Table of contents for Econometric analysis / William H. Greene.

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Brief Contents
Part I The Linear Regression Model
Chapter 1 Introduction
Chapter 2 The Classical Multiple Linear Regression Model
Chapter 3 Least Squares
Chapter 4 Properties of the Least Squares Estimator
Chapter 5 Inference and Prediction
Chapter 6 Functional Form and Structural Change
Chapter 7 Specification Analysis and Model Selection
Part II The Generalized Regression Model
Chapter 8 The Generalized Regression Model and Heteroscedasticity
Chapter 9 Models for Panel and Stratified Data
Chapter 10 Systems of Regression Equations
Chapter 11 Nonlinear Regressions and Nonlinear Least Squares
Part III Instrumental Variables and Simultaneous Equations Models
Chapter 12 Instrumental Variables Estimation
Chapter 13 Simultaneous-Equations Models
Part IV Estimation Methodology
Chapter 14 Estimation Frameworks in Econometrics
Chapter 15 Minimum Distance Estimation and The Generalized Method of Moments
Chapter 16 Maximum Likelihood
Chapter 17 Simulation Based Estimation and the Bootstrap
Chapter 18 Bayesian Inference in Econometrics
Part V Time Series and Macroeconometrics
Chapter 19 Serial Correlation
Chapter 20 Models with Lagged Variables
Chapter 21 Time Series Models
Chapter 22 Nonstationary Data
Part VI Cross Sections, Panel Data and Microeconometrics
Chapter 23 Models for Discrete Choice
Chapter 24 Limited Dependent Variable Models
Chapter 25 Sample Selection and Treatment Effects
Chapter 26 Even Counts and Duration Models
Part VII Appendices
Appendix A Matrix Algebra
Appendix B Probability and Distribution Theory
Appendix C Estimation and Inference
Appendix D Large Sample Distribution Theory
Appendix E Computation and Optimization
Appendix F Data Sets Used in Applications
Appendix G Statistical Tables
Author Index
Subject Index
Part I The Linear Regression Model
CHAPTER 1 Introduction
1.1 Econometrics
1.2 Econometric Modeling
1.3 Methodology
1.4 The Practice of Econometrics
1.5 Plan of the Book
CHAPTER 2 The Classical Multiple Linear Regression Model
2.1 Introduction
2.2 The Linear Regression Model
2.3 Assumptions of the Classical Linear Regression Model
2.3.1 Linearity of the Regression Model
2.3.2 Full Rank
2.3.3 Regression
2.3.4 Spherical Disturbances
2.3.5 Data Generating Process for the Regressors
2.3.6 Normality
2.4 Summary and Conclusions
CHAPTER 3 Least Squares
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 Projection
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 Summary and Conclusions
CHAPTER 4 Statistical Properties of the Least Squares Estimator
4.1 Introduction
4.2 Motivating Least Squares
4.2.1 The Population Orthogonality Conditions
4.2.2 Minimum Mean Squared Error Projection
4.2.3 Minimum Variance Linear Unbiased Estimation
4.3 Unbiased Estimation
4.4 The Variance of the Least Squares Estimator and the Gauss-Markov Theorem
4.5 The Implications of Stochastic Regressors
4.6 Estimating the Variance of the Least Squares Estimator
4.7 The Normality Assumption and Basic Statistical Inference
4.7.1 Testing a Hypothesis About a Coefficient
4.7.2 Confidence Intervals for Parameters
4.7.3 Confidence Interval for a Linear Combination of Coefficients: The Oaxaca Decomposition
4.7.4 Testing the Significance of the Regression
4.7.5 Marginal Distributions of the Test Statistics
4.8 Finite-Sample Properties of the Least Squares Estimator
4.8.1 Multicollinearity
4.8.2 Missing Observations
4.9 Large Sample Properties of the Least Squares Estimator
4.9.1 Consistency of the Least Squares Estimator of _
4.9.2 Asymptotic Normality of the Least Squares Estimator
4.9.3 Consistency of s_ and the Estimator of Asy.Var[_]
4.9.4 Asymptotic Distribution of a Function of b: The Delta Method and the Method of Krinsky and Robb
4.9.5 Asymptotic Efficiency
4.9.6 More General Data Generating Processes
4.10 Summary and Conclusions
CHAPTER 5 Inference and Prediction
5.1 Introduction
5.2 Restrictions and Nested Models
5.3 Two Approaches to Testing Hypotheses
5.3.1 The F Statistic and the Least Squares Discrepancy
5.3.2 The Restricted Least Squares Estimator
5.3.3 The Loss of Fit From Restricted Least Squares
5.4 Nonnormal Disturbances and Large Sample Tests
5.5 Testing Nonlinear Restrictions
5.6 Prediction
5.7 Summary and Conclusions
CHAPTER 6 Functional Form 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 Several Groupings
6.2.4 Threshold Effects and Categorical Variables
6.2.5 Spline Regression
6.3 Nonlinearity in the Variables
6.3.1 Functional Forms
6.3.2 Identifying Nonlinearity
6.3.3 Intrinsic Linearity and Identification
6.4 Modeling and Testing for a Structural Break
6.4.1 Different Parameter Vectors
6.4.2 Insufficient Observations
6.4.3 Change in a Subset of Coefficients
6.4.4 Tests of Structural Break with Unequal Variances
6.4.5 Predictive Test
6.5 Summary and Conclusions
CHAPTER 7 Specification Analysis and Model Selection
7.1 Introduction
7.2 Specification Analysis and Model Building
7.2.1 Bias Caused by Omission of Relevant Variables
7.2.2 Pretest Estimation
7.2.3 Inclusion of Irrelevant Variables
7.2.4 Model Building - A General to Simple Strategy
7.3 Choosing Between Nonnested Models
7.3.1 Testing Nonnested Hypotheses
7.3.2 An Encompassing Model
7.3.3 Comprehensive Approach - The J Test
7.3.4 Vuong's Test and Kullback-Leibler Information Criterion
7.4 Model Selection Criteria
7.5 Model Selection
7.5.1 Classical Model Selection
7.5.2 Bayesian Model Averaging
7.6 Summary and Conclusions
Part II The Generalized Regression Model
CHAPTER 8 The Generalized Regression Model and Heteroscedasticity
8.1 Introduction
8.2 Least Squares Estimation
8.2.1 Finite-Sample Properties of Least Squares
8.2.2 Asymptotic Properties of Least Squares
8.2.3 Robust Estimation of Asymptotic Covariance Matrices
8.3 Efficient Estimation by Generalized Least Squares
8.3.1 Generalized Least Squares (GLS)
8.3.2 Feasible Generalized Least Squares (FGLS)
8.4 Heteroscedasticity
8.4.1 Ordinary Least Squares Estimation
8.4.2 Inefficiency of Least Squares
8.4.3 The Estimated Covariance Matrix of b
8.4.4 Estimating the Appropriate Covariance Matrix for Ordinary Least Squares
8.5 Testing for Heteroscedasticity
8.5.1 White's General Test
8.5.2 The Breusch-Pagan-Godfrey LM Test
8.6 Weighted Least Squares When _ is Known
8.7 Estimation When _ Contains Unknown Parameters
8.8 Applications
8.8.1 Multiplicative Heteroscedasticity
8.8.2 Groupwise Heteroscedasticity
8.9 Summary and Conclusions
CHAPTER 9 Models for Panel Data
9.1 Introduction
9.2 Panel Data Models
9.2.1 General Modeling Structures for Analyzing Panel Data
9.2.2 Model Structures
9.2.3 Extensions
9.2.4 Balanced and Unbalanced Panels
9.3 The Pooled Regression Model
9.3.1 Least Squares Estimation of the Pooled Model
9.3.2 Robust Covariance Matrix Estimation
9.3.3 Clustering and Stratification
9.3.4 Robust Estimation Using Group Means
9.3.5 Estimation with First Differences
9.3.6 The Within- and Between-Groups Estimators
9.4 The Fixed Effects Model
9.4.1 Least Squares Estimation
9.4.2 Small T Asymptotics
9.4.3 Testing the Significance of the Group Effects
9.4.4 Fixed Time and Group Effects
9.5 Random Effects
9.5.1 Generalized Least Squares
9.5.2 Feasible Generalized Least Squares when _ is Unknown
9.5.3 Testing for Random Effects
9.5.4 Hausman's Specification Test for the Random Effects Model
9.5.5 Extending the Unobserved Effects Model: Mundlak's Approach
9.6 Nonspherical Disturbances and Robust Covariance Matrix Estimation
9.6.1 Robust Estimation of the Fixed Effects Model
9.6.2 Heteroscedasticity in the Random Effects Model
9.6.3 Autocorrelation in Panel Data Models
9.7 Extensions of the Random Effects Model
9.7.1 Nested Random Effects
9.7.2 Spatial Autocorrelation
9.8 Parameter Heterogeneity
9.8.1 The Random Coefficients Model
9.8.2 Random Parameters and Simulation Based Estimation
9.8.3 Two Step estimation of Panel Data Models
9.8.4 Hierarchical Models
9.8.5 Parameter Heterogeneity and Dynamic Panel Data Models
9.8.6 Nonstationary Data and Panel Data Models
9.9 Consistent Estimation of Dynamic Panel Data Models
9.10 Summary and Conclusions
CHAPTER 10 System of Regression Equations
10.1 Introduction
10.2 The Seemingly Unrelated Regressions Model
10.2.1 Generalized Least Squares
10.2.2 Seemingly Unrelated Regressions with Identical Regressors
10.2.3 Feasible Generalized Least Squares
10.2.4 Testing Hypotheses
10.2.5 Heteroscedasticity
10.2.6 Autocorrelation
10.2.7 A Specification Test for the SUR Model
10.2.8 The Pooled Model
10.3 Panel Data Applications
10.3.1 Random Effects SUR Models
10.3.2 The Random and Fixed Effects Models
10.4 Systems of Demand Equations: Singular Systems
10.4.1 Cobb-Douglas Cost Function
10.4.2 Flexible Functional Forms: The Translog Cost Function
10.5 Summary and Conclusions
CHAPTER 11 Nonlinear Regressions and Nonlinear Least Squares
11.1 Introduction
11.2 Nonlinear Regression Models
11.2.1 Assumptions of the Nonlinear Regression Model
11.2.2 The Orthogonality Condition and the Sum of Squares
11.2.3 The Linearized Regression
11.2.4 Large Sample Properties of the Nonlinear Least Squares Estimator
11.2.5 Computing the Nonlinear Least Squares Estimator
11.3 Applications
11.3.1 A Nonlinear Consumption Function
11.3.2 The Box-Cox Transformation
11.4 Hypothesis Testing and Parametric Restrictions
11.4.1 Significance Tests for Restrictions: F and Wald Tests
11.4.2 Tests Based on the LM Statistic
11.5 Nonlinear Systems of Equations
11.6 Two-Step Nonlinear Least Squares Estimation
11.7 Panel Data Applications
11.7.1 A Robust Covariance Matrix for Nonlinear Least Squares
11.7.2 Fixed Effects
11.7.3 Random Effects
11.8 Summary and Conclusions
Part III Instrumental Variables and Simultaneous Equations Models
CHAPTER 12 Instrumental Variables Estimation
12.1 Introduction
12.2 Assumptions of the Model
12.3 Estimation
12.3.1 Ordinary Least Squares
12.3.2 The Instrumental Variables Estimator
12.3.3 Two Stage Least Squares
12.4 The Hausman and Wu Specification Tests and an Application to Instrumental Variable Estimation
12.5 Measurement Error
12.5.1 Least Squares Attenuation
12.5.2 Instrumental Variables Estimation
12.5.3 Proxy Variables
12.6 Estimation of the Generalized Regression Model
12.7 Nonlinear Instrumental Variables Estimation
12.8 Panel Data Applications
12.8.1 Instrumental Variables Estimation of the Random Effects Model
12.8.2 Dynamic Panel Data Models the Anderson/Hsiao and Arellano/Bond Estimator
12.9 Weak Instruments
12.10 Summary and Conclusions
CHAPTER 13 Simultaneous-Equations Models
13.1 Introduction
13.2 Fundamental Issues in Simultaneous Equations Models
13.2.1 Illustrative Systems of Equations
13.2.2 Endogeneity and Causality
13.2.3 A General Notation for Linear Simultaneous Equations Models
13.3 The Problem of Identification
13.3.1 The Rank and Order Conditions for Identification
13.3.2 Identification Through Other Nonsample Information
13.4 Methods of Estimation
13.5 Single Equation: Limited Information Estimation Methods
13.5.1 Ordinary Least Squares
13.5.2 Estimation by Instrumental Variables
13.5.3 Two Stage Least Squares
13.5.4 Limited Information Maximum Likelihood and the K Class of Estimators
13.5.5 Testing in the Presence of Weak Instruments
13.5.6 Two Stage Least Squares in models that Are Nonlinear in Variables
13.6 System Methods of Estimation
13.6.1 Three Stage Least Squares
13.6.2 Full Information Maximum Likelihood
13.7 Comparison of Methods - Klein's Model I
13.8 Specification Tests
13.9 Properties of Dynamic Models
13.9.1 Dynamic Models and Their Multipliers
13.9.2 Stability
13.9.3 Adjustment to Equilibrium
13.10 Summary and Conclusions
Part IV Estimation Methodology
CHAPTER 14 Estimation Frameworks in Econometrics
14.1 Introduction
14.2 Parametric Estimation and Inference
14.2.1 Classical Likelihood Based Estimation
14.2.2 Modeling Joint Distributions with Copula Functions
14.3 Semiparametric Estimation
14.3.1 GMM Estimation in Econometrics
14.3.2 Least Absolute Deviations Estimation
14.3.3 Partially Linear Regression
14.3.4 Kernel Density Methods
14.3.5 Comparing Parametric and Semiparametric Analyses
14.4 Nonparametric Estimation
14.4.1 Kernel Density Estimation
14.4.2 Nonparametric Regression
14.5 Properties of Estimators
14.5.1 Statistical Properties of Estimators
14.5.2 Extremum Estimators
14.5.3 Assumptions for Asymptotic Properties of Extremum Estimators
14.5.4 Properties of Extremum Estimators
14.5.5 Testing Hypotheses
14.6 Summary and Conclusions
CHAPTER 15 Minimum Distance Estimation and The Generalized Method of Moments
15.1 Introduction
15.2 Consistent Estimation: The Method of Moments
15.2.1 Random Sampling and Estimating the Parameters of Distributions
15.2.2 Asymptotic Properties of the Method of Moments Estimator
15.2.3 Summary - The Method of Moments
15.3 Minimum Distance Estimation
15.4 The Generalized Method of Moments Estimator
15.4.1 Estimation Based on Orthogonality Conditions
15.4.2 Generalizing the Method of Moments
15.4.3 Properties of the GMM Estimator
15.5 Testing Hypothesis in the GMM Framework
15.5.1 Testing the Validity of the Moment Restrictions
15.5.2 GMM Counterparts to the Wald, LM and LR Tests
15.6 GMM Estimation of Econometric Models
15.6.1 Single Equation Linear Models
15.6.2 Single Equation Nonlinear Models
15.6.3 Seemingly Unrelated Regression Models
15.6.4 Simultaneous Equations Models with Heteroscedasticity
15.6.5 GMM Estimation of Dynamic Panel Data Models
15.7 Summary and Conclusions
CHAPTER 16 Maximum Likelihood
16.1 Introduction
16.2 The Likelihood Function and Identification of Parameters
16.3 Efficient Estimation: The Principle of Maximum Likelihood
16.4 Properties of Maximum Likelihood Estimators
16.4.1 Regularity Conditions
16.4.2 Properties of Regular Densities
16.4.3 The Likelihood Equation
16.4.4 The Information Matrix Equality
16.4.5 Asymptotic Properties of the Maximum Likelihood Estimator
16.4.5.a Consistency
16.4.5.b Asymptotic Normality
16.4.5.c Asymptotic Efficiency
16.4.5.d Invariance
16.4.5.e Conclusion
16.4.6 Estimating the Asymptotic Variance of the Maximum Likelihood Estimator
16.5 Conditional Likelihoods, Econometric models and the GMM Estimator
16.6 Hypothesis and Specification Tests and Fit Measures
16.6.1 The Likelihood Ratio Test
16.6.2 The Wald Test
16.6.3 The Lagrange Multiplier Test
16.6.4 An Application of the Likelihood Based Procedures
16.6.5 Comparing Models and Computing Model Fit
16.7 Two Step Maximum Likelihood Estimation
16.8 Pseudo-Maximum Likelihood Estimation and Robust Asymptotic Covariance Matrices
16.8.1 Maximum Likelihood and GMM Estimation
16.8.2 Maximum Likelihood Estimation and M Estimation
16.8.3 Sandwich Estimators
16.8.4 Cluster Estimators
16.9 Applications of Maximum Likelihood Estimation
16.9.1 The Normal Linear Regression Model
16.9.2 The Generalized Regression Model
16.9.2.a Multiplicative Heteroscedasticity
16.9.2.b Autocorrelation
16.9.3 Seemingly Unrelated Regression Models
16.9.3.a The Pooled Model
16.9.3.b The SUR Model
16.9.3.c Exclusion Restrictions
16.9.4 Simultaneous Equations Models
16.9.5 Maximum Likelihood Estimation of Nonlinear Regression Models
16.9.5.a Nonnormal Disturbances - The Stochastic Frontier Model
16.9.5.b ML Estimation of a Geometric Regression Model for Count Data
16.9.6 Panel Data Applications
16.9.6.a ML Estimation of the Linear Random Effects Model
16.9.6.b Random Effects in Nonlinear Models: MLE Using rature
16.9.6.c Fixed Effects in Nonlinear Models: Full MLE
16.9.7 Latent Class and Finite Mixture Models
16.9.7.a A Finite Mixture Model
16.9.7.b Measured and Unmeasured Heterogeneity
16.9.7.c Predicting Class Membership
16.9.7.d A Conditional Latent Class Model
16.9.7.e Determining the Number of Classes
16.9.7.f A Panel Data Application
16.9.8 Summary and Conclusions
CHAPTER 17 Simulation Based Estimation and Inference
17.1 Introduction
17.2 Random Number Generation
17.2.1 Generating Pseudo-Random Numbers
17.2.2 Sampling from a Standard Uniform Population
17.2.3 Sampling from a Continuous Distributions
17.2.4 Sampling from a Multivaraite Normal Population
17.2.5 Sampling from a Discrete Population
17.3 Monte Carlo Integration
17.3.1 Halton Sequences and Random Draws for Simulation Based Integration
17.3.2 Importance Sampling
17.3.3 Computing Multivvariate Normal Probabilities Using the GHK Simulator
17.4 Monte Carlo Studies
17.4.1 A Monte Carlo Study: Behavior of a Test Statistic
17.4.2 A Monte Carlo Study: The Incidental Parameters Problem
17.5 Simulation Based Estimation
17.5.1 Maximum Simulated Likelihood Estimation of Random Parameters Models
17.5.2 The Method of Simulated Moments
17.6 Bootstrapping
17.7 Summary and Conclusion
CHAPTER 18 Bayesian Inference in Econometrics
18.1 Introduction
18.2 Bayes Theorem and the Posterior Density
18.3 Bayesian Analysis of the Classical Regression Model
18.3.1 Analysis with a Noninformative Prior
18.3.2 Estimation with an Informative Prior Density
18.4 Bayesian Inference
18.4.1 Point Estimation
18.4.2 Interval Estimation
18.4.3 Hypothesis Testing
18.4.4 Large Sample Results
18.5 Posterior Distributions and the Gibbs Sampler
18.6 Application: Binomial Probit Model
18.7 Panel Data Application: Individual Effects Models
18.8 Hierarchical Bayes Estimation of a Random Parameters Model
18.9 Summary and Conclusions
Part V Time Series and Macroeconometrics
CHAPTER 19 Serial Correlation
19.1 Introduction
19.2 The Analysis of Time Series Data
19.3 Disturbance Processes
19.3.1 Characteristics of Disturbance Processes
19.3.2 AR(1) Disturbances
19.4 Some Asymptotic Results for Analyzing Time Series Data
19.4.1 Convergence of Moments - The Ergodic Theorem
19.4.2 Convergence to Normality - A Central Limit Theorem
19.5 Least Squares Estimation
19.5.1 Asymptotic Properties of Least Squares
19.5.2 Estimating the Variance of the Least Squares Estimator
19.6 GMM Estimation
19.7 Test for Autocorrelation
19.7.1 Lagrange Multiplier Test
19.7.2 Box and Pierce's Test and Ljung's Refinement
19.7.3 The Durbin-Watson Test
19.7.4 Testing in the Presence of a Lagged Dependent Variable
19.7.5 Summary of Testing Procedures
19.8 Efficient Estimation when _ is Known
19.9 Estimation when _ is Unknown
19.9.1 AR(1) Disturbances
19.9.2 Application: Estimation of a Model with Autocorrelation
19.9.3 Estimation with a Lagged Dependent Variable
19.10 Autocorrelation in Panel Data
19.11 Common Factors
19.12 Forecasting in the Presence of Autocorrelation
19.13 Autoregressive Conditional Heteroscedasticity
19.13.1 The ARCH(1) Model
19.13.2 ARCH(q), ARCH-in-Mean and Generalized ARCH Models
19.13.3 Maximum Likelihood Estimation of the GARCH Model
19.13.4 Testing for GARCH Effects
19.13.5 Pseudo-Maximum Likelihood Estimation
19.14 Summary and Conclusions
CHAPTER 20 Models with Lagged Variables
20.1 Introduction
20.2 Dynamic Regression Models
20.2.1 Lagged Effects in a Dynamic Model
20.2.2 The Lag and Difference Operators
20.2.3 Specification Search for the Lag Length
20.3 Simple Distributed Lag Models
20.4 Autoregressive Distributed Lag Models
20.4.1 Estimation of the ARDL Model
20.4.2 Computation of the Lag Weights in the ARDL Model
20.4.3 Stability of a Dynamic Equation
20.4.4 Forecasts
20.5 Methodological Issues in the Analysis of Dynamic Models
20.5.1 An Error Correction Model Autocorrelation
20.5.2 Specification Analysis
20.6 Vector Autoregressions
20.6.1 Model Forms
20.6.2 Estimation
20.6.3 Testing Procedures
20.6.4 Exogeneity
20.6.5 Testing for Granger Causality
20.6.6 Impulse Response Functions
20.6.7 Structural VARs
20.6.8 Application: Policy Analysis with a VAR
20.6.8.a A VAR Model for Macroeconomic Variables
20.6.8.b The Sacrifice Ration
20.6.8.c Identification and Estimation of a Structural VAR Model
20.6.8.d Inference
20.6.8.e Empirical Results
20.6.9 VARs in Microeconomics
20.7 Summary and Conclusions
CHAPTER 21 Time-Series Models
21.1 Introduction
21.2 Stationary Stochastic Processes
21.2.1 Autoregressive Moving Average Models
21.2.2 Stationarity and Invertibility
21.2.3 Autocorrelations of a Stationary Stochastic Process
21.2.4 Parial Autocorrelations of a Stationary Stochastic Process
21.2.5 Modeling Univariate Time Series
21.2.6 Estimation of the Parameters of a Univariate Time Series
21.3 The Frequency Domain
21.3.1 Theoretical Results
21.3.2 Empirical Counterparts
21.4 Summary and Conclusions
CHAPTER 22 Nonstationary Data
22.1 Introduction
22.2 Nonstationary Processes and Unit Roots
22.2.1 Integrated Processes and Differences
22.2.2 Random Walks, Trends and Spurious Regressions
22.2.3 Tests for Unit Roots in Economic Data
22.2.4 The Dickey-Fuller Tests
22.2.5 The KPSS Test of Stationarity
22.3 Cointegration
22.3.1 Common Trends
22.3.2 Error Correction and VAR Representations
22.3.3 Testing for Cointegration
22.3.4 Estimating Cointegrating Relationships
22.3.5 Application: German Money Demand
22.3.5.a Cointegration Analysis and a Long Run Theoretical Model
22.3.5.b Testing for Model Instability
22.4 Nonstationary Panel Data
22.5 Summary and Conclusions
Part VI 
Cross Sections, Panel Data and Microeconometrics
CHAPTER 23 Models for Discrete Choice
23.1 Models for Discrete Choice 
23.2 Discrete Choice Models
23.3 Models for Binary Choice
23.3.1 The Regression Approach
23.3.2 Latent Regression - Index Function Models
23.3.3 Random Utility Models
23.4 Estimation and Inference in Binary Choice Models
23.4.1 Robust covariance Matrix Estimation
23.4.2 Marginal Effects and Average Partial Effects
23.4.3 Hypothesis Tests
23.4.4 Specification Tests for Binary Choice Models
23.4.4.a Omitted Variables
23.4.4.b Heteroscedasticity
23.4.5 Measuring Goodness of Fit
23.4.6 Choice Based Sampling
23.4.7 Dynamic Binary Choice Models
23.5 Binary Choice Models for Panel Data
23.5.1 Random Effects Models
23.5.2 Fixed Effects Models
23.5.3 Modeling Heterogeneity
23.5.4 Parameter Heterogeneity
23.6 Semiparametric Analysis
23.6.1 Semiparametric Estimation
23.6.2 A Kernel Estimator for a Nonparametric Regression Function
23.7 Endogenous Right Hand Side Variables in Binary Choice Models
23.8 Bivariate Probit Models
23.8.1 Maximum Likelihood Estimation
23.8.2 Testing for Zero Correlation
23.8.3 Marginal Effects
23.8.4 Recursive Bivariate Probit Models
23.9 A Multivariate Probit Model
23.10 Analysis of Ordered Choice
23.10.1 The Ordered Probit Model
23.10.2 Bivariate Ordered Probit Models
23.10.3 Panel Data Applications
23.10.3.a Ordered Probit Models with Fixed Effects
23.10.3.b Ordered Probit Models with Random Effects
23.11 Models for Unordered Multiple Choices
23.11.1 The Multinomial Logit Model
23.11.2 The Conditional Logit Model
23.11.3 The Independence from Irrelevant Alternatives Assumption
23.11.4 Nested Logit Models
23.11.5 The Multinomial Probit Model
23.11.6 The Mixed Logit Model
23.11.7 Application: Conditional Logit Model for Travel Mode Choice
23.11.8 Panel Data and Stated Choice Experiments
23.12 Summary and Conclusions
Truncation, Censoring and Sample Selection
24.1 Introduction
24.2 Truncation
24.2.1 Truncated Distributions
24.2.2 Moments of Truncated Distributuions
24.2.3 The Truncated Regression Model
24.3 Censored Data
24.3.1 The Censored Normal Distribution
24.3.2 The Censored Regression (Tobit) Model
24.3.3 Estimation
24.3.4 Some Issues in Specification
24.3.4.a Heteroscedasticity
24.3.4.b Misspecification of Prob[y*<0]
24.3.4.c Corner Solutions
24.3.4.d Nonnormality
24.3.4.e Conditional Moment Tests
24.4 Panel Data Applications
24.5 Sample Selection
24.5.1 Incidental Truncation in a Bivariate Distribution
24.5.2 Regression in a Model of Selection
24.5.3 Estimation
24.5.4 Regression Analysis of Treatment Effects
24.5.5 The Normality Assumption
24.5.6 Estimating the Effect of Treatment on the Treated
24.5.7 Sample Selection in Nonlinear Models
24.5.8 Panel Data Applications of Sample Selection Models
24.5.8.a Common Effects in Sample Selection Models
24.5.8.b Attrition
24.6 Summary and Conclusion
CHAPTER 25 Models for Event Counts and Duration
25.1 Introduction
25.2 Models for Counts of Events
25.2.1 Measuring Goodness of Fit
25.2.2 Testing for Overdispersion
25.2.3 Heterogeneity and the Negative Binomial Regression Model
25.2.4 Functional Forms for Count Data
25.3 Panel Data Models
25.3.1 Robust Covariance Matrices
25.3.2 Fixed Effects
25.3.3 Random Effects
25.4 Hurdle and Zero Altered Poisson Models
25.5 Censoring and Truncation in Models for Counts
25.5.1 Censoring and Truncation in the Poisson Model
25.5.2 Application: Censoring in the Tobit and Poisson Regression Models
25.6 Models for Duration Data
25.6.1 Duration Data
25.6.2 A Regression-Like Approach: Parametric Models of Duration
25.6.2.a Theoretical Background
25.6.2.b Models of the Hazard Function
25.6.2.c Maximum Likelihood Estimation
25.6.2.d Exogenous Variables
25.6.2.e Heterogeneity
25.6.3 Nonparametric and Semiparametric Approaches
25.7 Summary and Conclusions
Part VII 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 Matrix Addition
A.2.4 Vector Multiplication
A.2.5 A Notation for Rows and Columns of a Matrix
A.2.6 Matrix Multiplication and Scalar Multiplication
A.2.7 Sums of Values
A.2.8 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 Solution of a System of Linear Equations
A.4.2 Inverse Matrices
A.4.3 Nonhomogeneous Systems of Equation
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
A.6.12 The Generalized Inverse of a Matrix
A.7 ratic Forms and Definite Matrices
A.7.1 Nonnegative Definite Matrices
A.7.2 Idempotent ratic 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 Distribution
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.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
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 ratic Forms in a Standard Normal Vector
B.11.5 The F Distribution
B.11.6 A Full Rank ratic Form
B.11.7 Independence of a Linear and a ratic 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 Internal 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 rature
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 Application
APPENDIX G Statistical Tables
 Examples and Applications
CHAPTER 1 Introduction
Example 1.1 Behavioral Models and the Nobel Laureates
Example 1.2 Keynes's Consumption Function
CHAPTER 2 The Classical Multiple Linear Regression Model
Example 2.1 Keynes's Consumption Function
Example 2.2 Earnings and Education
Example 2.3 The U.S. Gasoline Market
Example 2.4 The Translog Model
Example 2.5 Short Rank
CHAPTER 3 Least Squares
Example 3.1 Partial Correlations
Example 3.2 Fit of a Consumption Function
Example 3.3 Analysis of Variance for an Investment Equation
CHAPTER 4 Statistical Properties of the Least Squares Estimator
Example 4.1 The Sampling Distribution of a Least Squares Estimator
Example 4.2 Sampling Variance in the Two-Variable Regression Model
Example 4.3 Earning Estimation
Example 4.4 Confidence Interval for the Income Elasticity of Demand for Gasoline
Example 4.5 F Test for the Earnings Equation
Example 4.6 Multicollinearity in the Longley Data
Example 4.7 Nonlinear Functions of Parameters: The Delta Method
Example 4.8 Nonlinear Functions of Parameters: The Krinsky and Robb Method
Example 4.9 The Gamma Regression Model
CHAPTER 5 Inference and Prediction
Example 5.1 Restricted Investment Equation
Example 5.2 Production Function
Example 5.3 A Long-Run Marginal Propensity to Consume
Example 5.4 Prediction for Investment
CHAPTER 6 Functional Form and Structural Change
Example 6.1 Dummy Variables in an Earnings Function
Example 6.2 Analysis of Covariance
Example 6.3 Functional Form for a Nonlinear Cost Function
Example 6.4 Intrinsically Linear Regression
Example 6.5 CES Production Function
Example 6.6 The World Health Report
Example 6.7 Structural Break in the Gasoline Market
CHAPTER 7 Specification Analysis and Model Selection
Example 7.1 Omitted Variable
Example 7.2 J Test for a Consumption Function
Example 7.3 Vuong Test for a Consumption Function
Example 7.4 Bayesian Averaging of Classical Estimates
CHAPTER 8 The Generalized Regression Model and Heteroscedasticity
Example 8.1 Heteroscedastic Regression
Example 8.2 The White Estimator
Example 8.3 Testing for Heteroscedasticity
Example 8.4 Multiplicative Heteroscedasticity
Example 8.5 Groupwise Heteroscedasticity
CHAPTER 9 Models for Panel Data
Example 9.1 Wage Equation
Example 9.2 Robust Estimators of the Wage Equation
Example 9.3 Analysis of Covariance and the World Health Organization Data
Example 9.4 Fixed Effects Wage Equation
Example 9.5 Testing for Random Effects
Example 9.6 Estimates of the Random Effects Model
Example 9.7 Hausman Test for Fixed vs. Random Effects
Example 9.8 Variable Addition Test for Fixed vs. Random Effects
Example 9.9 Staewide Productivity
Example 9.10 Spatial Autocorrelation in Real Estate Sales
Example 9.11 Spatial Lags in Health Expenditures
Example 9.12 Random Coefficients Model
Example 9.13 Minimum Sum of Squares Estimates of the Production Function
Example 9.14 Two Step Estimation of Cornwell and Rupert's Wage Equation
Example 9.15 Fammie Mae's Pass Through
Example 9.16 Hierarchical Linear Model of Home Sales
Example 9.17 Mixed Linear Model for Wages
Example 9.18 Dynamic Panel Data Models
Example 9.19 A Mixed Fixed Growth Model for Developing Countries
CHAPTER 10 Systems of Regression Equations
Example 10.1 Munnell's Statewide Production Data
Example 10.2 Estimated SUR Model for Regional Output
Example 10.3 Hypothesis Tests in the SUR Model
Example 10.4 Testing for Cross Equation Correlation
Example 10.5 Demand for Electricity and Gas
Example 10.6 Hospital Costs
Example 10.7 Stone's Expenditure System
Example 10.8 A Cost Function for U.S. Manufacturing
CHAPTER 11 Nonlinear Regressions and Nonlinear Least Squares
Example 11.1 CES Production Function
Example 11.2 Translog Demand System
Example 11.3 First Order Conditions for a Nonlinear Model
Example 11.4 Linearized Regression
Example 11.5 Analysis of a Nonlinear Consumption Function
Example 11.6 Multicollinearity in Nonlinear Regression
Example 11.7 Flexible Cost Function
Example 11.8 Hypothesis Tests in a Nonlinear Regression Model
Example 11.9 Two-Step Estimation of a Credit Scoring Model
Example 11.10 Health Care Utilization
Example 11.11 Exponential Model with Fixed Effects
CHAPTER 12 Instrumental Variables Estimation
Example 12.1 Models in Which Least Squares is Inconsistent
Example 12.2 Streams as Instruments
Example 12.3 Labor Supply Market
Example 12.4 Hausman Test for a Consumption Function
Example 12.5 Income and Education in a Study of Twins
Example 12.6 Instrumental Variable Estimation of the Consumption Function
Example 12.7 The Returns to Schooling
Example 12.8 Dynamic Labor Supply Equation
Simultaneous-Equations Models
Example 13.1 A Small Macroeconomic Model
Example 13.2 Klein's Model I
Example 13.3 Structure and Reduced Form
Example 13.4 Observational Equivalence
Example 13.5 Identification
Example 13.6 Identification of Klein's Model I
Example 13.7 Testing Overidentifying Restrictions
Example 13.8 Dynamic Model
CHAPTER 14 Estimation Frameworks in Econometrics
Example 14.1 The Linear Regression Model
Example 14.2 The Stochastic Frontier Model
Example 14.3 Joint Modeling of a Pair of Event Counts
Example 14.4 LAD Estimation of a Cobb-Douglas Function
Example 14.5 Partially Linear Translog Cost Function
Example 14.6 Semiparametric Estimation of Binary Choice Models
Example 14.7 A Model of Vacation Expenditures
CHAPTER 15 Minimum Distance Estimation and The Generalized Method of Moments
Example 15.1 Euler Equations and Life Cycle Consumption
Example 15.2 Method of Moments Estimator for N[_,__]
Example 15.3 Inverse Gaussian (Wald) Distribution
Example 15.4 Mixtures of Normal Distributions
Example 15.5 Gamma Distribution
Example 15.6 Minimum Distance Estimation of a Hospital Cost Function
Example 15.7 GMM Estimation of the Parameters of a Gamma Distribution
Example 15.8 Empirical Moment Equation for Instrumental Variables
Example 15.9 Overidentifying Restrictions
Example 15.10 GMM Estimation of a Dynamic Model of Local Government Expenditures
CHAPTER 16 Maximum Likelihood
Example 16.1 Identification of Parameters
Example 16.2 Log Likelihood Function and Likelihood Equations for the Normal Distribution
Example 16.3 Information Matrix for the Normal Distribution
Example 16.4 Variance Estimators for an MLE
Example 16.5 Two Step ML Estimation
Example 16.6 Heteroscedastic Regression
Example 16.7 Autocorrelation in a Money Demand Equation
Example 16.8 ML Estimates of a Seemingly Unrelated Regressions Model
Example 16.9 Stochastic Frontier Model
Example 16.10 Geometric Model for Doctor visits
Example 16.11 Maximum Likelihood and FGLS Estimates of a Wage Equation
Example 16.12 Random Effects Geometric Regression Model
Example 16.13 Fixed and Random Effects Geometric Regression Model
Example 16.14 Latent Class Model for Grade Point Averages
Example 16.15 Latent Class Regression Model for Grade Point Averages
Example 16.16 Latent Class Model for Health Care Utilization
CHAPTER 17 Simulation Based Estimation and Inference
Example 17.1 Fractional Moments of the Truncated Normal Distribution
Example 17.2 Estimating the Lognormal Mean
Example 17.3 Mean of a Lognormal Distribution
Example 17.4 Monte Carlo Study of the Mean versus the Median
17.4.1 A Monte Carlo Study: Behavior of a Test Statistic
17.4.2 A Monte Carlo Study: The Incidental Parameters Problem
Example 17.5 Random Effects Geometric Regression
Example 17.6 Maximum Simulated Likelihood Estimation of a Binary Choice Model
Example 17.7 Bootstrapping the Variance of the Median
CHAPTER 18 Bayesian Inference in Econometrics
Example 18.1 Bayesian Estimation of a Proportion
Example 18.2 Estimation with a Conjugate Prior
Example 18.3 Bayesian Estimate of the Marginal Propensity to Consume
Example 18.4 Posterior Odds for the Classical Regression Model
Example 18.5 Gibbs Sampling from the Normal Distribution
Example 18.6 Application: Binomial Probit Model
Example 18.7 Gibbs Sampler for a Probit Model
CHAPTER 19 Serial Correlation
Example 19.1 Money Demand Equation
Example 19.2 Autocorrelation Induced by Misspecification of the Model
Example 19.3 Negative Autocorrelation in the Phillips Curve
Example 19.4 Autocorrelation Consistent Covariance Matrix
Example 19.5 Panel Data Models with Autocorrelation
Example 19.6 Test for Common Factors
Example 19.7 Stochastic Volatility
CHAPTER 20 Models with Lagged Variables
Example 20.1 A Structural Model of the Demand for Gasoline
Example 20.2 Expectations Augmented Phillips Curve
Example 20.3 Price and Income Elasticities of Demand for Gasoline
Example 20.4 A Rational Lag Model
Example 20.5 An Error Correction Model for Consumption
Example 20.6 Granger Causality
20.6.8 Application: Policy Analysis with a VAR
Example 20.7 VAR for Municipal Expenditures
CHAPTER 21 Time-Series Models
Example 21.1 ACF and PACF for a Series of Bond Yields
Example 21.2 Spectral Density Function for an AR(1) Process
Example 21.3 Spectral Analysis of the Growth Rate of Real GNP
CHAPTER 22 Nonstationary Data
Example 22.1 A Nonstationary Series
Example 22.2 Tests for Unit Roots
Example 22.3 Augmented Dicky-Fuller Test for a Unit Root in GNP
Example 22.4 Is There a Unit Root in GNP?
22.4.5 Application: German Money Demand
Example 22.5 Cointegration in Consumption and Output
Example 22.6 Several Cointegrated Series
Example 22.7 Multiple Cointegrating Vectors
Example 22.8 Cointegration in Consumption and Output
CHAPTER 23 Models for Discrete Choice
Example 23.1 Labor Force Participation Model
Example 23.2 Structural Equations for a Probit Model
Example 23.3 Probability Models
Example 23.4 Average Partial Effects
Example 23.5 Specification Tests in a Labor Force Participation Model
Example 23.6 Prediction with a Probit Model
Example 23.7 An Intertemporal Labor Force Participation Equation
Example 23.8 Binary Choice Models for Panel Data
Example 23.9 Fixed Effects Logit Models: Magazine Prices Revisited
Example 23.10 Semiparametric Models of Heterogeneity
Example 23.11 Parameter Heterogeneity in a Binary Choice Model
23.11.1 Application: Conditional Logit Model for Travel Mode Choice
Example 23.12 A Comparison of Binary Choice Estimators
Example 23.13 Labor Supply Model
Example 23.14 Tetrachoric Correlation
Example 23.15 Bivariate Probit Model for Health Care Utilization
Example 23.16 A Multivariate Probit Model for Product Innovations
Example 23.17 Rating Assignments
Example 23.18 Calculus and Intermediate Economics Courses
Example 23.19 Health Satisfaction
CHAPTER 24 Truncation, Censoring and Sample Selection
Example 24.1 Truncated Uniform Distribution
Example 24.2 A Truncated Lognormal Income Distribution
Example 24.3 Censored Random Variable
Example 24.4 Estimated Tobit Equations for Hours Worked
Example 24.5 Multiplicative Heteroscedasticity in the Tobit Model
Example 24.6 Incidental Truncation
Example 24.7 A Model of Labor Supply
Example 24.8 Female Labor Supply
Example 24.9 A Mover Stayer Model for Migration
Example 24.10 Treatment Effects on Earnings
Example 24.11 Doctor Visits and Insurance
CHAPTER 25 Models for Event Counts and Duration
Example 25.1 Count Data Models for Doctor Visits
Example 25.2 Panel Datra Models for Doctor Visits
Example 25.3 A Split Population Model for Major Derogatory Reports
Example 25.4 Survival Models for Strike Duration
25.5.2 Application: Censoring in the Tobit and Poisson Regression Models
APPENDIX C Models for Event Counts and Duration
Example C.1 Descriptive Statistics for Random Sample
Example C.2 Kernel Density for the Income Data
Example C.3 Sampling Distribution of a Sample Mean
Example C.4 Sampling Distribution of the Sample Minimum
Example C.5 Mean-Squared Error of the Sample Variance
Example C.6 Likelihood Functions for Exponential and Normal Distributions
Example C.7 Variance Bound for the Poisson Distribution
Example C.8 Confidence Intervals for the Normal Mean
Example C.9 Confidence Intervals for a Normal Mean and Variance
Example C.10 Testing a Hypothesis About a Mean
Example C.11 Consistent Test About a Mean
Example C.12 Testing a Hypothesis About a Mean with a Confidence Interval
Example C.13 One-Sided Test About a Mean
APPENDIX D Large Sample Distribution Theory
Example D.1 Mean Square Convergence of the Sample Minimum in Exponential Sampling
Example D.2 Estimating a Function of the Mean
Example D.3 Probability Limit of a Function of x and s_
Example D.4 Limiting Distribution of tn-1
Example D.5 The F Distribution
Example D.6 The Lindeberg-Levy Central Limit Theorem
Example D.7 Asymptotic Distribution of the Mean of an Exponential Sample
Example D.8 Asymptotic Inefficiency of the Median in Normal Sampling
Example D.9 Asymptotic Moments of the Sample Variance
APPENDIX E Computation and Optimization
Example E.1 Function of One Parameter
Example E.2 Function of Two Parameters: The Gamma Distribution
Example E.3 A Concentrated Log-Likelihood Function

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