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• Title Page
• Copyright Page
• Brief Contents
• Contents
• Examples and Applications
• Preface
• Part I: The Linear Regression Model
• CHAPTER 1 Econometrics
• 1.1 Introduction
• 1.2 The Paradigm of Econometrics
• 1.3 The Practice of Econometrics
• 1.4 Microeconometrics and Macroeconometrics
• 1.5 Econometric Modeling
• 1.6 Plan of the Book
• 1.7 Preliminaries
• 1.7.1 Numerical Examples
• 1.7.2 Software and Replication
• 1.7.3 Notational Conventions
• CHAPTER 2 The Linear Regression Model
• 2.1 Introduction
• 2.2 The Linear Regression Model
• 2.3 Assumptions of the Linear Regression Model
• 2.3.1 Linearity of the Regression Model
• 2.3.2 Full Rank
• 2.3.3 Regression
• 2.3.4 Homoscedastic and Nonautocorrelated Disturbances
• 2.3.5 Data Generating Process for the Regressors
• 2.3.6 Normality
• 2.3.7 Independence and Exogeneity
• 2.4 Summary and Conclusions
• CHAPTER 3 Least Squares Regression
• 3.1 Introduction
• 3.2 Least Squares Regression
• 3.2.1 The Least Squares Coefficient Vector
• 3.2.2 Application: An Investment Equation
• 3.2.3 Algebraic Aspects of the Least Squares Solution
• 3.2.4 Projection
• 3.3 Partitioned Regression and Partial Regression
• 3.4 Partial Regression and Partial Correlation Coefficients
• 3.5 Goodness of Fit and the Analysis of Variance
• 3.5.1 The Adjusted R-Squared and a Measure of Fit
• 3.5.2 R-Squared and the Constant Term in the Model
• 3.5.3 Comparing Models
• 3.6 Linearly Transformed Regression
• 3.7 Summary and Conclusions
• CHAPTER 4 Estimating the Regression Model by Least Squares
• 4.1 Introduction
• 4.2 Motivating Least Squares
• 4.2.1 Population Orthogonality Conditions
• 4.2.2 Minimum Mean Squared Error Predictor
• 4.2.3 Minimum Variance Linear Unbiased Estimation
• 4.3 Statistical Properties of the Least Squares Estimator
• 4.3.1 Unbiased Estimation
• 4.3.2 Omitted Variable Bias
• 4.3.3 Inclusion of Irrelevant Variables
• 4.3.4 Variance of the Least Squares Estimator
• 4.3.5 The Gauss–Markov Theorem
• 4.3.6 The Normality Assumption
• 4.4 Asymptotic Properties of the Least Squares Estimator
• 4.4.1 Consistency of the Least Squares Estimator of ß
• 4.4.2 The Estimator of Asy. Var[b]
• 4.4.3 Asymptotic Normality of the Least Squares Estimator
• 4.4.4 Asymptotic Efficiency
• 4.4.5 Linear Projections
• 4.5 Robust Estimation and Inference
• 4.5.1 Consistency of the Least Squares Estimator
• 4.5.2 A Heteroscedasticity Robust Covariance Matrix for Least Squares
• 4.5.3 Robustness to Clustering
• 4.5.4 Bootstrapped Standard Errors with Clustered Data
• 4.6 Asymptotic Distribution of a Function of b: The Delta Method
• 4.7 Interval Estimation
• 4.7.1 Forming a Confidence Interval for a Coefficient
• 4.7.2 Confidence Interval for a Linear Combination of Coefficients: the Oaxaca Decomposition
• 4.8 Prediction and Forecasting
• 4.8.1 Prediction Intervals
• 4.8.2 Predicting y when the Regression Model Describes Log y
• 4.8.3 Prediction Interval for y when the Regression Model Describes Log y
• 4.8.4 Forecasting
• 4.9 Data Problems
• 4.9.1 Multicollinearity
• 4.9.2 Principal Components
• 4.9.3 Missing Values and Data Imputation
• 4.9.4 Measurement Error
• 4.9.5 Outliers and Influential Observations
• 4.10 Summary and Conclusions
• CHAPTER 5 Hypothesis Tests and Model Selection
• 5.1 Introduction
• 5.2 Hypothesis Testing Methodology
• 5.2.1 Restrictions and Hypotheses
• 5.2.2 Nested Models
• 5.2.3 Testing Procedures
• 5.2.4 Size, Power, and Consistency of a Test
• 5.2.5 A Methodological Dilemma: Bayesian Versus Classical Testing
• 5.3 Three Approaches to Testing Hypotheses
• 5.3.1 Wald Tests Based on the Distance Measure
• 5.3.1.a Testing a Hypothesis About a Coefficient
• 5.3.1.b The F Statistic
• 5.3.2 Tests Based on the Fit of the Regression
• 5.3.2.a The Restricted Least Squares Estimator
• 5.3.2.b The Loss of Fit from Restricted Least Squares
• 5.3.2.c Testing the Significance of the Regression
• 5.3.2.d Solving Out the Restrictions and a Caution about R2
• 5.3.3 Lagrange Multiplier Tests
• 5.4 Large-Sample Tests and Robust Inference
• 5.5 Testing Nonlinear Restrictions
• 5.6 Choosing Between Nonnested Models
• 5.6.1 Testing Nonnested Hypotheses
• 5.6.2 An Encompassing Model
• 5.6.3 Comprehensive Approach—The J Test
• 5.7 A Specification Test
• 5.8 Model Building—A General to Simple Strategy
• 5.8.1 Model Selection Criteria
• 5.8.2 Model Selection
• 5.8.3 Classical Model Selection
• 5.8.4 Bayesian Model Averaging
• 5.9 Summary and Conclusions
• CHAPTER 6 Functional Form, Difference in Differences, and Structural Change
• 6.1 Introduction
• 6.2 Using Binary Variables
• 6.2.1 Binary Variables in Regression
• 6.2.2 Several Categories
• 6.2.3 Modeling Individual Heterogeneity
• 6.2.4 Sets of Categories
• 6.2.5 Threshold Effects and Categorical Variables
• 6.2.6 Transition Tables
• 6.3 Difference in Differences Regression
• 6.3.1 Treatment Effects
• 6.3.2 Examining the Effects of Discrete Policy Changes
• 6.4 Using Regression Kinks and Discontinuities to Analyze Social Policy
• 6.4.1 Regression Kinked Design
• 6.4.2 Regression Discontinuity Design
• 6.5 Nonlinearity in the Variables
• 6.5.1 Functional Forms
• 6.5.2 Interaction Effects
• 6.5.3 Identifying Nonlinearity
• 6.5.4 Intrinsically Linear Models
• 6.6 Structural Break and Parameter Variation
• 6.6.1 Different Parameter Vectors
• 6.6.2 Robust Tests of Structural Break with Unequal Variances
• 6.6.3 Pooling Regressions
• 6.7 Summary And Conclusions
• CHAPTER 7 Nonlinear, Semiparametric, and Nonparametric Regression Models
• 7.1 Introduction
• 7.2 Nonlinear Regression Models
• 7.2.1 Assumptions of the Nonlinear Regression Model
• 7.2.2 The Nonlinear Least Squares Estimator
• 7.2.3 Large-Sample Properties of the Nonlinear Least Squares Estimator
• 7.2.4 Robust Covariance Matrix Estimation
• 7.2.5 Hypothesis Testing and Parametric Restrictions
• 7.2.6 Applications
• 7.2.7 Loglinear Models
• 7.2.8 Computing the Nonlinear Least Squares Estimator
• 7.3 Median and Quantile Regression
• 7.3.1 Least Absolute Deviations Estimation
• 7.3.2 Quantile Regression Models
• 7.4 Partially Linear Regression
• 7.5 Nonparametric Regression
• 7.6 Summary and Conclusions
• CHAPTER 8 Endogeneity and Instrumental Variable Estimation
• 8.1 Introduction
• 8.2 Assumptions of the Extended Model
• 8.3 Instrumental Variables Estimation
• 8.3.1 Least Squares
• 8.3.2 The Instrumental Variables Estimator
• 8.3.3 Estimating the Asymptotic Covariance Matrix
• 8.3.4 Motivating the Instrumental Variables Estimator
• 8.4 Two-Stage Least Squares, Control Functions, and Limited Information Maximum Likelihood
• 8.4.1 Two-Stage Least Squares
• 8.4.2 A Control Function Approach
• 8.4.3 Limited Information Maximum Likelihood
• 8.5 Endogenous Dummy Variables: Estimating Treatment Effects
• 8.5.1 Regression Analysis of Treatment Effects
• 8.5.2 Instrumental Variables
• 8.5.3 A Control Function Estimator
• 8.5.4 Propensity Score Matching
• 8.6 Hypothesis Tests
• 8.6.1 Testing Restrictions
• 8.6.2 Specification Tests
• 8.6.3 Testing for Endogeneity: The Hausman and Wu Specification Tests
• 8.6.4 A Test for Overidentification
• 8.7 Weak Instruments and LIML
• 8.8 Measurement Error
• 8.8.1 Least Squares Attenuation
• 8.8.2 Instrumental Variables Estimation
• 8.8.3 Proxy Variables
• 8.9 Nonlinear Instrumental Variables Estimation
• 8.10 Natural Experiments and the Search for Causal Effects
• 8.11 Summary and Conclusions
• Part II: Generalized Regression Model and Equation Systems
• CHAPTER 9 The Generalized Regression Model and Heteroscedasticity
• 9.1 Introduction
• 9.2 Robust Least Squares Estimation and Inference
• 9.3 Properties of Least Squares and Instrumental Variables
• 9.3.1 Finite-Sample Properties of Least Squares
• 9.3.2 Asymptotic Properties of Least Squares
• 9.3.3 Heteroscedasticity and Var[b|X]
• 9.3.4 Instrumental Variable Estimation
• 9.4 Efficient Estimation by Generalized Least Squares
• 9.4.1 Generalized Least Squares (GLS)
• 9.4.2 Feasible Generalized Least Squares (FGLS)
• 9.5 Heteroscedasticity and Weighted Least Squares
• 9.5.1 Weighted Least Squares
• 9.5.2 Weighted Least Squares with Known Ω
• 9.5.3 Estimation When Ω Contains Unknown Parameters
• 9.6 Testing for Heteroscedasticity
• 9.6.1 White’s General Test
• 9.6.2 The Lagrange Multiplier Test
• 9.7 Two Applications
• 9.7.1 Multiplicative Heteroscedasticity
• 9.7.2 Groupwise Heteroscedasticity
• 9.8 Summary and Conclusions
• CHAPTER 10 Systems of Regression Equations
• 10.1 Introduction
• 10.2 The Seemingly Unrelated Regressions Model
• 10.2.1 Ordinary Least Squares And Robust Inference
• 10.2.2 Generalized Least Squares
• 10.2.3 Feasible Generalized Least Squares
• 10.2.4 Testing Hypotheses
• 10.2.5 The Pooled Model
• 10.3 Systems of Demand Equations: Singular Systems
• 10.3.1 Cobb–Douglas Cost Function
• 10.3.2 Flexible Functional Forms: The Translog Cost Function
• 10.4 Simultaneous Equations Models
• 10.4.1 Systems of Equations
• 10.4.2 A General Notation for Linear Simultaneous Equations Models
• 10.4.3 The Identification Problem
• 10.4.4 Single Equation Estimation and Inference
• 10.4.5 System Methods of Estimation
• 10.5 Summary and Conclusions
• CHAPTER 11 Models for Panel Data
• 11.1 Introduction
• 11.2 Panel Data Modeling
• 11.2.1 General Modeling Framework for Analyzing Panel Data
• 11.2.2 Model Structures
• 11.2.3 Extensions
• 11.2.4 Balanced and Unbalanced Panels
• 11.2.5 Attrition and Unbalanced Panels
• 11.2.6 Well-Behaved Panel Data
• 11.3 The Pooled Regression Model
• 11.3.1 Least Squares Estimation of the Pooled Model
• 11.3.2 Robust Covariance Matrix Estimation and Bootstrapping
• 11.3.3 Clustering and Stratification
• 11.3.4 Robust Estimation Using Group Means
• 11.3.5 Estimation with First Differences
• 11.3.6 The Within and Between-Groups Estimators
• 11.4 The Fixed Effects Model
• 11.4.1 Least Squares Estimation
• 11.4.2 A Robust Covariance Matrix for bLSDV
• 11.4.3 Testing the Significance of the Group Effects
• 11.4.4 Fixed Time and Group Effects
• 11.4.5 Reinterpreting the Within Estimator: Instrumental Variables and Control Functions
• 11.4.6 Parameter Heterogeneity
• 11.5 Random Effects
• 11.5.1 Least Squares Estimation
• 11.5.2 Generalized Least Squares
• 11.5.3 Feasible Generalized Least Squares Estimation of the Random Effects Model when Σ is Unknown
• 11.5.4 Robust Inference and Feasible Generalized Least Squares
• 11.5.5 Testing for Random Effects
• 11.5.6 Hausman’s Specification Test for the Random Effects Model
• 11.5.7 Extending the Unobserved Effects Model: Mundlak’s Approach
• 11.5.8 Extending the Random and Fixed Effects Models: Chamberlain’s Approach
• 11.6 Nonspherical Disturbances and Robust Covariance Matrix Estimation
• 11.6.1 Heteroscedasticity in the Random Effects Model
• 11.6.2 Autocorrelation in Panel Data Models
• 11.7 Spatial Autocorrelation
• 11.8 Endogeneity
• 11.8.1 Instrumental Variable Estimation
• 11.8.2 Hausman and Taylor’s Instrumental Variables Estimator
• 11.8.3 Consistent Estimation of Dynamic Panel Data Models: Anderson and Hsiao’s Iv Estimator
• 11.8.4 Efficient Estimation of Dynamic Panel Data Models: The Arellano/Bond Estimators
• 11.8.5 Nonstationary Data and Panel Data Models
• 11.9 Nonlinear Regression with Panel Data
• 11.9.1 A Robust Covariance Matrix for Nonlinear Least Squares
• 11.9.2 Fixed Effects in Nonlinear Regression Models
• 11.9.3 Random Effects
• 11.10 Parameter Heterogeneity
• 11.10.1 A Random Coefficients Model
• 11.10.2 A Hierarchical Linear Model
• 11.10.3 Parameter Heterogeneity and Dynamic Panel Data Models
• 11.11 Summary and Conclusions
• Part III: Estimation Methodology
• CHAPTER 12 Estimation Frameworks in Econometrics
• 12.1 Introduction
• 12.2 Parametric Estimation and Inference
• 12.2.1 Classical Likelihood-Based Estimation
• 12.2.2 Modeling Joint Distributions with Copula Functions
• 12.3 Semiparametric Estimation
• 12.3.1 Gmm Estimation in Econometrics
• 12.3.2 Maximum Empirical Likelihood Estimation
• 12.3.3 Least Absolute Deviations Estimation and Quantile Regression
• 12.3.4 Kernel Density Methods
• 12.3.5 Comparing Parametric and Semiparametric Analyses
• 12.4 Nonparametric Estimation
• 12.4.1 Kernel Density Estimation
• 12.5 Properties of Estimators
• 12.5.1 Statistical Properties of Estimators
• 12.5.2 Extremum Estimators
• 12.5.3 Assumptions for Asymptotic Properties of Extremum Estimators
• 12.5.4 Asymptotic Properties of Estimators
• 12.5.5 Testing Hypotheses
• 12.6 Summary and Conclusions
• CHAPTER 13 Minimum Distance Estimation and the Generalized Method of Moments
• 13.1 Introduction
• 13.2 Consistent Estimation: The Method of Moments
• 13.2.1 Random Sampling and Estimating the Parameters of Distributions
• 13.2.2 Asymptotic Properties of the Method of Moments Estimator
• 13.2.3 Summary—The Method of Moments
• 13.3 Minimum Distance Estimation
• 13.4 The Generalized Method of Moments (Gmm) Estimator
• 13.4.1 Estimation Based on Orthogonality Conditions
• 13.4.2 Generalizing the Method of Moments
• 13.4.3 Properties of the Gmm Estimator
• 13.5 Testing Hypotheses in the Gmm Framework
• 13.5.1 Testing the Validity of the Moment Restrictions
• 13.5.2 Gmm Wald Counterparts to the WALD, LM, and LR Tests
• 13.6 Gmm Estimation of Econometric Models
• 13.6.1 Single-Equation Linear Models
• 13.6.2 Single-Equation Nonlinear Models
• 13.6.3 Seemingly Unrelated Regression Equations
• 13.6.4 Gmm Estimation of Dynamic Panel Data Models
• 13.7 Summary and Conclusions
• CHAPTER 14 Maximum Likelihood Estimation
• 14.1 Introduction
• 14.2 The Likelihood Function and Identification of the Parameters
• 14.3 Efficient Estimation: The Principle of Maximum Likelihood
• 14.4 Properties of Maximum Likelihood Estimators
• 14.4.1 Regularity Conditions
• 14.4.2 Properties of Regular Densities
• 14.4.3 The Likelihood Equation
• 14.4.4 The Information Matrix Equality
• 14.4.5 Asymptotic Properties of the Maximum Likelihood Estimator
• 14.4.5.a Consistency
• 14.4.5.b Asymptotic Normality
• 14.4.5.c Asymptotic Efficiency
• 14.4.5.d Invariance
• 14.4.5.e Conclusion
• 14.4.6 Estimating the Asymptotic Variance of the Maximum Likelihood Estimator
• 14.5 Conditional Likelihoods and Econometric Models
• 14.6 Hypothesis and Specification Tests and Fit Measures
• 14.6.1 The Likelihood Ratio Test
• 14.6.2 The Wald Test
• 14.6.3 The Lagrange Multiplier Test
• 14.6.4 An Application of the Likelihood-Based Test Procedures
• 14.6.5 Comparing Models and Computing Model Fit
• 14.6.6 Vuong’s Test and the Kullback–Leibler Information Criterion
• 14.7 Two-Step Maximum Likelihood Estimation
• 14.8 Pseudo-Maximum Likelihood Estimation and Robust Asymptotic Covariance Matrices
• 14.8.1 A Robust Covariance Matrix Estimator for the MLE
• 14.8.2 Cluster Estimators
• 14.9 Maximum Likelihood Estimation of Linear Regression Models
• 14.9.1 Linear Regression Model with Normally Distributed Disturbances
• 14.9.2 Some Linear Models with Nonnormal Disturbances
• 14.9.3 Hypothesis Tests for Regression Models
• 14.10 The Generalized Regression Model
• 14.10.1 GLS With Known Ω
• 14.10.2 Iterated Feasible GLS With Estimated Ω
• 14.10.3 Multiplicative Heteroscedasticity
• 14.10.4 The Method of Scoring
• 14.11 Nonlinear Regression Models and Quasi-Maximum Likelihood Estimation
• 14.11.1 Maximum Likelihood Estimation
• 14.11.2 Quasi-Maximum Likelihood Estimation
• 14.12 Systems of Regression Equations
• 14.12.1 The Pooled Model
• 14.12.2 The SUR Model
• 14.13 Simultaneous Equations Models
• 14.14 Panel Data Applications
• 14.14.1 ML Estimation of the Linear Random Effects Model
• 14.14.2 Nested Random Effects
• 14.14.3 Clustering Over More than One Level
• 14.14.4 Random Effects in Nonlinear Models: Mle Using Quadrature
• 14.14.5 Fixed Effects in Nonlinear Models: The Incidental Parameters Problem
• 14.15 Latent Class and Finite Mixture Models
• 14.15.1 A Finite Mixture Model
• 14.15.2 Modeling the Class Probabilities
• 14.15.3 Latent Class Regression Models
• 14.15.4 Predicting Class Membership and ßi
• 14.15.5 Determining the Number of Classes
• 14.15.6 A Panel Data Application
• 14.15.7 A Semiparametric Random Effects Model
• 14.16 Summary and Conclusions
• CHAPTER 15 Simulation-Based Estimation and Inference and Random Parameter Models
• 15.1 Introduction
• 15.2 Random Number Generation
• 15.2.1 Generating Pseudo-Random Numbers
• 15.2.2 Sampling from a Standard Uniform Population
• 15.2.3 Sampling from Continuous Distributions
• 15.2.4 Sampling from a Multivariate Normal Population
• 15.2.5 Sampling from Discrete Populations
• 15.3 Simulation-Based Statistical Inference: The Method of Krinsky and Robb
• 15.4 Bootstrapping Standard Errors and Confidence Intervals
• 15.4.1 Types of Bootstraps
• 15.4.2 Bias Reduction with Bootstrap Estimators
• 15.4.3 Bootstrapping Confidence Intervals
• 15.4.4 Bootstrapping with Panel Data: The Block Bootstrap
• 15.5 Monte Carlo Studies
• 15.5.1 A Monte Carlo Study: Behavior of a Test Statistic
• 15.5.2 A Monte Carlo Study: The Incidental Parameters Problem
• 15.6 Simulation-Based Estimation
• 15.6.1 Random Effects in a Nonlinear Model
• 15.6.2 Monte Carlo Integration
• 15.6.2a Halton Sequences and Random Draws for Simulation-Based Integration
• 15.6.2.b Computing Multivariate Normal Probabilities Using the GHK Simulator
• 15.6.3 Simulation-Based Estimation of Random Effects Models
• 15.7 A Random Parameters Linear Regression Model
• 15.8 Hierarchical Linear Models
• 15.9 Nonlinear Random Parameter Models
• 15.10 Individual Parameter Estimates
• 15.11 Mixed Models and Latent Class Models
• 15.12 Summary and Conclusions
• CHAPTER 16 Bayesian Estimation and Inference
• 16.1 Introduction
• 16.2 Bayes’ Theorem and the Posterior Density
• 16.3 Bayesian Analysis of the Classical Regression Model
• 16.3.1 Analysis with a Noninformative Prior
• 16.3.2 Estimation with an Informative Prior Density
• 16.4 Bayesian Inference
• 16.4.1 Point Estimation
• 16.4.2 Interval Estimation
• 16.4.3 Hypothesis Testing
• 16.4.4 Large-Sample Results
• 16.5 Posterior Distributions and the Gibbs Sampler
• 16.6 Application: Binomial Probit Model
• 16.7 Panel Data Application: Individual Effects Models
• 16.8 Hierarchical Bayes Estimation of a Random Parameters Model
• 16.9 Summary and Conclusions
• Part IV: Cross Sections, Panel Data, and Microeconometrics
• CHAPTER 17 Binary Outcomes and Discrete Choices
• 17.1 Introduction
• 17.2 Models for Binary Outcomes
• 17.2.1 Random Utility
• 17.2.2 The Latent Regression Model
• 17.2.3 Functional Form and Probability
• 17.2.4 Partial Effects in Binary Choice Models
• 17.2.5 Odds Ratios in Logit Models
• 17.2.6 The Linear Probability Model
• 17.3 Estimation and Inference for Binary Choice Models
• 17.3.1 Robust Covariance Matrix Estimation
• 17.3.2 Hypothesis Tests
• 17.3.3 Inference for Partial Effects
• 17.3.3.a The Delta Method
• 17.3.3.b An Adjustment to the Delta Method
• 17.3.3.c The Method of Krinsky and Robb
• 17.3.3.d Bootstrapping
• 17.3.4 Interaction Effects
• 17.4 Measuring Goodness of Fit for Binary Choice Models
• 17.4.1 Fit Measures Based on the Fitting Criterion
• 17.4.2 Fit Measures Based on Predicted Values
• 17.4.3 Summary of Fit Measures
• 17.5 Specification Analysis
• 17.5.1 Omitted Variables
• 17.5.2 Heteroscedasticity
• 17.5.3 Distributional Assumptions
• 17.5.4 Choice-Based Sampling
• 17.6 Treatment Effects and Endogenous Variables in Binary Choice Models
• 17.6.1 Endogenous Treatment Effect
• 17.6.2 Endogenous Continuous Variable
• 17.6.2.a IV and GMM Estimation
• 17.6.2.b Partial ML Estimation
• 17.6.2.c Full Information Maximum Likelihood Estimation
• 17.6.2.d Residual Inclusion and Control Functions
• 17.6.2.e A Control Function Estimator
• 17.6.3 Endogenous Sampling
• 17.7 Panel Data Models
• 17.7.1 The Pooled Estimator
• 17.7.2 Random Effects
• 17.7.3 Fixed Effects
• 17.7.3.a A Conditional Fixed Effects Estimator
• 17.7.3.b Mundlak’s Approach, Variable Addition, and Bias Reduction
• 17.7.4 Dynamic Binary Choice Models
• 17.7.5 A Semiparametric Model for Individual Heterogeneity
• 17.7.6 Modeling Parameter Heterogeneity
• 17.7.7 Nonresponse, Attrition, and Inverse Probability Weighting
• 17.8 Spatial Binary Choice Models
• 17.9 The Bivariate Probit Model
• 17.9.1 Maximum Likelihood Estimation
• 17.9.2 Testing for Zero Correlation
• 17.9.3 Partial Effects
• 17.9.4 A Panel Data Model for Bivariate Binary Response
• 17.9.5 A Recursive Bivariate Probit Model
• 17.10 A Multivariate Probit Model
• 17.11 Summary and Conclusions
• CHAPTER 18 Multinomial Choices and Event Counts
• 18.1 Introduction
• 18.2 Models for Unordered Multiple Choices
• 18.2.1 Random Utility Basis of the Multinomial Logit Model
• 18.2.2 The Multinomial Logit Model
• 18.2.3 The Conditional Logit Model
• 18.2.4 The Independence from Irrelevant Alternatives Assumption
• 18.2.5 Alternative Choice Models
• 18.2.5.a Heteroscedastic Extreme Value Model
• 18.2.5.b Multinomial Probit Model
• 18.2.5.c The Nested Logit Model
• 18.2.6 Modeling Heterogeneity
• 18.2.6.a The Mixed Logit Model
• 18.2.6.b A Generalized Mixed Logit Model
• 18.2.6.c Latent Classes
• 18.2.6.d Attribute Nonattendance
• 18.2.7 Estimating Willingness to Pay
• 18.2.8 Panel Data and Stated Choice Experiments
• 18.2.8.a The Mixed Logit Model
• 18.2.8.b Random Effects and the Nested Logit Model
• 18.2.8.c A Fixed Effects Multinomial Logit Model
• 18.2.9 Aggregate Market Share Data—The Blp Random Parameters Model
• 18.3 Random Utility Models for Ordered Choices
• 18.3.1 The Ordered Probit Model
• 18.3.2.A Specification Test for the Ordered Choice Model
• 18.3.3 Bivariate Ordered Probit Models
• 18.3.4 Panel Data Applications
• 18.3.4.a Ordered Probit Models with Fixed Effects
• 18.3.4.b Ordered Probit Models with Random Effects
• 18.3.5 Extensions of the Ordered Probit Model
• 18.3.5.a Threshold Models—Generalized Ordered Choice Models
• 18.3.5.b Thresholds and Heterogeneity—Anchoring Vignettes
• 18.4 Models for Counts of Events
• 18.4.1 The Poisson Regression Model
• 18.4.2 Measuring Goodness of Fit
• 18.4.3 Testing for Overdispersion
• 18.4.4 Heterogeneity and the Negative Binomial Regression Model
• 18.4.5 Functional Forms for Count Data Models
• 18.4.6 Truncation and Censoring in Models for Counts
• 18.4.7 Panel Data Models
• 18.4.7.a Robust Covariance Matrices for Pooled Estimators
• 18.4.7.b Fixed Effects
• 18.4.7.c Random Effects
• 18.4.8 Two-Part Models: Zero-Inflation and Hurdle Models
• 18.4.9 Endogenous Variables and Endogenous Participation
• 18.5 Summary and Conclusions
• CHAPTER 19 Limited Dependent Variables–Truncation, Censoring, and Sample Selection
• 19.1 Introduction
• 19.2 Truncation
• 19.2.1 Truncated Distributions
• 19.2.2 Moments of Truncated Distributions
• 19.2.3 The Truncated Regression Model
• 19.2.4 The Stochastic Frontier Model
• 19.3 Censored Data
• 19.3.1 The Censored Normal Distribution
• 19.3.2 The Censored Regression (Tobit) Model
• 19.3.3 Estimation
• 19.3.4 Two-Part Models and Corner Solutions
• 19.3.5 Specification Issues
• 19.3.5.a Endogenous Right-Hand-Side Variables
• 19.3.5.b Heteroscedasticity
• 19.3.5.c Nonnormality
• 19.3.6 Panel Data Applications
• 19.4 Sample Selection and Incidental Truncation
• 19.4.1 Incidental Truncation in a Bivariate Distribution
• 19.4.2 Regression in a Model of Selection
• 19.4.3 Two-Step and Maximum Likelihood Estimation
• 19.4.4 Sample Selection in Nonlinear Models
• 19.4.5 Panel Data Applications of Sample Selection Models
• 19.4.5.a Common Effects in Sample Selection Models
• 19.4.5.b Attrition
• 19.5 Models for Duration
• 19.5.1 Models for Duration Data
• 19.5.2 Duration Data
• 19.5.3 A Regression-Like Approach: Parametric Models of Duration
• 19.5.3.a Theoretical Background
• 19.5.3.b Models of the Hazard Function
• 19.5.3.c Maximum Likelihood Estimation
• 19.5.3.d Exogenous Variables
• 19.5.3.e Heterogeneity
• 19.5.4 Nonparametric and Semiparametric Approaches
• 19.6 Summary and Conclusions
• Part V: Time Series and Macroeconometrics
• CHAPTER 20 Serial Correlation
• 20.1 Introduction
• 20.2 The Analysis of TimeSeries Data
• 20.3 Disturbance Processes
• 20.3.1 Characteristics of Disturbance Processes
• 20.3.2 Ar(1) Disturbances
• 20.4 Some Asymptotic Results for Analyzing Time-Series Data
• 20.4.1 Convergence of Moments—The Ergodic Theorem
• 20.4.2 Convergence to Normality—A Central Limit Theorem
• 20.5 Least Squares Estimation
• 20.5.1 Asymptotic Properties of Least Squares
• 20.5.2 Estimating the Variance of the Least Squares Estimator
• 20.6 GMM Estimation
• 20.7 Testing for Autocorrelation
• 20.7.1 Lagrange Multiplier Test
• 20.7.2 Box And Pierce’s Test and Ljung’s Refinement
• 20.7.3 The Durbin–Watson Test
• 20.7.4 Testing in the Presence of a Lagged Dependent Variable
• 20.7.5 Summary of Testing Procedures
• 20.8 Efficient Estimation when is Known
• 20.9 Estimation when is Unknown
• 20.9.1 AR(1) Disturbances
• 20.9.2 Application: Estimation of a Model with Autocorrelation
• 20.9.3 Estimation with a Lagged Dependent Variable
• 20.10 Autoregressive Conditional Heteroscedasticity
• 20.10.1 The Arch(1) Model
• 20.10.2 ARCH(q), ARCH-In-Mean, and Generalized ARCH Models
• 20.10.3 Maximum Likelihood Estimation of the Garch Model
• 20.10.4 Testing for GARCH Effects
• 20.10.5 Pseudo–Maximum Likelihood Estimation
• 20.11 Summary and Conclusions
• CHAPTER 21 Nonstationary Data
• 21.1 Introduction
• 21.2 Nonstationary Processes and Unit Roots
• 21.2.1 The Lag and Difference Operators
• 21.2.2 Integrated Processes and Differencing
• 21.2.3 Random Walks, Trends, and Spurious Regressions
• 21.2.4 Tests for Unit Roots in Economic Data
• 21.2.5 The Dickey–Fuller Tests
• 21.2.6 The Kpss Test of Stationarity
• 21.3 Cointegration
• 21.3.1 Common Trends
• 21.3.2 Error Correction and Var Representations
• 21.3.3 Testing for Cointegration
• 21.3.4 Estimating Cointegration Relationships
• 21.3.5 Application: German Money Demand
• 21.3.5.a Cointegration Analysis and a Long-Run Theoretical Model
• 21.3.5.b Testing for Model Instability
• 21.4 Nonstationary Panel Data
• 21.5 Summary and Conclusions
• References
• Index
• A
• B
• C
• D
• E
• F
• G
• H
• I
• J
• K
• L
• M
• N
• O
• P
• Q
• R
• S
• T
• U
• V
• W
• Y
• Z
• Part VI Online Appendices
• Appendix A Matrix Algebra
• A.1 Terminology
• A.2 Algebraic Manipulation of Matrices
• A.2.1 Equality of Matrices
• A.2.2 Transposition
• A.2.3 Vectorization
• A.2.4 Matrix Addition
• A.2.5 Vector Multiplication
• A.2.6 A Notation for Rows and Columns of a Matrix
• A.2.7 Matrix Multiplication and Scalar Multiplication
• A.2.8 Sums of Values
• A.2.9 A Useful Idempotent Matrix
• A.3 Geometry of Matrices
• A.3.1 Vector Spaces
• A.3.2 Linear Combinations of Vectors and Basis Vectors
• A.3.3 Linear Dependence
• A.3.4 Subspaces
• A.3.5 Rank of a Matrix
• A.3.6 Determinant of a Matrix
• A.3.7 A Least Squares Problem
• A.4 Solution of a System of Linear Equations
• A.4.1 Systems of Linear Equations
• A.4.2 Inverse Matrices
• A.4.3 Nonhomogeneous Systems of Equations
• A.4.4 Solving the Least Squares Problem
• A.5 Partitioned Matrices
• A.5.1 Addition and Multiplication of Partitioned Matrices
• A.5.2 Determinants of Partitioned Matrices
• A.5.3 Inverses of Partitioned Matrices
• A.5.4 Deviations From Means
• A.5.5 Kronecker Products
• A.6 Characteristic Roots And Vectors
• A.6.1 The Characteristic Equation
• A.6.2 Characteristic Vectors
• A.6.3 General Results for Characteristic Roots And Vectors
• A.6.4 Diagonalization and Spectral Decomposition of a Matrix
• A.6.5 Rank of a Matrix
• A.6.6 Condition Number of a Matrix
• A.6.7 Trace of a Matrix
• A.6.8 Determinant of a Matrix
• A.6.9 Powers of a Matrix
• A.6.10 Idempotent Matrices
• A.6.11 Factoring a Matrix: The Cholesky Decomposition
• A.6.12 Singular Value Decomposition
• A.6.13 QR Decomposition
• A.6.14 The Generalized Inverse of a Matrix
• A.7 Quadratic Forms And Definite Matrices
• A.7.1 Nonnegative Definite Matrices
• A.7.2 Idempotent Quadratic Forms
• A.7.3 Comparing Matrices
• A.8 Calculus And Matrix Algebra
• A.8.1 Differentiation and the Taylor Series
• A.8.2 Optimization
• A.8.3 Constrained Optimization
• A.8.4 Transformations
• Appendix B Probability and Distribution Theory
• B.1 Introduction
• B.2 Random Variables
• B.2.1 Probability Distributions
• B.2.2 Cumulative Distribution Function
• B.3 Expectations of a Random Variable
• B.4 Some Specific Probability Distributions
• B.4.1 The Normal and Skew Normal Distributions
• B.4.2 The Chi-Squared, T, and F Distributions
• B.4.3 Distributions with Large Degrees of Freedom
• B.4.4 Size Distributions: The Lognormal Distribution
• B.4.5 The Gamma and Exponential Distributions
• B.4.6 The Beta Distribution
• B.4.7 The Logistic Distribution
• B.4.8 The Wishart Distribution
• B.4.9 Discrete Random Variables
• B.5 The Distribution of a Function of a Random Variable
• B.6 Representations of a Probability Distribution
• B.7 Joint Distributions
• B.7.1 Marginal Distributions
• B.7.2 Expectations in a Joint Distribution
• B.7.3 Covariance and Correlation
• B.7.4 Distribution of a Function of Bivariate Random Variables
• B.8 Conditioning in a Bivariate Distribution
• B.8.1 Regression: The Conditional Mean
• B.8.2 Conditional Variance
• B.8.3 Relationships among Marginal and Conditional Moments
• B.8.4 The Analysis of Variance
• B.8.5 Linear Projection
• B.9 The Bivariate Normal Distribution
• B.10 Multivariate Distributions
• B.10.1 Moments
• B.10.2 Sets of Linear Functions
• B.10.3 Nonlinear Functions: The Delta Method
• B.11 The Multivariate Normal Distribution
• B.11.1 Marginal and Conditional Normal Distributions
• B.11.2 The Classical Normal Linear Regression Model
• B.11.3 Linear Functions of a Normal Vector
• B.11.4 Quadratic Forms in a Standard Normal Vector
• B.11.5 The F Distribution
• B.11.6 A Full Rank Quadratic Form
• B.11.7 Independence of a Linear and a Quadratic Form
• Appendix C Estimation and Inference
• C.1 Introduction
• C.2 Samples and Random Sampling
• C.3 Descriptive Statistics
• C.4 Statistics as Estimators—Sampling Distributions
• C.5 Point Estimation of Parameters
• C.5.1 Estimation in a Finite Sample
• C.5.2 Efficient Unbiased Estimation
• C.6 Interval Estimation
• C.7 Hypothesis Testing
• C.7.1 Classical Testing Procedures
• C.7.2 Tests Based on Confidence Intervals
• C.7.3 Specification Tests
• Appendix D Large-Sample Distribution Theory
• D.1 Introduction
• D.2 Large-Sample Distribution Theory
• D.2.1 Convergence in Probability
• D.2.2 Other forms of Convergence and Laws of Large Numbers
• D.2.3 Convergence of Functions
• D.2.4 Convergence to a Random Variable
• D.2.5 Convergence in Distribution: Limiting Distributions
• D.2.6 Central Limit Theorems
• D.2.7 The Delta Method
• D.3 Asymptotic Distributions
• D.3.1 Asymptotic Distribution of a Nonlinear Function
• D.3.2 Asymptotic Expectations
• D.4 Sequences and the Order of a Sequence
• Appendix E Computation and Optimization
• E.1 Introduction
• E.2 Computation in Econometrics
• E.2.1 Computing Integrals
• E.2.2 The Standard Normal Cumulative Distribution Function
• E.2.3 The Gamma and Related Functions
• E.2.4 Approximating Integrals by Quadrature
• E.3 Optimization
• E.3.1 Algorithms
• E.3.2 Computing Derivatives
• E.3.3 Gradient Methods
• E.3.4 Aspects of Maximum Likelihood Estimation
• E.3.5 Optimization with Constraints
• E.3.6 Some Practical Considerations
• E.3.7 The EM Algorithm
• E.4 Examples
• E.4.1 Function of one Parameter
• E.4.2 Function of two Parameters: The Gamma Distribution
• E.4.3 A Concentrated Log-Likelihood Function
• Appendix F Data Sets Used in Applications