Note continued: 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 --Suggested Problems --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 --Suggested Problems --4. Predictors in Spatial Models --4.1. Preliminaries on pectations --4.2. Information Sets and Predictors of the Dependent Variable --4.3. Mean Squared Errors of the Predictors --Suggested Problems --5. Problems in Estimating Weighting Matrices --5.1. The Spatial Model --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 --Suggested Problems --6. Additional Endogenous Variables: Possible Nonlinearities --6.1. Introductory Comments. Note continued: 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 --6.8. Problems With MLE --Suggested Problems --7. Bayesian Analysis --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 --Suggested Problems --8. Pretest and Sample Selection Issues in Spatial Analysis --8.1. Introductory Comments --8.2.A Preliminary Result --8.3. Illustrations --8.4. Mean Squared Errors. Note continued: 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 --Suggested Problems --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 --Suggested 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. Note continued: Suggested Problems --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 --11.8. The Wald Test --11.9. Spatial Correlation Tests: Comments and Caveats --Suggested Problems --12. Nonnested Models and the J-Test --12.1. Introductory Comments --12.2. The Null Model: Nonparametric Error Terms --12.3. The Alternative Models --12.4. Two Predictors --12.5. The Augmented Equation and the J-Test --12.6. The J-Test: SAR Error Terms --12.7.J-Test and Nonlinear Alternatives --Suggested Problems --13. Endogenous Weighting Matrices: Specifications and Estimation --13.1. Introductory Comments --13.2. The Model. Note continued: 13.3. Issues Concerning Error Term Specification --13.4. Further Specifications --13.5. The Instrument Matrix --13.6. Estimation and Inference --Suggested Problems --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 --Suggested Problems --15. Panel Data Models --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 --Suggested Problems --A. Introduction to Large Sample Theory --A.1. An Intuitive Introduction. Note continued: A.2. Application of the Large Sample Result in (A.1.6) --A.3. More Formalism: Convergence in Probability --A.4. Khinchine's Theorem --A.5. An Important Property of Convergence in Probability --A.6.A Matrix Illustration of Consistency --A.7. eneralizations 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. Spatial Models in R --B.1. Introduction --B.2. Introductory Tools --B.3. Reading Data and Creating Weights --B.4. Estimating Spatial Models.