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This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Professor Kenneth E. Train teaches econometrics, regulation, and industrial organization at the University of California, Berkeley. He also serves as Vice President of National Economic Research Associates (NERA), Inc., in San Francisco, California. The author of Optimal Regulation: The Economic Theory of Natural Monopoly (1991) and Qualitative Choice Analysis (1986), Dr. Train has written more than 60 articles on economic theory and regulation. He chaired the Center for Regulatory Policy at the University of California, Berkeley, from 1993 to 2000 and has testified as an expert witness in regulatory proceedings and court cases. He has received numerous awards for his teaching and research.

Introduction | p. 1 |

Motivation | p. 1 |

Choice Probabilities and Integration | p. 3 |

Outline of Book | p. 7 |

A Couple of Notes | p. 8 |

Behavioral Models | |

Properties of Discrete Choice Models | p. 11 |

Overview | p. 11 |

The Choice Set | p. 11 |

Derivation of Choice Probabilities | p. 14 |

Specific Models | p. 17 |

Identification of Choice Models | p. 19 |

Aggregation | p. 29 |

Forecasting | p. 32 |

Recalibration of Constants | p. 33 |

Logit | p. 34 |

Choice Probabilities | p. 34 |

The Scale Parameter | p. 40 |

Power and Limitations of Logit | p. 42 |

Nonlinear Representative Utility | p. 52 |

Consumer Surplus | p. 55 |

Derivatives and Elasticities | p. 57 |

Estimation | p. 60 |

Goodness of Fit and Hypothesis Testing | p. 67 |

Case Study: Forecasting for a New Transit System | p. 71 |

Derivation of Logit Probabilities | p. 74 |

GEV | p. 76 |

Introduction | p. 76 |

Nested Logit | p. 77 |

Three-Level Nested Logit | p. 86 |

Overlapping Nests | p. 89 |

Heteroskedastic Logit | p. 92 |

The GEV Family | p. 93 |

Probit | p. 97 |

Choice Probabilities | p. 97 |

Identification | p. 100 |

Taste Variation | p. 106 |

Substitution Patterns and Failure of IIA | p. 108 |

Panel Data | p. 110 |

Simulation of the Choice Probabilities | p. 114 |

Mixed Logit | p. 134 |

Choice Probabilities | p. 134 |

Random Coefficients | p. 137 |

Error Components | p. 139 |

Substitution Patterns | p. 141 |

Approximation to Any Random Utility Model | p. 141 |

Simulation | p. 144 |

Panel Data | p. 145 |

Case Study | p. 147 |

Variations on a Theme | p. 151 |

Introduction | p. 151 |

Stated-Preference and Revealed-Preference Data | p. 152 |

Ranked Data | p. 156 |

Ordered Responses | p. 159 |

Contingent Valuation | p. 164 |

Mixed Models | p. 166 |

Dynamic Optimization | p. 169 |

Estimation | |

Numerical Maximization | p. 185 |

Motivation | p. 185 |

Notation | p. 185 |

Algorithms | p. 187 |

Convergence Criterion | p. 198 |

Local versus Global Maximum | p. 199 |

Variance of the Estimates | p. 200 |

Information Identity | p. 202 |

Drawing from Densities | p. 205 |

Introduction | p. 205 |

Random Draws | p. 205 |

Variance Reduction | p. 214 |

Simulation-Assisted Estimation | p. 237 |

Motivation | p. 237 |

Definition of Estimators | p. 238 |

The Central Limit Theorem | p. 245 |

Properties of Traditional Estimators | p. 247 |

Properties of Simulation-Based Estimators | p. 250 |

Numerical Solution | p. 257 |

Individual-Level Parameters | p. 259 |

Introduction | p. 259 |

Derivation of Conditional Distribution | p. 262 |

Implications of Estimation of $$ | p. 264 |

Monte Carlo Illustration | p. 267 |

Average Conditional Distribution | p. 269 |

Case Study: Choice of Energy Supplier | p. 270 |

Discussion | p. 280 |

Bayesian Procedures | p. 282 |

Introduction | p. 282 |

Overview of Bayesian Concepts | p. 284 |

Simulation of the Posterior Mean | p. 291 |

Drawing from the Posterior | p. 293 |

Posteriors for the Mean and Variance of a Normal Distribution | p. 294 |

Hierarchical Bayes for Mixed Logit | p. 299 |

Case Study: Choice of Energy Supplier | p. 305 |

Bayesian Procedures for Probit Models | p. 313 |

Endogeneity | p. 315 |

Overview | p. 315 |

The BLP Approach | p. 318 |

Supply Side | p. 328 |

Control Functions | p. 334 |

Maximum Likelihood Approach | p. 340 |

Case Study: Consumers' Choice among New Vehicles | p. 342 |

EM Algorithms | p. 347 |

Introduction | p. 347 |

General Procedure | p. 348 |

Examples of EM Algorithms | p. 355 |

Case Study: Demand for Hydrogen Cars | p. 365 |

Bibliography | p. 371 |

Index | p. 385 |

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