Gary Koop is Professor of Economics at the University of Glasgow.

• Preface xiii1 An Overview of Bayesian Econometrics 11.1 Bayesian Theory 11.2 Bayesian Computation 61.3 Bayesian Computer Software 101.4 Summary 111.5 Exercises 112 The Normal Linear Regression Model with Natural Conjugate Prior and a Single Explanatory Variable 152.1 Introduction 152.2 The Likelihood Function 162.3 The Prior 182.4 The Posterior 192.5 Model Comparison 232.6 Prediction 262.7 Empirical Illustration 282.8 Summary 312.9 Exercises 313 The Normal Linear Regression Model with Natural Conjugate Prior and Many Explanatory Variables 333.1 Introduction 333.2 The Linear Regression Model in Matrix Notation 343.3 The Likelihood Function 353.4 The Prior 363.5 The Posterior 363.6 Model Comparison 383.7 Prediction 453.8 Computational Methods: Monte Carlo Integration 463.9 Empirical Illustration 473.10 Summary 543.11 Exercises 544 The Normal Linear Regression Model with Other Priors 594.1 Introduction 594.2 The Normal Linear Regression Model with Independent Normal-Gamma Prior 604.3 The Normal Linear Regression Model Subject to Inequality Constraints 774.4 Summary 854.5 Exercises 865 The Nonlinear Regression Model 895.1 Introduction 895.2 The Likelihood Function 915.3 The Prior 915.4 The Posterior 915.5 Bayesian Computation: The Metropolis–Hastings Algorithm 925.6 A Measure of Model Fit: The Posterior Predictive P-Value 1005.7 Model Comparison: The Gelfand–Dey Method 1045.8 Prediction 1065.9 Empirical Illustration 1075.10 Summary 1125.11 Exercises 1136 The Linear Regression Model with General Error Covariance Matrix 1176.1 Introduction 1176.2 The Model with General 1186.3 Heteroskedasticity of Known Form 1216.4 Heteroskedasticity of an Unknown Form: Student-t Errors 1246.5 Autocorrelated Errors 1306.6 The Seemingly Unrelated Regressions Model 1376.7 Summary 1436.8 Exercises 1447 The Linear Regression Model with Panel Data 1477.1 Introduction 1477.2 The Pooled Model 1487.3 Individual Effects Models 1497.4 The Random Coefficients Model 1557.5 Model Comparison: The Chib Method of Marginal Likelihood Calculation 1577.6 Empirical Illustration 1627.7 Efficiency Analysis and the Stochastic Frontier Model 1687.8 Extensions 1767.9 Summary 1777.10 Exercises 1778 Introduction to Time Series: State Space Models 1818.1 Introduction 1818.2 The Local Level Model 1838.3 A General State Space Model 1948.4 Extensions 2028.5 Summary 2058.6 Exercises 2069 Qualitative and Limited Dependent Variable Models 2099.1 Introduction 2099.2 Overview: Univariate Models for Qualitative and Limited Dependent Variables 2119.3 The Tobit Model 2129.4 The Probit Model 2149.5 The Ordered Probit Model 2189.6 The Multinomial Probit Model 2219.7 Extensions of the Probit Models 2299.8 Other Extensions 2309.9 Summary 2329.10 Exercises 23210 Flexible Models: Nonparametric and Semiparametric Methods 23510.1 Introduction 23510.2 Bayesian Non- and Semiparametric Regression 23610.3 Mixtures of Normals Models 25210.4 Extensions and Alternative Approaches 26210.5 Summary 26310.6 Exercises 26311 Bayesian Model Averaging 26511.1 Introduction 26511.2 Bayesian Model Averaging in the Normal Linear Regression Model 26611.3 Extensions 27811.4 Summary 28011.5 Exercises 28012 Other Models, Methods and Issues 28312.1 Introduction 28312.2 Other Methods 28412.3 Other Issues 28812.4 Other Models 29212.5 Summary 308Appendix A: Introduction to Matrix Algebra 311Appendix B: Introduction to Probability and Statistics 317B.1 Basic Concepts of Probability 317B.2 Common Probability Distributions 324B.3 Introduction to Some Concepts in Sampling Theory 330B.4 Other Useful Theorems 333Bibliography 335Index 347

Gary Koop is Professor of Economics at the University of Glasgow.

• Preface xiii1 An Overview of Bayesian Econometrics 11.1 Bayesian Theory 11.2 Bayesian Computation 61.3 Bayesian Computer Software 101.4 Summary 111.5 Exercises 112 The Normal Linear Regression Model with Natural Conjugate Prior and a Single Explanatory Variable 152.1 Introduction 152.2 The Likelihood Function 162.3 The Prior 182.4 The Posterior 192.5 Model Comparison 232.6 Prediction 262.7 Empirical Illustration 282.8 Summary 312.9 Exercises 313 The Normal Linear Regression Model with Natural Conjugate Prior and Many Explanatory Variables 333.1 Introduction 333.2 The Linear Regression Model in Matrix Notation 343.3 The Likelihood Function 353.4 The Prior 363.5 The Posterior 363.6 Model Comparison 383.7 Prediction 453.8 Computational Methods: Monte Carlo Integration 463.9 Empirical Illustration 473.10 Summary 543.11 Exercises 544 The Normal Linear Regression Model with Other Priors 594.1 Introduction 594.2 The Normal Linear Regression Model with Independent Normal-Gamma Prior 604.3 The Normal Linear Regression Model Subject to Inequality Constraints 774.4 Summary 854.5 Exercises 865 The Nonlinear Regression Model 895.1 Introduction 895.2 The Likelihood Function 915.3 The Prior 915.4 The Posterior 915.5 Bayesian Computation: The Metropolis–Hastings Algorithm 925.6 A Measure of Model Fit: The Posterior Predictive P-Value 1005.7 Model Comparison: The Gelfand–Dey Method 1045.8 Prediction 1065.9 Empirical Illustration 1075.10 Summary 1125.11 Exercises 1136 The Linear Regression Model with General Error Covariance Matrix 1176.1 Introduction 1176.2 The Model with General 1186.3 Heteroskedasticity of Known Form 1216.4 Heteroskedasticity of an Unknown Form: Student-t Errors 1246.5 Autocorrelated Errors 1306.6 The Seemingly Unrelated Regressions Model 1376.7 Summary 1436.8 Exercises 1447 The Linear Regression Model with Panel Data 1477.1 Introduction 1477.2 The Pooled Model 1487.3 Individual Effects Models 1497.4 The Random Coefficients Model 1557.5 Model Comparison: The Chib Method of Marginal Likelihood Calculation 1577.6 Empirical Illustration 1627.7 Efficiency Analysis and the Stochastic Frontier Model 1687.8 Extensions 1767.9 Summary 1777.10 Exercises 1778 Introduction to Time Series: State Space Models 1818.1 Introduction 1818.2 The Local Level Model 1838.3 A General State Space Model 1948.4 Extensions 2028.5 Summary 2058.6 Exercises 2069 Qualitative and Limited Dependent Variable Models 2099.1 Introduction 2099.2 Overview: Univariate Models for Qualitative and Limited Dependent Variables 2119.3 The Tobit Model 2129.4 The Probit Model 2149.5 The Ordered Probit Model 2189.6 The Multinomial Probit Model 2219.7 Extensions of the Probit Models 2299.8 Other Extensions 2309.9 Summary 2329.10 Exercises 23210 Flexible Models: Nonparametric and Semiparametric Methods 23510.1 Introduction 23510.2 Bayesian Non- and Semiparametric Regression 23610.3 Mixtures of Normals Models 25210.4 Extensions and Alternative Approaches 26210.5 Summary 26310.6 Exercises 26311 Bayesian Model Averaging 26511.1 Introduction 26511.2 Bayesian Model Averaging in the Normal Linear Regression Model 26611.3 Extensions 27811.4 Summary 28011.5 Exercises 28012 Other Models, Methods and Issues 28312.1 Introduction 28312.2 Other Methods 28412.3 Other Issues 28812.4 Other Models 29212.5 Summary 308Appendix A: Introduction to Matrix Algebra 311Appendix B: Introduction to Probability and Statistics 317B.1 Basic Concepts of Probability 317B.2 Common Probability Distributions 324B.3 Introduction to Some Concepts in Sampling Theory 330B.4 Other Useful Theorems 333Bibliography 335Index 347

Gary Koop is Professor of Economics at the University of Glasgow.

• Preface xiii1 An Overview of Bayesian Econometrics 11.1 Bayesian Theory 11.2 Bayesian Computation 61.3 Bayesian Computer Software 101.4 Summary 111.5 Exercises 112 The Normal Linear Regression Model with Natural Conjugate Prior and a Single Explanatory Variable 152.1 Introduction 152.2 The Likelihood Function 162.3 The Prior 182.4 The Posterior 192.5 Model Comparison 232.6 Prediction 262.7 Empirical Illustration 282.8 Summary 312.9 Exercises 313 The Normal Linear Regression Model with Natural Conjugate Prior and Many Explanatory Variables 333.1 Introduction 333.2 The Linear Regression Model in Matrix Notation 343.3 The Likelihood Function 353.4 The Prior 363.5 The Posterior 363.6 Model Comparison 383.7 Prediction 453.8 Computational Methods: Monte Carlo Integration 463.9 Empirical Illustration 473.10 Summary 543.11 Exercises 544 The Normal Linear Regression Model with Other Priors 594.1 Introduction 594.2 The Normal Linear Regression Model with Independent Normal-Gamma Prior 604.3 The Normal Linear Regression Model Subject to Inequality Constraints 774.4 Summary 854.5 Exercises 865 The Nonlinear Regression Model 895.1 Introduction 895.2 The Likelihood Function 915.3 The Prior 915.4 The Posterior 915.5 Bayesian Computation: The Metropolis–Hastings Algorithm 925.6 A Measure of Model Fit: The Posterior Predictive P-Value 1005.7 Model Comparison: The Gelfand–Dey Method 1045.8 Prediction 1065.9 Empirical Illustration 1075.10 Summary 1125.11 Exercises 1136 The Linear Regression Model with General Error Covariance Matrix 1176.1 Introduction 1176.2 The Model with General 1186.3 Heteroskedasticity of Known Form 1216.4 Heteroskedasticity of an Unknown Form: Student-t Errors 1246.5 Autocorrelated Errors 1306.6 The Seemingly Unrelated Regressions Model 1376.7 Summary 1436.8 Exercises 1447 The Linear Regression Model with Panel Data 1477.1 Introduction 1477.2 The Pooled Model 1487.3 Individual Effects Models 1497.4 The Random Coefficients Model 1557.5 Model Comparison: The Chib Method of Marginal Likelihood Calculation 1577.6 Empirical Illustration 1627.7 Efficiency Analysis and the Stochastic Frontier Model 1687.8 Extensions 1767.9 Summary 1777.10 Exercises 1778 Introduction to Time Series: State Space Models 1818.1 Introduction 1818.2 The Local Level Model 1838.3 A General State Space Model 1948.4 Extensions 2028.5 Summary 2058.6 Exercises 2069 Qualitative and Limited Dependent Variable Models 2099.1 Introduction 2099.2 Overview: Univariate Models for Qualitative and Limited Dependent Variables 2119.3 The Tobit Model 2129.4 The Probit Model 2149.5 The Ordered Probit Model 2189.6 The Multinomial Probit Model 2219.7 Extensions of the Probit Models 2299.8 Other Extensions 2309.9 Summary 2329.10 Exercises 23210 Flexible Models: Nonparametric and Semiparametric Methods 23510.1 Introduction 23510.2 Bayesian Non- and Semiparametric Regression 23610.3 Mixtures of Normals Models 25210.4 Extensions and Alternative Approaches 26210.5 Summary 26310.6 Exercises 26311 Bayesian Model Averaging 26511.1 Introduction 26511.2 Bayesian Model Averaging in the Normal Linear Regression Model 26611.3 Extensions 27811.4 Summary 28011.5 Exercises 28012 Other Models, Methods and Issues 28312.1 Introduction 28312.2 Other Methods 28412.3 Other Issues 28812.4 Other Models 29212.5 Summary 308Appendix A: Introduction to Matrix Algebra 311Appendix B: Introduction to Probability and Statistics 317B.1 Basic Concepts of Probability 317B.2 Common Probability Distributions 324B.3 Introduction to Some Concepts in Sampling Theory 330B.4 Other Useful Theorems 333Bibliography 335Index 347