Contents

Preface xiii

1 An Overview of Bayesian Econometrics 1

1.1 Bayesian Theory 1

1.2 Bayesian Computation 6

1.3 Bayesian Computer Software 10

1.4 Summary 11

1.5 Exercises 11

2 The Normal Linear Regression Model with Natural Conjugate

Prior and a Single Explanatory Variable 15

2.1 Introduction 15

2.2 The Likelihood Function 16

2.3 The Prior 18

2.4 The Posterior 19

2.5 Model Comparison 23

2.6 Prediction 26

2.7 Empirical Illustration 28

2.8 Summary 31

3 The Normal Linear Regression Model with Natural Conjugate

Prior and Many Explanatory Variables 33

3.1 Introduction 33

3.2 The Linear Regression Model in Matrix Notation 34

3.3 The Likelihood Function 35

3.4 The Prior 36

3.5 The Posterior 36

3.6 Model Comparison 38

3.7 Prediction 45

3.8 Computational Methods: Monte Carlo Integration 46

3.9 Empirical Illustration 47

3.10 Summary 54

3.11 Exercises 54

4 The Normal Linear Regression Model with Other Priors 59

4.1 Introduction 59

4.2 The Normal Linear Regression Model with Independent

Normal-Gamma Prior 60

4.3 The Normal Linear Regression Model Subject

to Inequality Constraints 77

4.4 Summary 85

4.5 Exercises 86

5 The Nonlinear Regression Model 89

5.1 Introduction 89

5.2 The Likelihood Function 91

5.3 The Prior 91

5.4 The Posterior 91

5.5 Bayesian Computation: The Metropolis–Hastings Algorithm 92

5.6 A Measure of Model Fit: The Posterior Predictive P-Value 100

5.7 Model Comparison: The Gelfand–Dey Method 104

5.8 Prediction 106

5.9 Empirical Illustration 107

5.10 Summary 112

6 The Linear Regression Model with General Error

Covariance Matrix 117

6.1 Introduction 117

6.2 The Model with General _ 118

6.3 Heteroskedasticity of Known Form 121

6.4 Heteroskedasticity of an Unknown Form: Student-t Errors 124

6.5 Autocorrelated Errors 130

6.6 The Seemingly Unrelated Regressions Model 137

6.7 Summary 143

6.8 Exercises 144

7 The Linear Regression Model with Panel Data 147

7.1 Introduction 147

7.2 The Pooled Model 148

7.3 Individual Effects Models 149

7.4 The Random Coefficients Model 155

7.5 Model Comparison: The Chib Method of Marginal

Likelihood Calculation 157

7.6 Empirical Illustration 162

7.7 Efficiency Analysis and the Stochastic Frontier Model 168

7.8 Extensions 176

7.9 Summary 177

7.10 Exercises 177

8 Introduction to Time Series: State Space Models 181

8.1 Introduction 181

8.2 The Local Level Model 183

8.3 A General State Space Model 194

8.4 Extensions 202

8.5 Summary 205

9 Qualitative and Limited Dependent Variable Models 209

9.1 Introduction 209

9.2 Overview: Univariate Models for Qualitative and Limited

Dependent Variables 211

9.3 The Tobit Model 212

9.4 The Probit Model 214

9.5 The Ordered Probit Model 218

9.6 The Multinomial Probit Model 221

9.7 Extensions of the Probit Models 229

9.8 Other Extensions 230

9.9 Summary 232

9.10 Exercises 232

10 Flexible Models: Nonparametric and Semiparametric Methods 235

10.1 Introduction 235

10.2 Bayesian Non- and Semiparametric Regression 236

10.3 Mixtures of Normals Models 252

10.4 Extensions and Alternative Approaches 262

10.5 Summary 263

10.6 Exercises 263

11 Bayesian Model Averaging 265

11.1 Introduction 265

11.2 Bayesian Model Averaging in the Normal

Linear Regression Model 266

11.3 Extensions 278

11.4 Summary 280

11.5 Exercises 280

12 Other Models, Methods and Issues 283

12.1 Introduction 283

12.2 Other Methods 284

12.3 Other Issues 288

12.4 Other Models 292

Appendix A: Introduction to Matrix Algebra 311

Appendix B: Introduction to Probability and Statistics 317

B.1 Basic Concepts of Probability 317

B.2 Common Probability Distributions 324

B.3 Introduction to Some Concepts in Sampling Theory 330

B.4 Other Useful Theorems 333

Bibliography 335