<P>contents</P>

<P>Statistical Analysis of Discrete Probability Models
Alternative Estimators and Sample Designs for Discrete
Choice Analysis
Charles F. Manski and Daniel McFadden
Introduction
The Likelihood of an Observation under Alternative
Stratified Sampling Processes
Estimation of the Choice Model Parameters
Estimation with p and Q Both Known
Estimation with p Known and Q Unknown
Estimation with p Unknown and Q Known
Estimation with p and Q Both Unknown
Estimation in a General Stratified Sample
Selection of a Sample Design and Estimation Method
Conclusion
Appendix : Consistency of the Estimators
Appendix : Asymptotic Normality
References
Efficient Estimation of Discrete-Choice Models
Stephen R. Cosslett
Introduction
Discrete Choice Models
Stratified Sampling and Choice-Based Sampling
Generalized Choice-Based Sample
Sample with Known Aggregate Shares
Aggregate Shares Estimated from an Auxiliary Sample
Supplemented Sample
General Considerations in Maximum Likelihood
Estimation
Notation for a General Choice-Based Sample
The Likelihood Function for Choice-Based Samples
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xvii
Contents
Maximization of the Likelihood
Asymptotic Properties of the Unconstrained Estimator
Estimation of Aggregate Shares
The Unconstrained Maximum Likelihood Estimator
The Logit Model as a Special Case
Estimation with Known Aggregate Shares
Consistency of the Constraint Equations
Asymptotic Properties with Known Aggregate Shares
The Constrained Maximum Likelihood Estimator
Estimation of the Logit Model with Known Aggregate
Shares
Estimation with Aggregate Shares Inferred from an
Auxiliary Sample
Asymptotic Variance of the Auxiliary Sample Estimator
Special Cases of the Auxiliary Sample Estimator
Estimation with a Supplementary Sample
Comparison of Estimators and Sample Designs
Appendix : Conditions on the Choice Probability Model
Appendix : Derivation of Asymptotic Properties
Appendix : Alternative Estimators for Generalized
Choice-Based Samples with Known Aggregate Shares
References
Dynamic Discrete Probability Models
Statistical Models for Discrete Panel Data
James J. Heckman
Introduction
A Framework for Analyzing Dynamic Choice
The General Model
An Independent Trials Bernoulli Model
A Random Effect Bernoulli Model and One-Factor
Schemes
A Fixed Effect Bernoulli Model
Models with General Correlation in the Errors: The
Concept of Heterogeneity Extended
Models with Structural State Dependence
A Renewal Model
Contents vii
A Model with Habit Persistence
Computation in the General Model
A Summary of Sections 3.2 through 3.11
Heterogeneity versus Structural State Dependence: An
Application of the Preceding Models
Testing for Heterogeneity versus State Dependence
Analogies with Time-Series Models
Examples of Models that Generate Structural State
Dependence
Summary and Conclusion
Appendix : Factor Analytic Probit Models
References
4 The Incidental Parameters Problem and the Problem of
Initial Conditions in Estimating a Discrete Time-Discrete
Data Stochastic Process
James J. Heckman
4.1 Introduction 179
4.2 The Problem of Initial Conditions and Some Formal
Solutions 181
4.3 Simpler Solutions and the Problem of Incidental
Parameters 185
4.4 Some Monte Carlo Evidence 189
4.5 Conclusions 194
References 195
Structural Discrete Probability Models Derived from
Theories of Choice
Econometric Models of Probabilistic Choice
Daniel McFadden
Economic Man
Discrete Choice
Probabilistic Consumer Theory
Probabilistic Choice Systems
The Random Utility Maximization Hypothesis
Stochastic Revealed Preference
Contents
Aggregation of Preferences
The Williams-Daly-Zachary Theorem
Criteria for Parametric Probabilistic Choice Systems
Specification of Variables
Functional Form
The Luce Model
Thurstone's Model V
Tversky Elimination Models
Generalized Extreme Value Models
Preference Trees
Estimation of Tree Extreme Value Models
Sequential Estimation
An Application
Appendix: Normalization in MNL and MNP Models
Appendix: Computational Formulas for a Simple Model
Appendix : Computational Formulas for the Nested
Multinornial Logit Model
Appendix : Proof of Theorem 5.1
Appendix : The Elimination-by-Strategy Model
References
Random versus Fixed Coefficient Quantal Choice Models
Gregory W. Fischer and Daniel Nagin
Introduction
Quantal Choice Theory and Variation in Tastes
An Empirical Comparison of the LPIID and RCCD
Models
Details of the Experiment
Results
Analysis of Individual Respondents
A Comparison of LPIID Probit and RCCD Probit
Estimation
Conclusions
Appendix : The Unestimable Models
Appendix: Mean Taste Estimates in the LPIID and
RCCD Models
References
Contents
On the Use of Simulated Frequencies to Approximate
Choice Probabilities
Steven R. Lerman and Charles F. Manski
Introduction
The Simulated Frequency Method
Bayesian Approach
Estimation of a Function of a Collection of Probabilities
Application to the Calculation of Multinomial Probit
Choice Probabilities
The Simulation Routine
The Clark Method
Numerical Test Objectives and Design
Test Results and Analysis
Conclusions
References
Application of a Continuous Spatial Choice Logit Model
Moshe Ben-Akiva and Thawat Watanatada
Introduction
Basic Definitions
Spatial Aggregation
The Discrete Logit Model
Spatial Aggregation Using Continuous Functions
The Continuous Logit Model
A Parametric Example of Spatial Aggregation
Continuous Logit with Featureless Plane
Basic Operations of the MIT-TRANS Model
References
Simultaneous Equations Models with Discrete Endogenous
Variables
Simultaneous Equations Models with Discrete and
Censored Variables
Lung-Fei Lee
Introduction
Contents
Two-Stage Methods and Amemiya's Principle
Structural Equations with Probit Structure
Structural Equations with Observable Continuous
Endogenous Variables
Structural Equations with Censored Dependent Variables
Structural Equations with Tobit Structure
Switching and Censored Models with Sample Separation
Information
Conclusion
References
Stratification on Endogenous Variables and Estimation: The
Gary Income Maintenance Experiment
Jerry A. Hausman and David A. Wise
Introduction
The Problem of Endogenous Sampling and Estimation
Methods
Relative Efficiencies of Weighted Least Squares versus
Maximum Likelihood Estimates
Empirical Results of the Selection Bias in the Gary
Income Maintenance Experiment
Alternative Sampling Procedures
Conclusion
Appendix: Extension of the Analysis to Two Time
Periods and Two Equations
References
A Switching Simultaneous Equations Model of Physician
Behavior in Ontario
Dale J. Poirier
Introduction
Econometric Model
Estimation
Estimation of the Switching (Option) Equation
Empirical Results
Estimated Option Equation
Estimated Referral Equation
Contents
11.8 Concluding Remarks
References
12 Constraints on the Parameters in Simultaneous Tobit and
Probit Models
Peter Schmidt
12.1 Introduction
12.2 Simultaneous Tobit Models
12.3 All Endogenous Variables Truncated
12.4 Some Endogenous Variables Truncated
12.5 Both Y and Y* as Explanatory Variables
12.6 Simultaneous Probit Models
12.7 All Endogenous Variables Truncated
12.8 Some Endogenous Variables Truncated
12.9 Both Y and Y* as Explanatory Variables
12.10 Conclusions
References
Estimating Credit Constraints by Switching Regressions
Robert B. Avery
Introduction
The Supply of Debt
The Model and Data
Simultaneous Switching Regression and Linear
Equations
The Evidence
Qualifications and Evaluations
Appendix : Proof of Theorem 13.1
Appendix : Empirical Reduced Form Equations
References
Index</P>