial spillovers | |
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| The role of spatial econometric models | |
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| The plan of the text | |
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| Motivating and Interpreting Spatial Econometric Models | |
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| A time-dependence motivation | |
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| An omitted variables motivation | |
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| A spatial heterogeneity motivation | |
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| An externalities-based motivation | |
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| A model uncertainty motivation | |
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| Spatial autoregressive regression models | |
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| Interpreting parameter estimates | |
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| Direct and indirect impacts in theory | |
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| Calculating summary measures of impacts | |
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| Measures of dispersion for the impact estimates | |
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| Partitioning the impacts by order of neighbors | |
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| Simplified alternatives to the impact calculations | |
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| Chapter summary | |
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| Maximum Likelihood Estimation | |
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| Model estimation | |
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| SAR and SDM model estimation | |
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| SEM model estimation | |
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| Estimates for models with two weight matrices | |
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| Estimates of dispersion for the parameters | |
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| A mixed analytical-numerical Hessian calculation | |
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| A comparison of Hessian calculations | |
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| Omitted variables with spatial dependence | |
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| A Hausman test for OLS and SEM estimates | |
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| Omitted variables bias of least-squares | |
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| Omitted variables bias for spatial regressions | |
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| An applied example | |
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| Coefficient estimates | |
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| Cumulative effects estimates | |
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| Spatial partitioning of the impact estimates | |
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| A comparison of impacts from different models | |
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| Chapter summary | |
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| Log-determinants and Spatial Weights | |
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| Determinants and transformations | |
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| Basic determinant computation | |
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| Determinants of spatial systems | |
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| Scalings and similarity transformations | |
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| Determinant domain | |
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| Special cases | |
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| Monte Carlo approximation of the log-determinant | |
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| Sensitivity of � estimates to approximation | |
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| Chebyshev approximation | |
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| Extrapolation | |
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| Determinant bounds | |
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| Inverses and other functions | |
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| Expressions for interpretation of spatial models | |
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| Closed-form solutions for single parameter spatial models | |
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| Forming spatial weights | |
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| Chapter summary | |
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| Bayesian Spatial Econometric Models | |
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| Bayesian methodology | |
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| Conventional Bayesian treatment of the SAR model | |
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| Analytical approaches to the Bayesian method | |
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| Analytical solution of the Bayesian spatial model | |
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| MCMC estimation of Bayesian spatial models | |
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| Sampling conditional distributions | |
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| Sampling for the parameter � | |
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| The MCMC algorithm | |
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| An applied illustration | |
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| Uses for Bayesian spatial models | |
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| Robust heteroscedastic spatial regression | |
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| Spatial effects estimates | |
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| Models with multiple weight matrices | |
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| Chapter summary | |
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| Model Comparison | |
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| Comparison of spatial and non-spatial models | |
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| An applied example of model comparison | |
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| The data sample used | |
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| Comparing models with different weight matrices | |
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| A test for dependence in technical knowledge | |
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| A test of the common factor restriction | |
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| Spatial effects estimates | |
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| Bayesian model comparison | |
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| Comparing models based on different weights | |
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| Comparing models based on different variables | |
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| An applied illustration of model comparison | |
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| An illustration of MC<sup>3</sup> and model averaging | |
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| Chapter summary | |
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| Chapter appendix | |
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| Spatiotemporal and Spatial Models | |
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| Spatiotemporal partial adjustment model | |
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| Relation between spatiotemporal and SAR models | |
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| Relation between spatiotemporal and SEM models | |
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| Covariance matrices | |
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| Monte Carlo experiment | |
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| Spatial econometric and statistical models | |
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| Patterns of temporal and spatial dependence | |
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| Chapter summary | |
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| Spatial Econometric Interaction Models | |
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| Interregional flows in a spatial regression context | |
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| Maximum likelihood and Bayesian estimation | |
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| Application of the spatial econometric interaction model | |
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| Extending the spatial econometric interaction model | |
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| Adjusting spatial weights using prior knowledge | |
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| Adjustments to address the zero flow problem | |
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| Spatially structured multilateral resistance effects | |
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| Flows as a rare event | |
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| Chapter summary | |
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| Matrix Exponential Spatial Models | |
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| The MESS model | |
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| The matrix exponential | |
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| Maximum likelihood estimation | |
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| A closed form solution for the parameters | |
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| An applied illustration | |
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| Spatial error models using MESS | |
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| Spatial model Monte Carlo experiments | |
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| An applied illustration | |
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| A Bayesian version of the model | |
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| The posterior for � | |
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| The posterior for � | |
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| Applied illustrations | |
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| Extensions of the model | |
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| More flexible weights | |
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| MCMC estimation | |
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| MCMC estimation of the model | |
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| The conditional distributions for �, � and V | |
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| Computational considerations | |
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| An illustration of the extended model | |
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| Fractional differencing | |
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| Empirical illustrations | |
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| Computational considerations | |
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| Chapter summary | |
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| Limited Dependent Variable Spatial Models | |
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| Bayesian latent variable treatment | |
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| The SAR probit model | |
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| An MCMC sampler for the SAR probit model | |
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| Gibbs sampling the conditional distribution for y* | |
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| Some observations regarding implementation | |
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| Applied illustrations of the spatial probit model | |
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| Marginal effects for the spatial probit model | |
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| The ordered spatial probit model | |
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| Spatial Tobit models | |
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| An example of the spatial Tobit model | |
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| The multinomial spatial probit model | |
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| The MCMC sampler for the SAR MNP model | |
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| Sampling for � and � | |
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| Sampling for � | |
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| Sampling for &ytilde;* | |
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| An applied illustration of spatial MNP | |
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| Effects estimates for the spatial MNP model | |
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| Spatially structured effects probit models | |
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| Chapter summary | |
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| References | |
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| Index | |