PAWEL ODATA
`
`UF CHOSS SECTION
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`2a ee ee
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`A
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`Regeneron Exhibit 1199.001
`Regeneron Exhibit 1199.001
`Regeneronv. Novartis
`Regeneron v. Novartis
`IPR2021-00816
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`
`

`

`Econometric Analysis of Cross Section and Panel Data
`
`Je¤rey M. Wooldridge
`
`The MIT Press
`Cambridge, Massachusetts
`London, England
`
`Regeneron Exhibit 1199.002
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`IPR2021-00816
`
`

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`Contents
`
`I
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`1
`1.1
`1.2
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`1.3
`1.4
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`2
`2.1
`2.2
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`2.3
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`3
`3.1
`3.2
`3.3
`3.4
`3.5
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`Preface
`Acknowledgments
`
`INTRODUCTION AND BACKGROUND
`
`Introduction
`Causal Relationships and Ceteris Paribus Analysis
`The Stochastic Setting and Asymptotic Analysis
`1.2.1 Data Structures
`1.2.2 Asymptotic Analysis
`Some Examples
`Why Not Fixed Explanatory Variables?
`
`Conditional Expectations and Related Concepts in Econometrics
`The Role of Conditional Expectations in Econometrics
`Features of Conditional Expectations
`2.2.1 Definition and Examples
`2.2.2
`Partial E¤ects, Elasticities, and Semielasticities
`2.2.3 The Error Form of Models of Conditional Expectations
`2.2.4
`Some Properties of Conditional Expectations
`2.2.5 Average Partial E¤ects
`Linear Projections
`Problems
`Appendix 2A
`2.A.1 Properties of Conditional Expectations
`2.A.2 Properties of Conditional Variances
`2.A.3 Properties of Linear Projections
`
`Basic Asymptotic Theory
`Convergence of Deterministic Sequences
`Convergence in Probability and Bounded in Probability
`Convergence in Distribution
`Limit Theorems for Random Samples
`Limiting Behavior of Estimators and Test Statistics
`3.5.1 Asymptotic Properties of Estimators
`3.5.2 Asymptotic Properties of Test Statistics
`Problems
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`II
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`4
`4.1
`4.2
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`4.3
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`4.4
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`5
`5.1
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`5.2
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`5.3
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`LINEAR MODELS
`
`The Single-Equation Linear Model and OLS Estimation
`Overview of the Single-Equation Linear Model
`Asymptotic Properties of OLS
`4.2.1 Consistency
`4.2.2 Asymptotic Inference Using OLS
`4.2.3 Heteroskedasticity-Robust Inference
`4.2.4 Lagrange Multiplier (Score) Tests
`OLS Solutions to the Omitted Variables Problem
`4.3.1 OLS Ignoring the Omitted Variables
`4.3.2 The Proxy Variable–OLS Solution
`4.3.3 Models with Interactions in Unobservables
`Properties of OLS under Measurement Error
`4.4.1 Measurement Error in the Dependent Variable
`4.4.2 Measurement Error in an Explanatory Variable
`Problems
`
`Instrumental Variables Estimation of Single-Equation Linear Models
`Instrumental Variables and Two-Stage Least Squares
`5.1.1 Motivation for Instrumental Variables Estimation
`5.1.2 Multiple Instruments: Two-Stage Least Squares
`General Treatment of 2SLS
`5.2.1 Consistency
`5.2.2 Asymptotic Normality of 2SLS
`5.2.3 Asymptotic E‰ciency of 2SLS
`5.2.4 Hypothesis Testing with 2SLS
`5.2.5 Heteroskedasticity-Robust Inference for 2SLS
`5.2.6
`Potential Pitfalls with 2SLS
`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
`6.1
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`Additional Single-Equation Topics
`Estimation with Generated Regressors and Instruments
`
`Contents
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`Contents
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`6.2
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`6.3
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`7
`7.1
`7.2
`7.3
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`7.4
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`7.5
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`7.6
`7.7
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`6.1.1 OLS with Generated Regressors
`6.1.2
`2SLS with Generated Instruments
`6.1.3 Generated Instruments and Regressors
`Some Specification Tests
`6.2.1 Testing for Endogeneity
`6.2.2 Testing Overidentifying Restrictions
`6.2.3 Testing Functional Form
`6.2.4 Testing for Heteroskedasticity
`Single-Equation Methods under Other Sampling Schemes
`6.3.1
`Pooled Cross Sections over Time
`6.3.2 Geographically Stratified Samples
`6.3.3
`Spatial Dependence
`6.3.4 Cluster Samples
`Problems
`Appendix 6A
`
`Estimating Systems of Equations by OLS and GLS
`Introduction
`Some Examples
`System OLS Estimation of a Multivariate Linear System
`7.3.1
`Preliminaries
`7.3.2 Asymptotic Properties of System OLS
`7.3.3 Testing Multiple Hypotheses
`Consistency and Asymptotic Normality of Generalized Least
`Squares
`7.4.1 Consistency
`7.4.2 Asymptotic Normality
`Feasible GLS
`7.5.1 Asymptotic Properties
`7.5.2 Asymptotic Variance of FGLS under a Standard
`Assumption
`Testing Using FGLS
`Seemingly Unrelated Regressions, Revisited
`7.7.1 Comparison between OLS and FGLS for SUR Systems
`7.7.2
`Systems with Cross Equation Restrictions
`7.7.3
`Singular Variance Matrices in SUR Systems
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`7.8
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`8
`8.1
`8.2
`8.3
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`8.4
`8.5
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`8.6
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`9
`9.1
`9.2
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`9.3
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`9.4
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`The Linear Panel Data Model, Revisited
`7.8.1 Assumptions for Pooled OLS
`7.8.2 Dynamic Completeness
`7.8.3 A Note on Time Series Persistence
`7.8.4 Robust Asymptotic Variance Matrix
`7.8.5 Testing for Serial Correlation and Heteroskedasticity after
`Pooled OLS
`7.8.6 Feasible GLS Estimation under Strict Exogeneity
`Problems
`
`System Estimation by Instrumental Variables
`Introduction and Examples
`A General Linear System of Equations
`Generalized Method of Moments Estimation
`8.3.1 A General Weighting Matrix
`8.3.2 The System 2SLS Estimator
`8.3.3 The Optimal Weighting Matrix
`8.3.4 The Three-Stage Least Squares Estimator
`8.3.5 Comparison between GMM 3SLS and Traditional 3SLS
`Some Considerations When Choosing an Estimator
`Testing Using GMM
`8.5.1 Testing Classical Hypotheses
`8.5.2 Testing Overidentification Restrictions
`More E‰cient Estimation and Optimal Instruments
`Problems
`
`Simultaneous Equations Models
`The Scope of Simultaneous Equations Models
`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
`Estimation after Identification
`9.3.1 The Robustness-E‰ciency Trade-o¤
`9.3.2 When Are 2SLS and 3SLS Equivalent?
`9.3.3 Estimating the Reduced Form Parameters
`Additional Topics in Linear SEMs
`
`Contents
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`Contents
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`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 E‰ciency in Linear
`Systems
`SEMs Nonlinear in Endogenous Variables
`9.5.1
`Identification
`9.5.2 Estimation
`Di¤erent Instruments for Di¤erent Equations
`Problems
`
`9.5
`
`9.6
`
`Basic Linear Unobserved E¤ects Panel Data Models
`10
`10.1 Motivation: The Omitted Variables Problem
`10.2 Assumptions about the Unobserved E¤ects and Explanatory
`Variables
`10.2.1 Random or Fixed E¤ects?
`10.2.2 Strict Exogeneity Assumptions on the Explanatory
`Variables
`10.2.3 Some Examples of Unobserved E¤ects Panel Data Models
`Estimating Unobserved E¤ects Models by Pooled OLS
`10.3
`10.4 Random E¤ects Methods
`10.4.1 Estimation and Inference under the Basic Random E¤ects
`Assumptions
`10.4.2 Robust Variance Matrix Estimator
`10.4.3 A General FGLS Analysis
`10.4.4 Testing for the Presence of an Unobserved E¤ect
`Fixed E¤ects Methods
`10.5.1 Consistency of the Fixed E¤ects Estimator
`10.5.2 Asymptotic Inference with Fixed E¤ects
`10.5.3 The Dummy Variable Regression
`10.5.4 Serial Correlation and the Robust Variance Matrix
`Estimator
`10.5.5 Fixed E¤ects GLS
`10.5.6 Using Fixed E¤ects Estimation for Policy Analysis
`First Di¤erencing Methods
`10.6.1
`Inference
`10.6.2 Robust Variance Matrix
`
`10.5
`
`10.6
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`10.7
`
`10.6.3 Testing for Serial Correlation
`10.6.4 Policy Analysis Using First Di¤erencing
`Comparison of Estimators
`10.7.1 Fixed E¤ects versus First Di¤erencing
`10.7.2 The Relationship between the Random E¤ects and Fixed
`E¤ects Estimators
`10.7.3 The Hausman Test Comparing the RE and FE Estimators
`Problems
`
`More Topics in Linear Unobserved E¤ects Models
`11
`11.1 Unobserved E¤ects Models without the Strict Exogeneity
`Assumption
`11.1.1 Models under Sequential Moment Restrictions
`11.1.2 Models with Strictly and Sequentially Exogenous
`Explanatory Variables
`11.1.3 Models with Contemporaneous Correlation between Some
`Explanatory Variables and the Idiosyncratic Error
`11.1.4 Summary of Models without Strictly Exogenous
`Explanatory Variables
`11.2 Models with Individual-Specific Slopes
`11.2.1 A Random Trend Model
`11.2.2 General Models with Individual-Specific Slopes
`11.3 GMM Approaches to Linear Unobserved E¤ects Models
`11.3.1 Equivalence between 3SLS and Standard Panel Data
`Estimators
`11.3.2 Chamberlain’s Approach to Unobserved E¤ects Models
`11.4 Hausman and Taylor-Type Models
`11.5 Applying Panel Data Methods to Matched Pairs and Cluster
`Samples
`Problems
`
`III
`
`GENERAL APPROACHES TO NONLINEAR ESTIMATION
`
`M-Estimation
`12
`Introduction
`12.1
`Identification, Uniform Convergence, and Consistency
`12.2
`12.3 Asymptotic Normality
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`Contents
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`12.4
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`12.5
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`Two-Step M-Estimators
`12.4.1 Consistency
`12.4.2 Asymptotic Normality
`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 The Newton-Raphson Method
`12.7.2 The Berndt, Hall, Hall, and Hausman Algorithm
`12.7.3 The Generalized Gauss-Newton Method
`12.7.4 Concentrating Parameters out of the Objective Function
`Simulation and Resampling Methods
`12.8.1 Monte Carlo Simulation
`12.8.2 Bootstrapping
`Problems
`
`12.8
`
`Maximum Likelihood Methods
`13
`Introduction
`13.1
`Preliminaries and Examples
`13.2
`13.3 General Framework for Conditional MLE
`13.4
`Consistency of Conditional MLE
`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 Likelihood Methods for Panel Data and Cluster Samples
`13.8.1 Setup for Panel Data
`13.8.2 Asymptotic Inference
`13.8.3
`Inference with Dynamically Complete Models
`13.8.4
`Inference under Cluster Sampling
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`Contents
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`13.9
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`Panel Data Models with Unobserved E¤ects
`13.9.1 Models with Strictly Exogenous Explanatory Variables
`13.9.2 Models with Lagged Dependent Variables
`13.10 Two-Step MLE
`Problems
`Appendix 13A
`
`Generalized Method of Moments and Minimum Distance Estimation
`14
`14.1 Asymptotic Properties of GMM
`14.2
`Estimation under Orthogonality Conditions
`14.3
`Systems of Nonlinear Equations
`14.4
`Panel Data Applications
`14.5
`E‰cient Estimation
`14.5.1 A General E‰ciency Framework
`14.5.2 E‰ciency of MLE
`14.5.3 E‰cient Choice of Instruments under Conditional Moment
`Restrictions
`Classical Minimum Distance Estimation
`Problems
`Appendix 14A
`
`14.6
`
`IV
`
`NONLINEAR MODELS AND RELATED TOPICS
`
`15.5
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`Discrete Response Models
`15
`Introduction
`15.1
`The Linear Probability Model for Binary Response
`15.2
`Index Models for Binary Response: Probit and Logit
`15.3
`15.4 Maximum Likelihood Estimation of Binary Response Index
`Models
`Testing in Binary Response Index Models
`15.5.1 Testing Multiple Exclusion Restrictions
`15.5.2 Testing Nonlinear Hypotheses about b
`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
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`Contents
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`15.8
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`15.7.3 A Binary Endogenous Explanatory Variable
`15.7.4 Heteroskedasticity and Nonnormality in the Latent
`Variable Model
`15.7.5 Estimation under Weaker Assumptions
`Binary Response Models for Panel Data and Cluster Samples
`15.8.1 Pooled Probit and Logit
`15.8.2 Unobserved E¤ects Probit Models under Strict Exogeneity
`15.8.3 Unobserved E¤ects Logit Models under Strict Exogeneity
`15.8.4 Dynamic Unobserved E¤ects Models
`15.8.5 Semiparametric Approaches
`15.8.6 Cluster Samples
`15.9 Multinomial Response Models
`15.9.1 Multinomial Logit
`15.9.2 Probabilistic Choice Models
`15.10 Ordered Response Models
`15.10.1 Ordered Logit and Ordered Probit
`15.10.2 Applying Ordered Probit to Interval-Coded Data
`Problems
`
`Corner Solution Outcomes and Censored Regression Models
`16
`Introduction and Motivation
`16.1
`16.2 Derivations of Expected Values
`16.3
`Inconsistency of OLS
`16.4
`Estimation and Inference with Censored Tobit
`16.5 Reporting the Results
`16.6
`Specification Issues in Tobit Models
`16.6.1 Neglected Heterogeneity
`16.6.2 Endogenous Explanatory Variables
`16.6.3 Heteroskedasticity and Nonnormality in the Latent
`Variable Model
`16.6.4 Estimation under Conditional Median Restrictions
`Some Alternatives to Censored Tobit for Corner Solution
`Outcomes
`16.8 Applying Censored Regression to Panel Data and Cluster Samples
`16.8.1 Pooled Tobit
`16.8.2 Unobserved E¤ects Tobit Models under Strict Exogeneity
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`16.7
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`Contents
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`16.8.3 Dynamic Unobserved E¤ects Tobit Models
`Problems
`
`17.3
`
`Sample Selection, Attrition, and Stratified Sampling
`17
`Introduction
`17.1
`17.2 When Can Sample Selection Be Ignored?
`17.2.1 Linear Models: OLS and 2SLS
`17.2.2 Nonlinear Models
`Selection on the Basis of the Response Variable: Truncated
`Regression
`17.4 A Probit Selection Equation
`17.4.1 Exogenous Explanatory Variables
`17.4.2 Endogenous Explanatory Variables
`17.4.3 Binary Response Model with Sample Selection
`17.5 A Tobit Selection Equation
`17.5.1 Exogenous Explanatory Variables
`17.5.2 Endogenous Explanatory Variables
`Estimating Structural Tobit Equations with Sample Selection
`Sample Selection and Attrition in Linear Panel Data Models
`17.7.1 Fixed E¤ects Estimation with Unbalanced Panels
`17.7.2 Testing and Correcting for Sample Selection Bias
`17.7.3 Attrition
`Stratified Sampling
`17.8.1 Standard Stratified Sampling and Variable Probability
`Sampling
`17.8.2 Weighted Estimators to Account for Stratification
`17.8.3 Stratification Based on Exogenous Variables
`Problems
`
`17.6
`17.7
`
`17.8
`
`Estimating Average Treatment E¤ects
`18
`Introduction
`18.1
`18.2 A Counterfactual Setting and the Self-Selection Problem
`18.3 Methods Assuming Ignorability of Treatment
`18.3.1 Regression Methods
`18.3.2 Methods Based on the Propensity Score
`Instrumental Variables Methods
`18.4.1 Estimating the ATE Using IV
`
`18.4
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`Contents
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`18.5
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`18.4.2 Estimating the Local Average Treatment E¤ect by IV
`Further Issues
`18.5.1 Special Considerations for Binary and Corner Solution
`Responses
`18.5.2 Panel Data
`18.5.3 Nonbinary Treatments
`18.5.4 Multiple Treatments
`Problems
`
`Count Data and Related Models
`19
`19.1 Why Count Data Models?
`19.2
`Poisson Regression Models with Cross Section Data
`19.2.1 Assumptions Used for Poisson Regression
`19.2.2 Consistency of the Poisson QMLE
`19.2.3 Asymptotic Normality of the Poisson QMLE
`19.2.4 Hypothesis Testing
`19.2.5 Specification Testing
`19.3 Other Count Data Regression Models
`19.3.1 Negative Binomial Regression Models
`19.3.2 Binomial Regression Models
`19.4 Other QMLEs in the Linear Exponential Family
`19.4.1 Exponential Regression Models
`19.4.2 Fractional Logit Regression
`Endogeneity and Sample Selection with an Exponential Regression
`Function
`19.5.1 Endogeneity
`19.5.2 Sample Selection
`Panel Data Methods
`19.6.1 Pooled QMLE
`19.6.2 Specifying Models of Conditional Expectations with
`Unobserved E¤ects
`19.6.3 Random E¤ects Methods
`19.6.4 Fixed E¤ects Poisson Estimation
`19.6.5 Relaxing the Strict Exogeneity Assumption
`Problems
`
`19.6
`
`19.5
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`Contents
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`Duration Analysis
`20
`Introduction
`20.1
`20.2 Hazard Functions
`20.2.1 Hazard Functions without Covariates
`20.2.2 Hazard Functions Conditional on Time-Invariant
`Covariates
`20.2.3 Hazard Functions Conditional on Time-Varying
`Covariates
`20.3 Analysis of Single-Spell Data with Time-Invariant Covariates
`20.3.1 Flow Sampling
`20.3.2 Maximum Likelihood Estimation with Censored Flow
`Data
`20.3.3 Stock Sampling
`20.3.4 Unobserved Heterogeneity
`20.4 Analysis of Grouped Duration Data
`20.4.1 Time-Invariant Covariates
`20.4.2 Time-Varying Covariates
`20.4.3 Unobserved Heterogeneity
`Further Issues
`20.5.1 Cox’s Partial Likelihood Method for the Proportional
`Hazard Model
`20.5.2 Multiple-Spell Data
`20.5.3 Competing Risks Models
`Problems
`
`20.5
`
`References
`Index
`
`685
`685
`686
`686
`
`690
`
`691
`693
`694
`
`695
`700
`703
`706
`707
`711
`713
`714
`
`714
`714
`715
`715
`
`721
`737
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`Acknowledgments
`
`My interest in panel data econometrics began in earnest when I was an assistant
`professor at MIT, after I attended a seminar by a graduate student, Leslie Papke,
`who would later become my wife. Her empirical research using nonlinear panel data
`methods piqued my interest and eventually led to my research on estimating non-
`linear panel data models without distributional assumptions. I dedicate this text to
`Leslie.
`My former colleagues at MIT, particularly Jerry Hausman, Daniel McFadden,
`Whitney Newey, Danny Quah, and Thomas Stoker, played significant roles in en-
`couraging my interest in cross section and panel data econometrics. I also have
`learned much about the modern approach to panel data econometrics from Gary
`Chamberlain of Harvard University.
`I cannot discount the excellent training I received from Robert Engle, Clive
`Granger, and especially Halbert White at the University of California at San Diego. I
`hope they are not too disappointed that this book excludes time series econometrics.
`I did not teach a course in cross section and panel data methods until I started
`teaching at Michigan State. Fortunately, my colleague Peter Schmidt encouraged me
`to teach the course at which this book is aimed. Peter also suggested that a text on
`panel data methods that uses ‘‘vertical bars’’ would be a worthwhile contribution.
`Several classes of students at Michigan State were subjected to this book in manu-
`script form at various stages of development. I would like to thank these students for
`their perseverance, helpful comments, and numerous corrections. I want to specifically
`mention Scott Baier, Linda Bailey, Ali Berker, Yi-Yi Chen, William Horrace, Robin
`Poston, Kyosti Pietola, Hailong Qian, Wendy Stock, and Andrew Toole. Naturally,
`they are not responsible for any remaining errors.
`I was fortunate to have several capable, conscientious reviewers for the manuscript.
`Jason Abrevaya (University of Chicago), Joshua Angrist (MIT), David Drukker
`(Stata Corporation), Brian McCall (University of Minnesota), James Ziliak (Uni-
`versity of Oregon), and three anonymous reviewers provided excellent suggestions,
`many of which improved the book’s organization and coverage.
`The people at MIT Press have been remarkably patient, and I have very much
`enjoyed working with them. I owe a special debt to Terry Vaughn (now at Princeton
`University Press) for initiating this project and then giving me the time to produce a
`manuscript with which I felt comfortable. I am grateful to Jane McDonald and
`Elizabeth Murry for reenergizing the project and for allowing me significant leeway
`in crafting the final manuscript. Finally, Peggy Gordon and her crew at P. M. Gordon
`Associates, Inc., did an expert job in editing the manuscript and in producing the
`final text.
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`Preface
`
`This book is intended primarily for use in a second-semester course in graduate
`econometrics, after a first course at the level of Goldberger (1991) or Greene (1997).
`Parts of the book can be used for special-topics courses, and it should serve as a
`general reference.
`My focus on cross section and panel data methods—in particular, what is often
`dubbed microeconometrics—is novel, and it recognizes that, after coverage of the
`basic linear model in a first-semester course, an increasingly popular approach is to
`treat advanced cross section and panel data methods in one semester and time series
`methods in a separate semester. This division reflects the current state of econometric
`practice.
`Modern empirical research that can be fitted into the classical linear model para-
`digm is becoming increasingly rare. For instance, it is now widely recognized that a
`student doing research in applied time series analysis cannot get very far by ignoring
`recent advances in estimation and testing in models with trending and strongly de-
`pendent processes. This theory takes a very di¤erent direction from the classical lin-
`ear model than does cross section or panel data analysis. Hamilton’s (1994) time
`series text demonstrates this di¤erence unequivocally.
`Books intended to cover an econometric sequence of a year or more, beginning
`with the classical linear model, tend to treat advanced topics in cross section and
`panel data analysis as direct applications or minor extensions of the classical linear
`model (if they are treated at all). Such treatment needlessly limits the scope of appli-
`cations and can result in poor econometric practice. The focus in such books on the
`algebra and geometry of econometrics is appropriate for a first-semester course, but
`it results in oversimplification or sloppiness in stating assumptions. Approaches to
`estimation that are acceptable under the fixed regressor paradigm so prominent in the
`classical linear model can lead one badly astray under practically important depar-
`tures from the fixed regressor assumption.
`Books on ‘‘advanced’’ econometrics tend to be high-level treatments that focus on
`general approaches to estimation, thereby attempting to cover all data configurations—
`including cross section, panel data, and time series—in one framework, without giving
`special attention to any. A hallmark of such books is that detailed regularity con-
`ditions are treated on par with the practically more important assumptions that have
`economic content. This is a burden for students learning about cross section and
`panel data methods, especially those who are empirically oriented: definitions and
`limit theorems about dependent processes need to be included among the regularity
`conditions in order to cover time series applications.
`In this book I have attempted to find a middle ground between more traditional
`approaches and the more recent, very unified approaches. I present each model and
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`xviii
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`Preface
`
`method with a careful discussion of assumptions of the underlying population model.
`These assumptions, couched in terms of correlations, conditional expectations, con-
`ditional variances and covariances, or conditional distributions, usually can be given
`behavioral content. Except for the three more technical chapters in Part III, regularity
`conditions—for example, the existence of moments needed to ensure that the central
`limit theorem holds—are not discussed explicitly, as these have little bearing on ap-
`plied work. This approach makes the assumptions relatively easy to understand, while
`at the same time emphasizing that assumptions concerning the underlying population
`and the method of sampling need to be carefully considered in applying any econo-
`metric method.
`A unifying theme in this book is the analogy approach to estimation, as exposited
`by Goldberger (1991) and Manski (1988). [For nonlinear estimation methods with
`cross section data, Manski (1988) covers several of the topics included here in a more
`compact format.] Loosely, the analogy principle states that an estimator is chosen to
`solve the sample counterpart of a problem solved by the population parameter. The
`analogy approach is complemented nicely by asymptotic analysis, and that is the focus
`here.
`By focusing on asymptotic properties I do not mean to imply that small-sample
`properties of estimators and test statistics are unimportant. However, one typically
`first applies the analogy principle to devise a sensible estimator and then derives its
`asymptotic properties. This approach serves as a relatively simple guide to doing
`inference, and it works well in large samples (and often in samples that are not so
`large). Small-sample adjustments may improve performance, but such considerations
`almost always come after a large-sample analysis and are often done on a case-by-
`case basis.
`The book contains proofs or outlines the proofs of many assertions, focusing on the
`role played by the assumptions with economic content while downplaying or ignoring
`regularity conditions. The book is primarily written to give applied researchers a very
`firm understanding of why certain methods work and to give students the background
`for developing new methods. But many of the arguments used throughout the book
`are representative of those made in modern econometric research (sometimes without
`the technical details). Students interested in doing research in cross section or panel
`data methodology will find much here that is not available in other graduate texts.
`I have also included several empirical examples with included data sets. Most of
`the data sets come from published work or are intended to mimic data sets used in
`modern empirical analysis. To save space I illustrate only the most commonly used
`methods on the most common data structures. Not surprisingly, these overlap con-
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`Preface
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`xix
`
`siderably with methods that are packaged in econometric software programs. Other
`examples are of models where, given access to the appropriate data set, one could
`undertake an empirical analysis.
`The numerous end-of-chapter problems are an important component of the book.
`Some problems contain important points that are not fully described in the text;
`others cover new ideas that can be analyzed using the tools presented in the current
`and previous chapters. Several of the problems require using the data sets that are
`included with the book.
`As with any book, the topics here are selective and reflect what I believe to be the
`methods needed most often by applied researchers. I also give coverage to topics that
`have recently become important but are not adequately treated in other texts. Part I
`of the book reviews some tools that are elusive in mainstream econometrics books—
`in particular, the notion of conditional expectations, linear projections, and various
`convergence results. Part II begins by applying these tools to the analysis of single-
`equation linear models using cross section data. In principle, much of this material
`should be review for students having taken a first-semester course. But starting with
`single-equation linear models provides a bridge from the classical analysis of linear
`models to a more modern treatment, and it is the simplest vehicle to illustrate the
`application of the tools in Part I. In addition, several methods that are used often
`in applications—but rarely covered adequately in texts—can be covered in a single
`framework.
`I approach estimation of linear systems of equations with endogenous variables
`from a di¤erent perspective than traditional treatments. Rather than begin with simul-
`taneous equations models, we study estimation of a general linear system by instru-
`mental variables. This approach allows us to later apply these results to models
`with the same statistical structure as simultaneous equations models,
`including
`panel data models. Importantly, we can study the generalized method of moments
`estimator from the beginning and easily relate it to the more traditional three-stage
`least squares estimator.
`The analysis of general estimation methods for nonlinear models in Part III begins
`with a general treatment of asymptotic theory of estimators obtained from non-
`linear optimization problems. Maximum likelihood, partial maximum likelihood,
`and generalized method of moments estimation are shown to be generally applicable
`estimation approaches. The method of nonlinear least squares is also covered as a
`method for estimating models of conditional means.
`Part IV covers several nonlinear models used by modern applied researchers.
`Chapters 15 and 16 treat limited dependent variable models, with attention given to
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`xx
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`Preface
`
`handling certain endogeneity problems in such models. Panel data methods for binary
`response and censored variables, including some new estimation approaches, are also
`covered in these chapters.
`Chapter 17 contains a treatment of sample selection problems for both cross sec-
`tion and panel data, including some recent advances. The focus is on the case where
`the population model is linear, but some results are given for nonlinear models as
`well. Attrition in panel data models is also covered, as are methods for dealing with
`stratified samples. Recent approaches to estimating average treatment e¤ects are
`treated in Chapter 18.
`Poisson and related regression models, both for cross section and panel data, are
`treated in Chapter 19. These rely heavily on the method of quasi-maximum likeli-
`hood estimation. A brief but modern treatment of duration models is provided in
`Chapter 20.
`I have given short shrift to some important, albeit more advanced, topics. The
`setting here is, at least in modern parlance, essentially parametric. I have not included
`detailed treatment of recent advances in semiparametric or nonparametric analysis.
`In many cases these topics are not conceptually di‰cult. In fact, many semiparametric
`methods focus primarily on estimating a finite dimensional parameter in the presence
`of an infinite dimensional nuisance parameter—a feature shared by traditional par-
`ametric methods, such as nonlinear least squares and partial maximum likelihood.
`It is estimating infinite dimensional parameters that is conceptually and technically
`challenging.
`At the appropriate point, in lieu of treating semiparametric and nonparametric
`methods, I mention when such extensions are possible, and I provide references. A
`benefit of a modern approach to parametric models is that it provides a seamless
`transition to semiparametric and nonparametric methods. General surveys of semi-
`parametric and nonparametric methods are available in Volume 4 of the Handbook
`of Econometrics—see Powell (1994) and Ha¨rdle and Linton (1994)—as well as in
`Volume 11 of the Handbook of Statistics—see Horowitz (1993) and Ullah and Vinod
`(1993).
`I only briefly treat simulation-based methods of estimation and inference. Com-
`puter simulations can be used to estimate complicated nonlinear models when tradi-
`tional optimization methods are ine¤ective. The bootstrap method of inference and
`confidence interval construction can improve on asymptotic analysis. Volume 4 of
`the Handbook of Econometrics and Volume 11 of the Handbook of Statistics contain
`nice surveys of these topics (Hajivassilou and Ruud, 1994; Hall, 1994; Hajivassilou,
`1993; and Keane, 1993).
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`Preface
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`xxi
`
`On an organizational note, I refer to sections throughout the book first by chapter
`number followed by section number and, sometimes, subsection number. Therefore,
`Section 6.3 refers to Section 3 in Chapter 6, and Section 13.8.3 refers to Subsection 3
`of Section 8 in Chapter 13. By always including the chapter number, I hope to
`minimize confusion.
`
`Possible Course Outlines
`
`If all chapters in the book are covered in detail, there is enough mate