Part III Applications
8 Linear Regression and Extensions 111
8.1 Continuous Dependent Variables 111
8.1.1 Normally Distributed Errors 111
8.1.2 Student-t Distributed Errors 114
8.2 Limited Dependent Variables 117
8.2.1 Tobit Model for Censored Data 117
8.2.2 Binary Probit Model 122
8.2.3 Binary Logit Model 126
8.3 Further Reading and References 129
8.4 Exercises 132
9 Multivariate Responses 134
9.1 SUR Model 134
9.2 Multivariate Probit Model 139
9.3 Panel Data 144
9.4 Further Reading and References 149
9.5 Exercises 151
10 Time Series 153
10.1 Autoregressive Models 153
10.2 Regime-Switching Models 158
10.3 Time-Varying Parameters 161
10.4 Time Series Properties of Models for Panel Data 165
10.5 Further Reading and References 166
10.6 Exercises 167
11 Endogenous Covariates and Sample Selection 168
11.1 Treatment Models 168
11.2 Endogenous Covariates 173
11.3 Incidental Truncation 175
11.4 Further Reading and References 179
11.5 Exercises 180
A Probability Distributions and Matrix Theorems 182
A.1 Probability Distributions 182
A.1.1 Bernoulli 182
A.1.2 Binomial 182
A.1.3 Negative Binomial 183
A.1.4 Multinomial 183
A.1.5 Poisson 183
A.1.6 Uniform 183
A.1.7 Gamma 184
A.1.8 Inverted or Inverse Gamma 184
A.1.9 Beta 185
A.1.10 Dirichlet 185
A.1.11 Normal or Gaussian 186
A.1.12 Multivariate and Matricvariate Normal or Gaussian 186
A.1.13 Truncated Normal 188
A.1.14 Univariate Student-t 188
A.1.15 Multivariate t 188
A.1.16 Wishart 190
A.1.17 Inverted or Inverse Wishart 190
A.1.18 Multiplication Rule of Probability 190
A.2 Matrix Theorems 191
B Computer Programs for MCMC Calculations 192
Bibliography 194
Author Index 200
Subject Index 202