| Conteúdo |
Contents<br/><br/>Preface<br/>Acknowledgments <br/><br/>1.INTRODUCTION AND BACKGROUND<br/><br/>1.Introduction<br/>1.1.Causal Relationships and Ceteris Paribus Analysis<br/>1.2.Stochastic Setting and Asymptotic Analysis<br/>1.2.1 Data Structures <br/>1.2.2 Asymptotic Analysis <br/>1.3 Some Examples <br/>1.4 Why Not Fixed Explanatory Variables? <br/><br/>2 Conditional Expectations and Related Concepts in Econometries <br/>2.1.Role of Conditional Expectations in Econometrics <br/>2.2 Features of Conditional Expectations <br/>2.2. 1 Definition and Examples <br/>2.2.2 Partial Effects. Elasticities. and Semielasticities <br/>2.2.3 Error Form of Models of Conditional Expectations<br/>2.2.4 Some Properties of Conditional Expectations<br/>2.2.5 Average Partial Effects <br/>2.3 Linear Projections<br/>Problems<br/>Appendix 2A <br/>2.A.1 Properties oí Conditional Expectations <br/>2.A.2 Properties of Conditional Variances and Covariances <br/>2.A.3 Properties of Linear Projections <br/><br/>3 Basic Asymptotic Theory <br/>3.1 Convergence Deterministic Sequences <br/>3.2 Convergence in Probability and Boundedness in Probability<br/>3.3 Convergence in Distribution <br/>3.4 Limit l'heorems for Random Samples <br/>3.5 Limiting Behavior of Estimators and Test Statistics<br/>3.5.1 Asymptotic Properties of Estimators <br/>3.5.2 Asymptotic Properties oof Test Statistics<br/>Problems<br/><br/>II LINEAR MODELS<br/><br/>4 SingIe-Equation Linear Model and Ordinary Last Squares Stimation<br/>4.1 Overview of the SingIe-Equation Linear Model <br/>4.2 Asymptotic Properties of Ordinary Least Squares<br/>4.2.1 Consistency<br/>4,2.2 Asyrnptotic Inference using Ordinary Least Squares<br/>4.2.3 Heteroskedasticity-Robust Inference<br/>4.2.4 Lagrange Multiplier (Score) Tests<br/>4.3 Ordinary Least Squares Solutions to the Omited Variables Problem<br/>4.3.1 Ordinary Least Squares Ignoring the Omitted Variables <br/>4.3.2 Proxy variable-Ordinary Least Square Solution<br/>4.3.3 Models with Interactions in unoberservables: Randorn coefficient models<br/>4.4 Properties of OrdinaryLeast Squares under measurement Error <br/>4.4. 1 Measuremet Error in the Dependen variable <br/>4.4.2 Measurement Error in an ExpIanatory Variable Problems<br/><br/>5.Instrumental Variables Estimation of Single-Equation Linear Models<br/>5.1 Instruniental variables and Two-Stage Least Squares<br/>5.1.1 Motivation for instrumental Variables Estimation<br/>5.1.2 Multiple Instruments: Two stage Leasi Squares <br/>5.2 General treatment of two-stage least Squares <br/>5.2.1 Consistency<br/>5.2.2 Asynptotic Normality of Two-Stage Least Squares <br/>5.2.3 Asynptotic Efficiency of two-Stage Least Squares <br/>5,2.4 hypothesis Testing with two-Stage Least Squares <br/>5.2.5 heteroskedasticity-Robust Inference for two-Stage Least Squares <br/>5.2.6 Potential Pitfaulls with To-Stage Least Squares<br/>5.3 IV Solutions to the omitted variables and Measurement Error Problems <br/>5.3 1 Leaving the Omitted Factors in the Error Term <br/>5.3.2 Solutions using lndicators of the unobservables Problems <br/><br/>6 Additional Single-Equation Topics <br/>6.1 Estirnation with Generated Regressors and instruments<br/>6.1. 1 Ordinary Least Squares with Generated Regressors <br/>6.1 .2 Two-Stage Least Squares with Generated lnstruments<br/>6.1.3 Generated lnstruments and Regressors <br/>6.2 Control Function Approach to Endogeneity <br/>6.3 Some Specification Tests <br/>6.3. 1 Testing for Endogeneity<br/>6.3.2 Testing Overidentifying Restrictions<br/>6.3.3 Testing Functional Form <br/>6.3.4 Testing for Heteroskedasticity <br/>6.4 Correlated Random Coefficient Models<br/>6.4.1 When Is the Usual IV Estimator Consistent?<br/>6.4.2 Control Functión Approach <br/>6.5 Pooled Cross Sections and Difference-ín-Differences Estimation <br/>6.5.1 Pooled Cross Sections over time <br/>6.5.2 Policy Analysis and Difference-in-Díferences Estimation Problems <br/>Appendix 6A<br/><br/>7 Estimating Systems of Equations by Ordinary Least Squares and Generalized Least Squares <br/>7.1 Introduction <br/>7.2 Some Examples <br/>7.3 System Ordinary Least Squares Estimation of a Multivariate Linear System <br/>7.3. 1 Preliminaries <br/>7.3.2 Asymptotic Properties of System Ordinary Least Squares<br/>7.3.3 Testing Multiple hypotheses<br/>7.4 Conssistencyn and Asymptotic Normality of Generalized Ieast Squares <br/>7.4.1 Consistency<br/>7.4.2 Asymptotic NormaIity<br/>7.5 Feasible Generalized Least Squares <br/>7.5.1 Asymptotic Properties <br/>7.5.2 Asymptotic Variance of Feasible Generalized Least Squares under Standard Assumption<br/>7.5.3 Propertíes of Feasible Generalized Least Squares with (Possibly lncorrect) Restrictions on the Unconditional Variance Matrix <br/>7.6 Testing the Use of Feasible Generalized Least Squares <br/>7.7 Seemingly unrelated Regressions Revisited <br/>7.7.1 Comparison between Ordinary Least Squares and Feasible Generalized Least Squares for Seemingly Unrelated Regressions Systems <br/>7. 7.2 Systems with Cross Equation Restrictions <br/>7.7.3 Singular Variance Matrices in Seemingly Unrelated Regresions Systems <br/>7.8 Linear Panel Data Model, Revisited <br/>7.8.1 Assumptions for Pooled Ordinary Least Squares <br/>7.8.2 Dynamic Completeness <br/>7.8.3 Note on Time Series Persistence <br/>7.8.4 Robust Asymptotic Variance Matrix <br/>7.8.5 Testing for Serial Correlation and Heteroskedasticity af'ter Pooled Ordinary Least Squares <br/>7.8.6 Feasible Generalized Least Squares Estimation under Strict Exogencity Problems<br/><br/>8 System Estimation by Instrumental Variables <br/>8.1 Introduction and Examples <br/>8.2 General Linear System of Equations <br/>8.3 Generalized Method of Momenis Estimation <br/>8.3.1 General Weighting Matrix<br/>8.3.2 System Two-Stage Least Squares Estimator <br/>8.3.3 Optimal Weighting Matrix <br/>8.3.4 The Generalized Method of Mornents Three-Stage Least Squares Estimator<br/>8.4 Generalized Instrumental variables Estimator <br/>8.4.1 Derivation of the Generalized Instrumental Variables Estimator and its Asymptotic Properties <br/>8.4.2 Comparison of Generalized Method of Moment, Generalized Instrumental Variables, and. the Traditional Three-Stage Leasi Squares Estimator <br/>8.5 Testing Using Generalized Method of Mornents<br/>8.5. 1 Testing Classical Hypotheses<br/>8.5.2 Testing Overidentification Restrictions<br/>8.6 More Efficient Estirnation and Optirnal lnstruments<br/>8.7 Summary Comrnents on Choosing an Estimator<br/>Problems<br/><br/>9 Simultaneous Equations Models<br/>9.1 Scope of Simultaneous Equations Models<br/>9.2 Identification in a Linear System <br/>9.2.1 Exclusion Restrictions and Reduced Forms<br/>9.2.2 General Linear Restrictions and Structural Equations<br/>9.2.3 Unidentified, Just Identified. and Overidentified Equations <br/>9.3 Estimation after Identification <br/>9.3. 1 Robustness-Efficiency Trade-off<br/>9.3.2 When Are 2SLS and 3SLS Equívalent? <br/>9.3.3 Estimating the Reduced Form Parameters<br/>9.4 Additional Topics in Linear Simultaneous Equations Methods<br/>9.4.1 Using Cross Equation Restrictions to Achieve Identification<br/>9.4.2 Using Covariance Restrictions to Achieve Identification <br/>9.4.3 Subtleties Concerning Identification and Efficiency in Linear Systems<br/>9.5 Simultaneous Equations Models Nonlinear in Endogenous variables<br/>9.5.1 Identification<br/>9.5.2 Estimation <br/>9,5.3 Control Function Estimation for Triangular Systems <br/>9.6 Different Instruments for Different Equations Problems <br/><br/>10 Basic Linear Unobserved Effects Panel Data Models<br/>10.1 Motivation; Omitted Variables Problem <br/>10.2 Assumptions about the Unobserved Effects and Explanatory Variables<br/>10.2.1 Random of Fixed Effects?<br/>10.2.2Strict Exogeneity Assumptions on the Explanatory Variables <br/>10.2.3 Some Examples of Unobserved Effects Panel Data Models <br/>10.3 Estimating Unobserved Eftects Models by Pooled Ordinary Least Squares<br/>10.4 Random Effects Methods <br/>10.4.1 Estirnation and inference under lhe Basic Random Effects Assumptions <br/>10. 4.2 Robust Variance Matrix Estirnator <br/>10.4.3 General Feasible generalized Least Squares Analysis <br/>10.4.4 Testing for the Presence of an Unobserved Effect <br/>10.5 Fixed Effects Methods <br/>10.5. 1 Consistency of the Fixed Effects Estimator <br/>10.5.2 Asyrnptotic Inference with Fixed Effects <br/>10.5.3 Dummy Variable Regression <br/>10.5.4 Serial Correlation and the Robust Variance Matrix Estimator <br/>10.5.5 Fixed Effects Generalized Least Squarcs <br/>10.5.6 Using Fixed effects estimation for policy analysis<br/>10.6 Fist diferencing methods<br/>10.6.1 lnference <br/>10.6.2 Robust Variance Matrix <br/>10.6.3 Testing for Serial Correlation <br/>10.6.4 Policy Analysis Using Firsi Differencing <br/>10.7 Comparison of Estimators <br/>10.7.1 Fixed Eflects versus First Differencing <br/>10.7.2 Relationship betwecn the Random Effects and Fixed Effects Estimators <br/>10.7.3 Hausman Test Comparing Random Effects and Fixed Effects Estimators Problems <br/><br/>11 More Topics in Linear Unobserved Effects Models <br/>11.1 Generalized Method of Moments Approaehes to the Standard Linear Unobserved Effects Models<br/>11.1.1 Equivalance between GMM 3SLS and Standard estimators <br/>11.1 .2 Chamberlains Approach to Unobserved Effects Models <br/>1 1.2 Random and Fixed Effects Instrumental Variables Methods<br/>11.3 Hausman and Taylor-Type Models <br/>11.4 first Differencing Instrumental Variables Methods <br/>11.5 Unobserved Effects Models with Measurement Error <br/>11.6 Estimation under Sequential Exogeneity <br/>11 .6.1 General Framework <br/>11.6.2 Models with Lagged Dependem Variables<br/>11.7 Models with individual-Specific Slopes <br/>11 .7.1 Random Trend Model <br/>11.7.2 General Models with Individual-Specific Slopes <br/>11.7.3 Robustness of standard Fixed Effects Methods <br/>11.7.4 Testing for Correlated Random Slopes Problems <br/><br/>III GENERAL APPROACHES TO NONLINEAR ESTIMATION <br/><br/>12 M-estimation, nonlinear Regression, and Quantile Regression<br/>12.1 Introduction <br/>12.2 Identitication ,uniform convergence, and Consistency <br/>12.3 Asymptotic Normality <br/>12.4 Two-Step M-Estimators <br/>12.4.1 Consistency <br/>12.4.2 Asymptotic Normalility<br/>12.5 Estimating the AsymptoticVariance <br/>12.5.1 Estimation without Nuisance Pararneters <br/>12.5.2 Adjustments for two-Step Estimation <br/>12.6 Hyporthesis Testing <br/>12.6.1 Wald Tests <br/>12.6.2 Score (of Lagrange Multiplier) Tests <br/>12.6.3 Tests based on the Change in the Objective Function <br/>12.6.4 Behavior of the Statislics under Alternatives <br/>12.7 Optimization Methods <br/>12.7.1 Newton-Raphson Method <br/>12.7.2 Berndt, haIl. hall. and Hausman Algorithm <br/>12.7.3Generalized Gauss-Newton Method <br/>12.7.4 Concentrating Parameteirs out of the Objective Function <br/>12.8 Simulation and Resampling Methods <br/>12.8.1 Monte Carlo Simulation <br/>12.8.2 Bootstrapping<br/>12.9 Multivariate Nonlinear Regression Methods <br/>12.9.1 Mutivariate Nonlinear Least Squares <br/>12.9.2 Weighted Multivariate Nonlinear Least Squares <br/>12.10 Quantile Estirnation <br/>12.10.1 Quantiles. the Estiniation Problem and Consistency <br/>12.10.2 Asymptotic Inference <br/>12.10.3 Quantile Regression for Panel Data<br/>Problems <br/><br/>13 Maximum Likelihood Methods <br/>13.1 Introduction <br/>13.2 Preliminaries and Exarnples <br/>13.3 General Framework for Conditional Maximum Likelihood Estimation<br/>13.4 Consistency of Conditional Maximum Likelihood estimation <br/>13.5 Asymptotic Normality and Asymptotic Variance Estimation <br/>13.5.1 Asymptotic Normality, <br/>13.5.2 Estimating the Asymptotic Variance <br/>13.6 Hypothesis Testing <br/>13,7 Specification Testing <br/>13.8 Partial (or Pooled) Likelihood Methods for Panel Data <br/>13.8.1 Setup for Panel Data <br/>13.8.2 Asymptotic !nference <br/>13.8.3 lnfèrence with DynamicallyComplete Models<br/>13.9 Panei Data Modeis with Unohserved Effects<br/>13.9.1 Models with Strictly Exogenous Explanatory Variables<br/>13.9.2 Models with Lagged Dependent Variables <br/>13.10 Two-Step Estimators involving Maximum Likelihood<br/>13.10 1 Second-Step Estimator Is Maximum Likelihood Estimator<br/>13.10 2 Surprising Efficiency Result When the Firt-Step estimator Is Conditional Maxiniurn..Likelihood Estirnator<br/>13,11 Quasi-Maximurn Likelihood Estimation<br/>13.11.1 General Misspecitication<br/>13.11.2 Model Selection Tests <br/>13.11.3 Quasi-Maxirnum Likelihood Estimation in the Linear Exponential Family <br/>13.11.4 Generalized Estimating Equations for Panel Data <br/>Problems <br/>Appendix 13A <br/><br/>14 Generalized Method of Moments and Minimum Distance Estimation <br/>14.1 Asymptotic Properties of Generalized Method of Mornents <br/>14.2 Estimation under Orthogonality Conditions <br/>14.3 Systems of Nonlinear Equations <br/>14.4 Efficient Estimation <br/>14.4.1 General Efficiency Framework <br/>14.4.2 Efficiency of Maximum Likelihood Estimator <br/>14.4.3 Efficient Choice of Instruments under Conditional Moment Restrictions <br/>14.5 Classical Minimum Distance Estimation <br/>14.6 Panel Data Applications <br/>14.6.1 Nonlinear Dvnamic Models <br/>14.6.2 Minimum Distance Approach to the Unobserved Effects Model <br/>14.6.3 Models with Time-Varying Coefficients on the Unobserved Effects <br/>Problems <br/>Appendix 14A<br/><br/>IV NONLINEAR MODELS AND RELATED TOPICS<br/><br/>15 Binary Response Models<br/>15.1 Introduction<br/>15.2 Linear Probability Model for Binary Response <br/>15.3 Index Models for Binary Response: Probit and Logit <br/>15.4 Maximum Likelihood Estimation of Binary Response Index Models<br/>15.5 Testing in Binary Response Index Models <br/>15.5.1 Testing Multiple Exciusion Restrictions <br/>15.5.2 Testing Nonlínear Hypotheses aboul B <br/>15.5.3 Tests against More General Alternatives <br/>1 5.6 Reporting the Results for Probit and Logit <br/>15.7 Speciflcation Issues in Binary Response Models<br/>15.7.1 Neglected Heterogencity<br/>15.7.2 Contínuous Endogenous Explanatory Variable <br/>15.7.3 Binary Endogenous Explanatory Variabie <br/>1 5.7.4 Heteroskedasticity and Nonnomality in the Latent Variable Model <br/>15.7.5 Estimation under Weaker Assumptions <br/>15.8 Binary Response Models for Panel Data <br/>15.8.1 Pooled Probit and Logit <br/>15.8.2 Unobserved Effects Probit Models under Strict Exogeneity, <br/>15.8.3 Unobserved Effects Logit Models under Strict Exogeneity <br/>15.8.4 Dynamic Unobserved Effects Models <br/>15.8.5 Probit Models with Heterogeneity and Endogenous Explanatory Variables <br/>15.8.6 Semiparametric Approaches <br/>Problems <br/><br/>16 Multinomial and Ordered Response Models<br/>16.1 Introduction<br/>16.2 Multinomial Response Models<br/>16.2.1 Multinomial Logit <br/>16.2.2 Probabilistic Choice Models<br/>16.2.3 Endogenous Explanatory Variables <br/>16.2.4 Panel Data Methods <br/>16.3 Ordered Response Models <br/>16.3.1 Ordered Logit and Ordered Probit <br/>16.3.2 Specification Issues in Ordered Models <br/>16.3.3 Endogenous Explanatory Varíables <br/>16.3.4 Panel Data Merhods <br/>Problems <br/><br/>17 Corner Solution Responses <br/>17.1 Motivation and Examples <br/>17.2 Useful Expressions for Type I Tobit <br/>17.3 Estirnation and Inference with the Type I Tobit Model <br/>17.4 Reporting the Results <br/>17.5 Specification Issues in Tobit Models <br/>17.5.1 Neglected Heterogeneity <br/>17.5.2 Endogenous Explanatory Models <br/>17.5.3 Heteroskedasticity and Nonnorrnality in the Latent Variable Model <br/>17.5.4 Estimating Parameters with Weaker Assumptions <br/>17.6 Two-Part Models and Type II Tobit for Corner Solutions <br/>17.6.1 Truncated Normal Hurdle Model <br/>17.6.2 Lognormal Hurdle Model and Exponential Conditional Mean <br/>17.6.3 Exponential Type IITobit Model <br/>17.7 Two-Limit Tobit Model <br/>17.8 Panel Data Methods <br/>17.8.1 Pooled Methods<br/>17.8.2 Unohserved Effeets Models under Strict Exogeneity <br/>17.8.3 Dynamic Unohserved Effects Tobit Models<br/>Problems <br/><br/>18 Count. Fractional, and Other Nonnegative Responses <br/>18.1 Introduction <br/>18.2 Poisson Regression <br/>18.2.1 Assumptions Used for Poisson Regression and Quantitíes of lnterest <br/>18.2.2 Consistency of the Poisson QMLE <br/>18.2.3 Asymptotic Normality of the Poisson QMLE <br/>18.2.4 Hypothesis Testing <br/>18.2.5 Specilication Testing <br/>18.3 Other Count Data Regression Models<br/>18.3.1 Negative Binomial Regression Models <br/>18.3.2 Binomial Regression Models<br/>18.4 Gamma (Exponential) Regression Model <br/>18.5 Endogeneity with an Exponential Regression Function <br/>18.6 Fractional Responses <br/>18.6.1 Exogenous Explanatory Variables <br/>18.6.2 Endogenous Explanatory Variables <br/>18.7 Panel Data Methods <br/>18.7.1 Pooled QMLE <br/>18.7.2 Speciíying Models of Conditional Expectations with Unobserved Effects <br/>18.7.3 Random Effects Methods <br/>18.7.4 Fixed Effects Poisson Estimation <br/>18.7.5 Relaxing the Strict Exogeneity Assumption <br/>18,7.6 Fractional Response Models for Panel Data <br/>Problems <br/><br/>19 Censored Data, Sample Selection. and Attrition <br/>19.1 Introduction <br/>19.2 Data Censoring <br/>19.2.1 Binary Censoring<br/>19.212 Interval Coding <br/>19.2.3 Censoring frorn Above and Below <br/>19.3 Overview of Sample Selection <br/>19.4 When Can Sample Selection Be lgnored? <br/>19.4.1 Linear Models: Estirnation by OLS and 2SLS <br/>19.4.2 Nonlinear Models <br/>19.5 Selection on the Basis of the Response Variable: Truncated Regression <br/>19,6 Incidental Truncation: A Probit Selection Equation <br/>19.6.1 Exogenous Explanatory Variables <br/>19.6.2 Endogenous Explanatory Variables <br/>19.6.3 Binary Response Model wiih Sample Selection <br/>19.6.4 An Exponential Response Function<br/>19.7 Incidental Truncation: A Tobit Selection Equation<br/>19.7. 1 Exogenous Explanatory Variables <br/>19.7.2 Endogenous Explanatory Variables <br/>19.7.3 Estirnating Structural Tobit Equations with Sample Selection <br/>19.8 Inverse probability Weighting for Missing Data <br/>19.9 Sample Selection and Attntion in Linear Panel Data Models<br/>19.9.1 Fixed and Random Effects Estimation with Unbalanced Panels <br/>19. 9.2 Testing and Correcting for Sample Selection bias <br/>19.9.3 Attrition<br/>Problerns<br/> <br/>20 Stratified Sampling and CIuster Sampling <br/>20.1 Introduction <br/>20.2 Stratilied Samplin<br/>20.2.1 Standard Stratified Sampling and Variable Probability Sampling<br/>20.2.2 Weighted estimator to Account for Stratification <br/>20.2.3 Stratification based on exogenous Variables<br/>20.3 Cluster Sampling <br/>20.3.1 Inference with a Large Number of Clusters and SmaII Cluster Sizes <br/>20.3.2 CLuster Samples with unit-Specific Panel Data <br/>20.3.3 Should We Apply cluster-Robust Inference with Large Group sizes?<br/>20.3.4 Inference When the Number of Clusters Is SmaII <br/>20.4 Cooplex Survey Sampling <br/>ProbIem <br/><br/>21 Estimating Average treatment Effects <br/>21.1 Introduction<br/>21.2 Counterfactual Setting and the Self-Selection Problem <br/>21.3 Methods Assuming ignorability (or unconfoundedness) of Trearment <br/>21.3.1 Identitication <br/>21.3.2 Regression Adjustment <br/>21.3.3 Propensity Score Methods <br/>21.3.4 Combining Regression Adjustment and Propensity Score Weighting <br/>21.3.5 Matching Methods <br/>21.4 Instrumental Variables Methods<br/>21.4.1 Estimating the Average Treatment Effct Using IV <br/>21.4.2 Correction and Control Function Approaches <br/>21.4.3 Estimating the Local Average Treatment Effect by IV <br/>21.5 Regression Discontinuity Designs <br/>21.5.1 The Sharp Regression Discontinuity Design <br/>21.5.2 The Fuzzy Regression Discontinuity Design <br/>21.5.3 Unconfoundedness versus the Fuzzy Regression Discontinuity<br/>21.6 Further Issues <br/>21 .6.1 Special Considerations for Responses with Discreteness or Limited Range <br/>21.6.2 Multivalued Treatments <br/>21.6.3 Multiple Treatrnents <br/>21.6.4 Panel Data <br/>Problems<br/><br/>22 Duration Analvsis <br/>22.1 Introduction <br/>22.2 Hazard Functions <br/>22.2.1 Hazard Functions without Covariates <br/>22.2.2 Hazard Functions Conditional on Time-lnvariant Covariates <br/>22.2.3 Hazard Functions Conditional on Time-Varying Covariates <br/>22.3 AnaIysis of Single-Spell Data with Time-Invariant Covariates <br/>22.3.1 Flow Sampling <br/>22.3.2 Maximum LikeIíhood Estimation with Censored Flow Data <br/>22.3.3 Stock Sampling <br/>22.3.4 Unobserved Heterogeneity <br/>22.4 Analysis of Grouped Duration Data <br/>22.4.1 Time-Invariant covariates <br/>22.4.2 Time-Varying Covariates <br/>22.4.3 unobserved Heterogeneity <br/>22.5 Further Issues <br/>22.5.1 Coxs Partia! Likelihood Method for the Proportional Hazard Model <br/>22.5.2 Multiple-Spell Data <br/>22.5.3 Competing Risks Models<br/>Problerns <br/><br/>References<br/>Index<br/><br/><br/> |
