Book , Print in English

Econometric analysis of cross section and panel data

Jeffrey M. Wooldridge.
  • Cambridge, Mass. : MIT Press, ©2010.
  • 2nd ed.
  • xxvii, 1064 pages : illustrations; 24 cm.
Subjects
Contents
  • I. INTRODUCTION AND BACKGROUND
  • 1. Introduction
  • 1.1. Causal Relationships and Ceteris Paribus Analysis
  • 1.2. Stochastic Setting and Asymptotic Analysis
  • 1.2.1. Data Structures
  • 1.2.2. Asymptotic Analysis
  • 1.3. Some Examples
  • 1.4. Why Not Fixed Explanatory Variables?
  • 2. Conditional Expectations and Related Concepts in Econometrics
  • 2.1. Role of Conditional Expectations in Econometrics
  • 2.2. Features of Conditional Expectations
  • 2.2.1. Definition and Examples
  • 2.2.2. Partial Effects, Elasticities, and Semielasticities
  • 2.2.3. Error Form of Models of Conditional Expectations
  • 2.2.4. Some Properties of Conditional Expectations
  • 2.2.5. Average Partial Effects
  • 2.3. Linear Projections
  • Problems
  • Appendix 2A
  • 2.A.1. Properties of Conditional Expectations
  • 2.A.2. Properties of Conditional Variances and Covariances
  • 2.A.3. Properties of Linear Projections
  • 3. Basic Asymptotic Theory
  • 3.1. Convergence of Deterministic Sequences
  • 3.2. Convergence in Probability and Boundedness in Probability
  • 3.3. Convergence in Distribution
  • 3.4. Limit Theorems for Random Samples
  • 3.5. Limiting Behavior of Estimators and Test Statistics
  • 3.5.1. Asymptotic Properties of Estimators
  • 3.5.2. Asymptotic Properties of Test Statistics
  • Problems
  • II. LINEAR MODELS
  • 4. Single-Equation Linear Model and Ordinary Least Squares Estimation
  • 4.1. Overview of the Single-Equation Linear Model
  • 4.2. Asymptotic Properties of Ordinary Least Squares
  • 4.2.1. Consistency
  • 4.2.2. Asymptotic Inference Using Ordinary Least Squares
  • 4.2.3. Heteroskedasticity-Robust Inference
  • 4.2.4. Lagrange Multiplier (Score) Tests
  • 4.3. Ordinary Least Squares Solutions to the Omitted Variables Problem
  • 4.3.1. Ordinary Least Squares Ignoring the Omitted Variables
  • 4.3.2. Proxy Variable-Ordinary Least Squares Solution
  • 4.3.3. Models with Interactions in Unobservables: Random Coefficient Models
  • 4.4. Properties of Ordinary Least Squares under Measurement Error
  • 4.4.1. Measurement Error in the Dependent Variable
  • 4.4.2. Measurement Error in an Explanatory Variable
  • Problems
  • 5. Instrumental Variables Estimation of Single-Equation Linear Models
  • 5.1. Instrumental Variables and Two-Stage Least Squares
  • 5.1.1. Motivation for Instrumental Variables Estimation
  • 5.1.2. Multiple Instruments: Two-Stage Least Squares
  • 5.2. General Treatment of Two-Stage Least Squares
  • 5.2.1. Consistency
  • 5.2.2. Asymptotic Normality of Two-Stage Least Squares
  • 5.2.3. Asymptotic Efficiency of Two-Stage Least Squares
  • 5.2.4. Hypothesis Testing with Two-Stage Least Squares
  • 5.2.5. Heteroskedasticity-Robust Inference for Two-Stage Least Squares
  • 5.2.6. Potential Pitfalls with Two-Stage Least Squares
  • 5.3. IV Solutions to the Omitted Variables and Measurement Error Problems
  • 5.3.1. Leaving the Omitted Factors in the Error Term
  • 5.3.2. Solutions Using Indicators of the Unobservables
  • Problems
  • 6. Additional Single-Equation Topics
  • 6.1. Estimation with Generated Regressors and Instruments
  • 6.1.1. Ordinary Least Squares with Generated Regressors
  • 6.1.2. Two-Stage Least Squares with Generated Instruments
  • 6.1.3. Generated Instruments and Regressors
  • 6.2. Control Function Approach to Endogeneity
  • 6.3. Some Specification Tests
  • 6.3.1. Testing for Endogeneity
  • 6.3.2. Testing Overidentifying Restrictions
  • 6.3.3. Testing Functional Form
  • 6.3.4. Testing for Heteroskedasticity
  • 6.4. Correlated Random Coefficient Models
  • 6.4.1. When Is the Usual IV Estimator Consistent?
  • 6.4.2. Control Function Approach
  • 6.5. Pooled Cross Sections and Difference-in-Differences Estimation
  • 6.5.1. Pooled Cross Sections over Time
  • 6.5.2. Policy Analysis and Difference-in-Differences Estimation
  • Problems
  • Appendix 6A
  • 7. Estimating Systems of Equations by Ordinary Least Squares and Generalized Least Squares
  • 7.1. Introduction
  • 7.2. Some Examples
  • 7.3. System Ordinary Least Squares Estimation of a Multivariate Linear System
  • 7.3.1. Preliminaries
  • 7.3.2. Asymptotic Properties of System Ordinary Least Squares
  • 7.3.3. Testing Multiple Hypotheses
  • 7.4. Consistency and Asymptotic Normality of Generalized Least Squares
  • 7.4.1. Consistency
  • 7.4.2. Asymptotic Normality
  • 7.5. Feasible Generalized Least Squares
  • 7.5.1. Asymptotic Properties
  • 7.5.2. Asymptotic Variance of Feasible Generalized Least Squares under a Standard Assumption
  • 7.5.3. Properties of Feasible Generalized Least Squares with (Possibly Incorrect) Restrictions on the Unconditional Variance Matrix
  • 7.6. Testing the Use of Feasible Generalized Least Squares
  • 7.7. Seemingly Unrelated Regressions, Revisited
  • 7.7.1. Comparison between Ordinary Least Squares and Feasible Generalized Least Squares for Seemingly Unrelated Regressions Systems
  • 7.7.2. Systems with Cross Equation Restrictions
  • 7.7.3. Singular Variance Matrices in Seemingly Unrelated Regressions Systems
  • 7.8. Linear Panel Data Model, Revisited
  • 7.8.1. Assumptions for Pooled Ordinary Least Squares
  • 7.8.2. Dynamic Completeness
  • 7.8.3. Note on Time Series Persistence
  • 7.8.4. Robust Asymptotic Variance Matrix
  • 7.8.5. Testing for Serial Correlation and Heteroskedasticity after Pooled Ordinary Least Squares
  • 7.8.6. Feasible Generalized Least Squares Estimation under Strict Exogeneity
  • Problems
  • 8. System Estimation by Instrumental Variables
  • 8.1. Introduction and Examples
  • 8.2. General Linear System of Equations
  • 8.3. Generalized Method of Moments Estimation
  • 8.3.1. General Weighting Matrix
  • 8.3.2. System Two-Stage Least Squares Estimator
  • 8.3.3. Optimal Weighting Matrix
  • 8.3.4. Generalized Method of Moments Three-Stage Least Squares Estimator
  • 8.4. Generalized Instrumental Variables Estimator
  • 8.4.1. Derivation of the Generalized Instrumental Variables Estimator and Its Asymptotic Properties
  • 8.4.2. Comparison of Generalized Method of Moment, Generalized Instrumental Variables, and the Traditional Three-Stage Least Squares Estimator
  • 8.5. Testing Using Generalized Method of Moments
  • 8.5.1. Testing Classical Hypotheses
  • 8.5.2. Testing Overidentification Restrictions
  • 8.6. More Efficient Estimation and Optimal Instruments
  • 8.7. Summary Comments on Choosing an Estimator
  • Problems
  • 9. Simultaneous Equations Models
  • 9.1. Scope of Simultaneous Equations Models
  • 9.2. Identification in a Linear System
  • 9.2.1. Exclusion Restrictions and Reduced Forms
  • 9.2.2. General Linear Restrictions and Structural Equations
  • 9.2.3. Unidentified, Just Identified, and Overidentified Equations
  • 9.3. Estimation after Identification
  • 9.3.1. Robustness-Efficiency Trade-off
  • 9.3.2. When Are 2SLS and 3SLS Equivalent?
  • 9.3.3. Estimating the Reduced Form Parameters
  • 9.4. Additional Topics in Linear Simultaneous Equations Methods
  • 9.4.1. Using Cross Equation Restrictions to Achieve Identification
  • 9.4.2. Using Covariance Restrictions to Achieve Identification
  • 9.4.3. Subtleties Concerning Identification and Efficiency in Linear Systems
  • 9.5. Simultaneous Equations Models Nonlinear in Endogenous Variables
  • 9.5.1. Identification
  • 9.5.2. Estimation
  • 9.5.3. Control Function Estimation for Triangular Systems
  • 9.6. Different Instruments for Different Equations
  • Problems
  • 10. Basic Linear Unobserved Effects and Explanatory Variables
  • 10.1. Motivation: Omitted Variables Problem
  • 10.2. Assumptions about the Unobserved Effects and Explanatory Variables
  • 10.2.1. Random or Fixed Effects?
  • 10.2.2. Strict Exogeneity Assumptions on the Explanatory Variables
  • 10.2.3. Some Examples of Unobserved Effects Panel Data Models
  • 10.3. Estimating Unobserved Effects Models by Pooled Ordinary Least Squares
  • 10.4. Random Effects Methods
  • 10.4.1. Estimation and Inference under the Basic Random Effects Assumptions
  • 10.4.2. Robust Variance Matrix Estimator
  • 10.4.3. General Feasible Generalized Least Squares Analysis
  • 10.4.4. Testing for the Presence of an Unobserved Effect
  • 10.5. Fixed Effects Methods
  • 10.5.1. Consistency of the Fixed Effects Estimator
  • 10.5.2. Asymptotic Inference with Fixed Effects
  • 10.5.3. Dummy Variable Regression
  • 10.5.4. Serial Correlation and the Robust Variance Matrix Estimator
  • 10.5.5. Fixed Effects Generalized Least Squares
  • 10.5.6. Using Fixed Effects Estimation for Policy Analysis
  • 10.6. First Differencing Methods
  • 10.6.1. Inference
  • 10.6.2. Robust Variance Matrix
  • 10.6.3. Testing for Serial Correlation
  • 10.6.4. Policy Analysis Using First Differencing
  • 10.7. Comparison of Estimators
  • 10.7.1. Fixed Effects versus First Differencing
  • 10.7.2. Relationship between the Random Effects and Fixed Effects Estimators
  • 10.7.3. Hausman Test Comparing Random Effects and Fixed Effects Estimators
  • Problems
  • 11. More Topics in Linear Unobserved Effects Models
  • 11.1. Generalized Method of Moments Approaches to the Standard Linear Unobserved Effects Model
  • 11.1.1. Equivalance between GMM 3SLS and Standard Estimators
  • 11.1.2. Chamberlain's Approach to Unobserved Effects Models
  • 11.2. Random and Fixed Effects Instrumental Variables Methods
  • 11.3. Hausman and Taylor-Type Models
  • 11.4. First Differencing Instrumental Variables Methods
  • 11.5. Unobserved Effects Models with Measurement Error
  • 11.6. Estimation under Sequential Exogeneity
  • 11.6.1. General Framework --
  • Contents note continued: 11.6.2. Models with Lagged Dependent Variables
  • 11.7. Models with Individual-Specific Slopes
  • 11.7.1. Random Trend Model
  • 11.7.2. General Models with Individual-Specific Slopes
  • 11.7.3. Robustness of Standard Fixed Effects Methods
  • 11.7.4. Testing for Correlated Random Slopes
  • Problems
  • III. GENERAL APPROACHES TO NONLINEAR ESTIMATION
  • 12. M-Estimation, Nonlinear Regression, and Quantile Regression
  • 12.1. Introduction
  • 12.2. Identification, Uniform Convergence, and Consistency
  • 12.3. Asymptotic Normality
  • 12.4. Two-Step M-Estimators
  • 12.4.1. Consistency
  • 12.4.2. Asymptotic Normality
  • 12.5. Estimating the Asymptotic Variance
  • 12.5.1. Estimation without Nuisance Parameters
  • 12.5.2. Adjustments for Two-Step Estimation
  • 12.6. Hypothesis Testing
  • 12.6.1. Wald Tests
  • 12.6.2. Score (or Lagrange Multiplier) Tests
  • 12.6.3. Tests Based on the Change in the Objective Function
  • 12.6.4. Behavior of the Statistics under Alternatives
  • 12.7. Optimization Methods
  • 12.7.1. Newton-Raphson Method
  • 12.7.2. Berndt, Hall, Hall, and Hausman Algorithm
  • 12.7.3. Generalized Gauss-Newton Method
  • 12.7.4. Concentrating Parameters out of the Objective Function
  • 12.8. Simulation and Resampling Methods
  • 12.8.1. Monte Carlo Simulation
  • 12.8.2. Bootstrapping
  • 12.9. Multivariate Nonlinear Regression Methods
  • 12.9.1. Multivariate Nonlinear Least Squares
  • 12.9.2. Weighted Multivariate Nonlinear Least Squares
  • 12.10. Quantile Estimation
  • 12.10.1. Quantiles, the Estimation Problem, and Consistency
  • 12.10.2. Asymptotic Inference
  • 12.10.3. Quantile Regression for Panel Data
  • Problems
  • 13. Maximum Likelihood Methods
  • 13.1. Introduction
  • 13.2. Preliminaries and Examples
  • 13.3. General Framework for Conditional Maximum Likelihood Estimation
  • 13.4. Consistency of Conditional Maximum Likelihood Estimation
  • 13.5. Asymptotic Normality and Asymptotic Variance Estimation
  • 13.5.1. Asymptotic Normality
  • 13.5.2. Estimating the Asymptotic Variance
  • 13.6. Hypothesis Testing
  • 13.7. Specification Testing
  • 13.8. Partial (or Pooled) Likelihood Methods for Panel Data
  • 13.8.1. Setup for Panel Data
  • 13.8.2. Asymptotic Inference
  • 13.8.3. Inference with Dynamically Complete Models
  • 13.9. Panel Data Models with Unobserved Effects
  • 13.9.1. Models with Strictly Exogenous Explanatory Variables
  • 13.9.2. Models with Lagged Dependent Variables
  • 13.10. Two-Step Estimators Involving Maximum Likelihood
  • 13.10.1. Second-Step Estimator Is Maximum Likelihood Estimator
  • 13.10.2. Surprising Efficiency Result When the First-Step Estimator Is Conditional Maximum Likelihood Estimator
  • 13.11. Quasi-Maximum Likelihood Estimation
  • 13.11.1. General Misspecification
  • 13.11.2. Model Selection Tests
  • 13.11.3. Quasi-Maximum Likelihood Estimation in the Linear Exponential Family
  • 13.11.4. Generalized Estimating Equations for Panel Data
  • Problems
  • Appendix 13A
  • 14. Generalized Method of Moments and Minimum Distance Estimation
  • 14.1. Asymptotic Properties of Generalized Method of Moments
  • 14.2. Estimation under Orthogonality Conditions
  • 14.3. Systems of Nonlinear Equations
  • 14.4. Efficient Estimation
  • 14.4.1. General Efficiency Framework
  • 14.4.2. Efficiency of Maximum Likelihood Estimator
  • 14.4.3. Efficienct Choice of Instruments under Conditional Moment Restrictions
  • 14.5. Classical Minimum Distance Estimation
  • 14.6. Panel Data Applications
  • 14.6.1. Nonlinear Dynamic Models
  • 14.6.2. Minimum Distance Approach to the Unobserved Effects Model
  • 14.6.3. Models with Time-Varying Coefficients on the Unobserved Effects
  • Problems
  • Appendix 14A
  • IV. NONLINEAR MODELS AND RELATED TOPICS
  • 15. Binary Response Models
  • 15.1. Introduction
  • 15.2. Linear Probability Model for Binary Response
  • 15.3. Index Models for Binary Response: Probit and Logit
  • 15.4. Maximum Likelihood Estimation of Binary Response Index Models
  • 15.5. Testing in Binary Response Index Models
  • 15.5.1. Testing Multiple Exclusion Restrictions
  • 15.5.2. Testing Nonlinear Hypotheses about β
  • 15.5.3. Tests against More General Alternatives
  • 15.6. Reporting the Results for Probit and Logit
  • 15.7. Specification Issues in Binary Response Models
  • 15.7.1. Neglected Heterogeneity
  • 15.7.2. Continuous Endogenous Explanatory Variables
  • 15.7.3. Binary Endogenous Explanatory Variable
  • 15.7.4. Heteroskedasticity and Nonnormality in the Latent Variable Model
  • 15.7.5. Estimation under Weaker Assumptions
  • 15.8. Binary Response Models for Panel Data
  • 15.8.1. Pooled Probit and Logit
  • 15.8.2. Unobserved Effects Probit Models under Strict Exogeneity
  • 15.8.3. Unobserved Effects Logit Models under Strict Exogeneity
  • 15.8.4. Dynamic Unobserved Effects Models
  • 15.8.5. Probit Models with Heterogeneity and Endogenous Explanatory Variables
  • 15.8.6. Semiparametric Approaches
  • Problems
  • 16. Multinomial and Ordered Response Models
  • 16.1. Introduction
  • 16.2. Multinomial Response Models
  • 16.2.1. Multinomial Logit
  • 16.2.2. Probabilistic Choice Models
  • 16.2.3. Endogenous Explanatory Variables
  • 16.2.4. Panel Data Methods
  • 16.3. Ordered Response Models
  • 16.3.1. Ordered Logit and Ordered Probit
  • 16.3.2. Specification Issues in Ordered Models
  • 16.3.3. Endogenous Explanatory Variables
  • 16.3.4. Panel Data Methods
  • Problems
  • 17. Corner Solution Responses
  • 17.1. Motivation and Examples
  • 17.2. Useful Expressions for Type I Tobit
  • 17.3. Estimation and Inference with the Type I Tobit Model
  • 17.4. Reporting the Results
  • 17.5. Specification Issues in Tobit Models
  • 17.5.1. Neglected Heterogeneity
  • 17.5.2. Endogenous Explanatory Models
  • 17.5.3. Heteroskedasticity and Nonnormality in the Latent Variable Model
  • 17.5.4. Estimating Parameters with Weaker Assumptions
  • 17.6. Two-Part Models and Type II Tobit for Corner Solutions
  • 17.6.1. Truncated Normal Hurdle Model
  • 17.6.2. Lognormal Hurdle Model and Exponential Conditional Mean
  • 17.6.3. Exponential Type II Tobit Model
  • 17.7. Two-Limit Tobit Model
  • 17.8. Panel Data Methods
  • 17.8.1. Pooled Methods
  • 17.8.2. Unobserved Effects Models under Strict Exogeneity
  • 17.8.3. Dynamic Unobserved Effects Tobit Models
  • Problems
  • 18. Count, Fractional, and Other Nonnegative Responses
  • 18.1. Introduction
  • 18.2. Poisson Regression
  • 18.2.1. Assumptions Used for Poission Regression and Quantities of Interest
  • 18.2.2. Consistency of the Poisson QMLE
  • 18.2.3. Asymptotic Normality of the Poisson QMLE
  • 18.2.4. Hypothesis Testing
  • 18.2.5. Specification Testing
  • 18.3. Other Count Data Regression Models
  • 18.3.1. Negative Binomial Regression Models
  • 18.3.2. Binomial Regression Models
  • 18.4. Gamma (Exponential) Regression Model
  • 18.5. Endogeneity with an Exponential Regression Function
  • 18.6. Fractional Responses
  • 18.6.1. Exogenous Explanatory Variables
  • 18.6.2. Endogenous Explanatory Variables
  • 18.7. Panel Data Methods
  • 18.7.1. Pooled QMLE
  • 18.7.2. Specifying Models of Conditional Expectations with Unobserved Effects
  • 18.7.3. Random Effects Methods
  • 18.7.4. Fixed Effects Poisson Estimation
  • 18.7.5. Relaxing the Strict Exogeneity Assumption
  • 18.7.6. Fractional Response Models for Panel Data
  • Problems
  • 19. Censored Data, Sample Selection, and Attrition
  • 19.1. Introduction
  • 19.2. Data Censoring
  • 19.2.1. Binary Censoring
  • 19.2.2. Interval Coding
  • 19.2.3. Censoring from Above and Below
  • 19.3. Overview of Sample Selection
  • 19.4. When Can Sample Selection Be Ignored?
  • 19.4.1. Linear Models: Estimation by OLS and 2SLS
  • 19.4.2. Nonlinear Models
  • 19.5. Selection on the Basis of the Response Variable: Truncated Regression
  • 19.6. Incidental Truncation: A Probit Selection Equation
  • 19.6.1. Exogenous Explanatory Variables
  • 19.6.2. Endogenous Explanatory Variables
  • 19.6.3. Binary Response Model with Sample Selection
  • 19.6.4. Exponential Response Function
  • 19.7. Incidental Truncation: A Tobit Selection Equation
  • 19.7.1. Exogenous Explanatory Variables
  • 19.7.2. Endogenous Explanatory Variables
  • 19.7.3. Estimating Structural Tobit Equations with Sample Selection
  • 19.8. Inverse Probability Weighting for Missing Data
  • 19.9. Sample Selection and Attrition in Linear Panel Data Models
  • 19.9.1. Fixed and Random Effects Estimation with Unbalanced Panels
  • 19.9.2. Testing and Correcting for Sample Selection Bias
  • 19.9.3. Attrition
  • Problems
  • 20. Stratified Sampling and Cluster Sampling
  • 20.1. Introduction
  • 20.2. Stratified Sampling
  • 20.2.1. Standard Stratified Sampling and Variable Probability Sampling
  • 20.2.2. Weighted Estimators to Account for Stratification
  • 20.2.3. Stratification Based on Exogenous Variables
  • 20.3. Cluster Sampling
  • 20.3.1. Inference with a Large Number of Clusters and Small Cluster Sizes
  • 20.3.2. Cluster Samples with Unit-Specific Panel Data
  • 20.3.3. Should We Apply Cluster-Robust Inference with Large Group Sizes?
  • 20.3.4. Inference When the Number of Clusters Is Small
  • 20.4. Complex Survey Sampling
  • Problems
  • 21. Estimating Average Treatment Effects
  • 21.1. Introduction
  • 21.2. Counterfactual Setting and the Self-Selection Problem
  • 21.3. Methods Assuming Ignorability (or Unconfoundedness) of Treatment
  • 21.3.1. Identification --
  • Contents note continued: 21.3.2. Regression Adjustment
  • 21.3.3. Propensity Score Methods
  • 21.3.4. Combining Regression Adjustment and Propensity Score Weighting
  • 21.3.5. Matching Methods
  • 21.4. Instrumental Variables Methods
  • 21.4.1. Estimating the Average Treatment Effect Using IV
  • 21.4.2. Correction and Control Function Approaches
  • 21.4.3. Estimating the Local Average Treatment Effect by IV
  • 21.5. Regression Discontinuity Designs
  • 21.5.1. Sharp Regression Discontinuity Design
  • 21.5.2. Fuzzy Regression Discontinuity Design
  • 21.5.3. Unconfoundedness versus the Fuzzy Regression Discontinuity
  • 21.6. Further Issues
  • 21.6.1. Special Considerations for Responses with Discreteness or Limited Range
  • 21.6.2. Multivalued Treatments
  • 21.6.3. Multiple Treatments
  • 21.6.4. Panel Data
  • Problems
  • 22. Duration Analysis
  • 22.1. Introduction
  • 22.2. Hazard Functions
  • 22.2.1. Hazard Functions without Covariates
  • 22.2.2. Hazard Functions Conditional on Time-Invariant Covariates
  • 22.2.3. Hazard Functions Conditional on Time-Varying Covariates
  • 22.3. Analysis of Single-Spell Data with Time-Invariant Covariates
  • 22.3.1. Flow Sampling
  • 22.3.2. Maximum Likelihood Estimation with Censored Flow Data
  • 22.3.3. Stock Sampling
  • 22.3.4. Unobserved Heterogeneity
  • 22.4. Analysis of Grouped Duration Data
  • 22.4.1. Time-Invariant Covariates
  • 22.4.2. Time-Varying Covariates
  • 22.4.3. Unobserved Heterogeneity
  • 22.5. Further Issues
  • 22.5.1. Cox's Partial Likelihood Method for the Proportional Hazard Model
  • 22.5.2. Multiple-Spell Data
  • 22.5.3. Competing Risks Models
  • Problems.
Other information
  • Includes bibliographical references (p. [1025]-1044) and index.
ISBN
  • 9780262232586 (hardcover : alk. paper)
  • 0262232588 (hardcover : alk. paper)
Identifying numbers
  • LCCN: 2010020912
  • OCLC: 627701062
  • OCLC: 627701062