Econometric Analysis Global Edition

Cover
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