[Money=45]<br>
<P align=left><FONT face="Times New Roman">Econometric Analysis of Cross Section and Panel Data<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Jeffrey M. Wooldridge<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">The MIT Press<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Cambridge, Massachusetts<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">London, England<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Preface xvii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Acknowledgments xxiii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">I INTRODUCTION AND BACKGROUND 1<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1 Introduction 3<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.1 Causal Relationships and Ceteris Paribus Analysis 3<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.2 The Stochastic Setting and Asymptotic Analysis 4<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.2.1 Data Structures 4<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.2.2 Asymptotic Analysis 7<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.3 Some Examples 7<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">1.4 Why Not Fixed Explanatory Variables? 9<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2 Conditional Expectations and Related Concepts in Econometrics 13<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.1 The Role of Conditional Expectations in Econometrics 13<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2 Features of Conditional Expectations 14<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2.1 De.nition and Examples 14<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2.2 Partial Effects, Elasticities, and Semielasticities 15<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2.3 The Error Form of Models of Conditional Expectations 18<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2.4 Some Properties of Conditional Expectations 19<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.2.5 Average Partial Effects 22<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.3 Linear Projections 24<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 27<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Appendix 2A 29<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.A.1 Properties of Conditional Expectations 29<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.A.2 Properties of Conditional Variances 31<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">2.A.3 Properties of Linear Projections 32<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3 Basic Asymptotic Theory 35<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.1 Convergence of Deterministic Sequences 35<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.2 Convergence in Probability and Bounded in Probability 36<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.3 Convergence in Distribution 38<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.4 Limit Theorems for Random Samples 39<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.5 Limiting Behavior of Estimators and Test Statistics 40<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.5.1 Asymptotic Properties of Estimators 40<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">3.5.2 Asymptotic Properties of Test Statistics 43<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 45<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">II LINEAR MODELS 47<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4 The Single-Equation Linear Model and OLS Estimation 49<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.1 Overview of the Single-Equation Linear Model 49<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.2 Asymptotic Properties of OLS 51<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.2.1 Consistency 52<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.2.2 Asymptotic Inference Using OLS 54<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.2.3 Heteroskedasticity-Robust Inference 55<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.2.4 Lagrange Multiplier (Score) Tests 58<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.3 OLS Solutions to the Omitted Variables Problem 61<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.3.1 OLS Ignoring the Omitted Variables 61<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.3.2 The Proxy Variable–OLS Solution 63<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.3.3 Models with Interactions in Unobservables 67<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.4 Properties of OLS under Measurement Error 70<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.4.1 Measurement Error in the Dependent Variable 71<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">4.4.2 Measurement Error in an Explanatory Variable 73<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 76<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5 Instrumental Variables Estimation of Single-Equation Linear Models 83<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.1 Instrumental Variables and Two-Stage Least Squares 83<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.1.1 Motivation for Instrumental Variables Estimation 83<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.1.2 Multiple Instruments: Two-Stage Least Squares 90<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2 General Treatment of 2SLS 92<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.1 Consistency 92<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.2 Asymptotic Normality of 2SLS 94<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.3 Asymptotic E‰ciency of 2SLS 96<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.4 Hypothesis Testing with 2SLS 97<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.5 Heteroskedasticity-Robust Inference for 2SLS 100<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.2.6 Potential Pitfalls with 2SLS 101<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.3 IV Solutions to the Omitted Variables and Measurement Error<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 105<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.3.1 Leaving the Omitted Factors in the Error Term 105<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">5.3.2 Solutions Using Indicators of the Unobservables 105<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 107<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6 Additional Single-Equation Topics 115<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.1 Estimation with Generated Regressors and Instruments 115<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents vi<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.1.1 OLS with Generated Regressors 115<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.1.2 2SLS with Generated Instruments 116<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.1.3 Generated Instruments and Regressors 117<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.2 Some Speci.cation Tests 118<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.2.1 Testing for Endogeneity 118<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.2.2 Testing Overidentifying Restrictions 122<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.2.3 Testing Functional Form 124<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.2.4 Testing for Heteroskedasticity 125<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.3 Single-Equation Methods under Other Sampling Schemes 128<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.3.1 Pooled Cross Sections over Time 128<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.3.2 Geographically Strati.ed Samples 132<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.3.3 Spatial Dependence 134<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">6.3.4 Cluster Samples 134<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 135<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Appendix 6A 139<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7 Estimating Systems of Equations by OLS and GLS 143<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.1 Introduction 143<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.2 Some Examples 143<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.3 System OLS Estimation of a Multivariate Linear System 147<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.3.1 Preliminaries 147<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.3.2 Asymptotic Properties of System OLS 148<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.3.3 Testing Multiple Hypotheses 153<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.4 Consistency and Asymptotic Normality of Generalized Least<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Squares 153<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.4.1 Consistency 153<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.4.2 Asymptotic Normality 156<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.5 Feasible GLS 157<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.5.1 Asymptotic Properties 157<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.5.2 Asymptotic Variance of FGLS under a Standard<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Assumption 160<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.6 Testing Using FGLS 162<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.7 Seemingly Unrelated Regressions, Revisited 163<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.7.1 Comparison between OLS and FGLS for SUR Systems 164<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.7.2 Systems with Cross Equation Restrictions 167<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.7.3 Singular Variance Matrices in SUR Systems 167<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents vii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8 The Linear Panel Data Model, Revisited 169<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.1 Assumptions for Pooled OLS 170<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.2 Dynamic Completeness 173<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.3 A Note on Time Series Persistence 175<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.4 Robust Asymptotic Variance Matrix 175<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.5 Testing for Serial Correlation and Heteroskedasticity after<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Pooled OLS 176<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">7.8.6 Feasible GLS Estimation under Strict Exogeneity 178<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 179<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8 System Estimation by Instrumental Variables 183<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.1 Introduction and Examples 183<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.2 A General Linear System of Equations 186<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3 Generalized Method of Moments Estimation 188<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3.1 A General Weighting Matrix 188<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3.2 The System 2SLS Estimator 191<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3.3 The Optimal Weighting Matrix 192<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3.4 The Three-Stage Least Squares Estimator 194<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.3.5 Comparison between GMM 3SLS and Traditional 3SLS 196<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.4 Some Considerations When Choosing an Estimator 198<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.5 Testing Using GMM 199<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.5.1 Testing Classical Hypotheses 199<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.5.2 Testing Overidenti.cation Restrictions 201<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">8.6 More E‰cient Estimation and Optimal Instruments 202<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 205<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9 Simultaneous Equations Models 209<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.1 The Scope of Simultaneous Equations Models 209<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.2 Identi.cation in a Linear System 211<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.2.1 Exclusion Restrictions and Reduced Forms 211<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.2.2 General Linear Restrictions and Structural Equations 215<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.2.3 Unidenti.ed, Just Identi.ed, and Overidenti.ed Equations 220<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.3 Estimation after Identi.cation 221<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.3.1 The Robustness-E‰ciency Trade-off 221<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.3.2 When Are 2SLS and 3SLS Equivalent? 224<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.3.3 Estimating the Reduced Form Parameters 224<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.4 Additional Topics in Linear SEMs 225<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents viii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.4.1 Using Cross Equation Restrictions to Achieve Identi.cation 225<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.4.2 Using Covariance Restrictions to Achieve Identi.cation 227<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.4.3 Subtleties Concerning Identi.cation and E‰ciency in Linear<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Systems 229<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.5 SEMs Nonlinear in Endogenous Variables 230<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.5.1 Identi.cation 230<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.5.2 Estimation 235<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">9.6 Different Instruments for Different Equations 237<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 239<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10 Basic Linear Unobserved Effects Panel Data Models 247<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.1 Motivation: The Omitted Variables Problem 247<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.2 Assumptions about the Unobserved Effects and Explanatory<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Variables 251<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.2.1 Random or Fixed Effects? 251<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.2.2 Strict Exogeneity Assumptions on the Explanatory<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Variables 252<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.2.3 Some Examples of Unobserved Effects Panel Data Models 254<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.3 Estimating Unobserved Effects Models by Pooled OLS 256<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.4 Random Effects Methods 257<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.4.1 Estimation and Inference under the Basic Random Effects<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Assumptions 257<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.4.2 Robust Variance Matrix Estimator 262<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.4.3 A General FGLS Analysis 263<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.4.4 Testing for the Presence of an Unobserved Effect 264<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5 Fixed Effects Methods 265<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.1 Consistency of the Fixed Effects Estimator 265<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.2 Asymptotic Inference with Fixed Effects 269<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.3 The Dummy Variable Regression 272<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.4 Serial Correlation and the Robust Variance Matrix<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Estimator 274<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.5 Fixed Effects GLS 276<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.5.6 Using Fixed Effects Estimation for Policy Analysis 278<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.6 First Differencing Methods 279<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.6.1 Inference 279<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.6.2 Robust Variance Matrix 282<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents ix<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.6.3 Testing for Serial Correlation 282<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.6.4 Policy Analysis Using First Differencing 283<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.7 Comparison of Estimators 284<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.7.1 Fixed Effects versus First Differencing 284<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.7.2 The Relationship between the Random Effects and Fixed<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Effects Estimators 286<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">10.7.3 The Hausman Test Comparing the RE and FE Estimators 288<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 291<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11 More Topics in Linear Unobserved Effects Models 299<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.1 Unobserved Effects Models without the Strict Exogeneity<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Assumption 299<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.1.1 Models under Sequential Moment Restrictions 299<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.1.2 Models with Strictly and Sequentially Exogenous<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Explanatory Variables 305<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.1.3 Models with Contemporaneous Correlation between Some<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Explanatory Variables and the Idiosyncratic Error 307<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.1.4 Summary of Models without Strictly Exogenous<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Explanatory Variables 314<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.2 Models with Individual-Speci.c Slopes 315<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.2.1 A Random Trend Model 315<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.2.2 General Models with Individual-Speci.c Slopes 317<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.3 GMM Approaches to Linear Unobserved Effects Models 322<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.3.1 Equivalence between 3SLS and Standard Panel Data<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Estimators 322<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.3.2 Chamberlain’s Approach to Unobserved Effects Models 323<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.4 Hausman and Taylor-Type Models 325<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">11.5 Applying Panel Data Methods to Matched Pairs and Cluster<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Samples 328<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 332<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">III GENERAL APPROACHES TO NONLINEAR ESTIMATION 339<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12 M-Estimation 341<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.1 Introduction 341<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.2 Identi.cation, Uniform Convergence, and Consistency 345<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.3 Asymptotic Normality 349<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents x<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.4 Two-Step M-Estimators 353<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.4.1 Consistency 353<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.4.2 Asymptotic Normality 354<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.5 Estimating the Asymptotic Variance 356<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.5.1 Estimation without Nuisance Parameters 356<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.5.2 Adjustments for Two-Step Estimation 361<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.6 Hypothesis Testing 362<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.6.1 Wald Tests 362<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.6.2 Score (or Lagrange Multiplier) Tests 363<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.6.3 Tests Based on the Change in the Objective Function 369<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.6.4 Behavior of the Statistics under Alternatives 371<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.7 Optimization Methods 372<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.7.1 The Newton-Raphson Method 372<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.7.2 The Berndt, Hall, Hall, and Hausman Algorithm 374<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.7.3 The Generalized Gauss-Newton Method 375<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.7.4 Concentrating Parameters out of the Objective Function 376<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.8 Simulation and Resampling Methods 377<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.8.1 Monte Carlo Simulation 377<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">12.8.2 Bootstrapping 378<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 380<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13 Maximum Likelihood Methods 385<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.1 Introduction 385<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.2 Preliminaries and Examples 386<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.3 General Framework for Conditional MLE 389<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.4 Consistency of Conditional MLE 391<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.5 Asymptotic Normality and Asymptotic Variance Estimation 392<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.5.1 Asymptotic Normality 392<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.5.2 Estimating the Asymptotic Variance 395<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.6 Hypothesis Testing 397<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.7 Speci.cation Testing 398<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.8 Partial Likelihood Methods for Panel Data and Cluster Samples 401<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.8.1 Setup for Panel Data 401<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.8.2 Asymptotic Inference 405<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.8.3 Inference with Dynamically Complete Models 408<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.8.4 Inference under Cluster Sampling 409<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xi<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.9 Panel Data Models with Unobserved Effects 410<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.9.1 Models with Strictly Exogenous Explanatory Variables 410<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.9.2 Models with Lagged Dependent Variables 412<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">13.10 Two-Step MLE 413<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 414<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Appendix 13A 418<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14 Generalized Method of Moments and Minimum Distance Estimation 421<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.1 Asymptotic Properties of GMM 421<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.2 Estimation under Orthogonality Conditions 426<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.3 Systems of Nonlinear Equations 428<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.4 Panel Data Applications 434<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.5 E‰cient Estimation 436<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.5.1 A General E‰ciency Framework 436<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.5.2 E‰ciency of MLE 438<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.5.3 E‰cient Choice of Instruments under Conditional Moment<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Restrictions 439<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">14.6 Classical Minimum Distance Estimation 442<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 446<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Appendix 14A 448<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">IV NONLINEAR MODELS AND RELATED TOPICS 451<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15 Discrete Response Models 453<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.1 Introduction 453<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.2 The Linear Probability Model for Binary Response 454<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.3 Index Models for Binary Response: Probit and Logit 457<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.4 Maximum Likelihood Estimation of Binary Response Index<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Models 460<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.5 Testing in Binary Response Index Models 461<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.5.1 Testing Multiple Exclusion Restrictions 461<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.5.2 Testing Nonlinear Hypotheses about <I>b </I>463<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.5.3 Tests against More General Alternatives 463<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.6 Reporting the Results for Probit and Logit 465<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7 Speci.cation Issues in Binary Response Models 470<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7.1 Neglected Heterogeneity 470<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7.2 Continuous Endogenous Explanatory Variables 472<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7.3 A Binary Endogenous Explanatory Variable 477<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7.4 Heteroskedasticity and Nonnormality in the Latent<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Variable Model 479<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.7.5 Estimation under Weaker Assumptions 480<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8 Binary Response Models for Panel Data and Cluster Samples 482<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.1 Pooled Probit and Logit 482<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.2 Unobserved Effects Probit Models under Strict Exogeneity 483<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.3 Unobserved Effects Logit Models under Strict Exogeneity 490<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.4 Dynamic Unobserved Effects Models 493<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.5 Semiparametric Approaches 495<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.8.6 Cluster Samples 496<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.9 Multinomial Response Models 497<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.9.1 Multinomial Logit 497<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.9.2 Probabilistic Choice Models 500<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.10 Ordered Response Models 504<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.10.1 Ordered Logit and Ordered Probit 504<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">15.10.2 Applying Ordered Probit to Interval-Coded Data 508<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 509<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16 Corner Solution Outcomes and Censored Regression Models 517<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.1 Introduction and Motivation 517<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.2 Derivations of Expected Values 521<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.3 Inconsistency of OLS 524<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.4 Estimation and Inference with Censored Tobit 525<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.5 Reporting the Results 527<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.6 Speci.cation Issues in Tobit Models 529<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.6.1 Neglected Heterogeneity 529<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.6.2 Endogenous Explanatory Variables 530<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.6.3 Heteroskedasticity and Nonnormality in the Latent<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Variable Model 533<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.6.4 Estimation under Conditional Median Restrictions 535<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.7 Some Alternatives to Censored Tobit for Corner Solution<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Outcomes 536<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.8 Applying Censored Regression to Panel Data and Cluster Samples 538<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.8.1 Pooled Tobit 538<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.8.2 Unobserved Effects Tobit Models under Strict Exogeneity 540<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xiii<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">16.8.3 Dynamic Unobserved Effects Tobit Models 542<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 544<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17 Sample Selection, Attrition, and Strati.ed Sampling 551<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.1 Introduction 551<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.2 When Can Sample Selection Be Ignored? 552<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.2.1 Linear Models: OLS and 2SLS 552<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.2.2 Nonlinear Models 556<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.3 Selection on the Basis of the Response Variable: Truncated<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Regression 558<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.4 A Probit Selection Equation 560<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.4.1 Exogenous Explanatory Variables 560<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.4.2 Endogenous Explanatory Variables 567<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.4.3 Binary Response Model with Sample Selection 570<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.5 A Tobit Selection Equation 571<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.5.1 Exogenous Explanatory Variables 571<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.5.2 Endogenous Explanatory Variables 573<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.6 Estimating Structural Tobit Equations with Sample Selection 575<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.7 Sample Selection and Attrition in Linear Panel Data Models 577<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.7.1 Fixed Effects Estimation with Unbalanced Panels 578<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.7.2 Testing and Correcting for Sample Selection Bias 581<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.7.3 Attrition 585<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.8 Strati.ed Sampling 590<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.8.1 Standard Strati.ed Sampling and Variable Probability<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Sampling 590<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.8.2 Weighted Estimators to Account for Strati.cation 592<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">17.8.3 Strati.cation Based on Exogenous Variables 596<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 598<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18 Estimating Average Treatment Effects 603<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.1 Introduction 603<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.2 A Counterfactual Setting and the Self-Selection Problem 603<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.3 Methods Assuming Ignorability of Treatment 607<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.3.1 Regression Methods 608<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.3.2 Methods Based on the Propensity Score 614<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.4 Instrumental Variables Methods 621<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.4.1 Estimating the ATE Using IV 621<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xiv<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.4.2 Estimating the Local Average Treatment Effect by IV 633<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.5 Further Issues 636<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.5.1 Special Considerations for Binary and Corner Solution<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Responses 636<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.5.2 Panel Data 637<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.5.3 Nonbinary Treatments 638<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">18.5.4 Multiple Treatments 642<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 642<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19 Count Data and Related Models 645<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.1 Why Count Data Models? 645<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2 Poisson Regression Models with Cross Section Data 646<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2.1 Assumptions Used for Poisson Regression 646<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2.2 Consistency of the Poisson QMLE 648<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2.3 Asymptotic Normality of the Poisson QMLE 649<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2.4 Hypothesis Testing 653<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.2.5 Speci.cation Testing 654<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.3 Other Count Data Regression Models 657<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.3.1 Negative Binomial Regression Models 657<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.3.2 Binomial Regression Models 659<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.4 Other QMLEs in the Linear Exponential Family 660<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.4.1 Exponential Regression Models 661<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.4.2 Fractional Logit Regression 661<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.5 Endogeneity and Sample Selection with an Exponential Regression<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Function 663<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.5.1 Endogeneity 663<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.5.2 Sample Selection 666<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6 Panel Data Methods 668<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6.1 Pooled QMLE 668<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6.2 Specifying Models of Conditional Expectations with<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Unobserved Effects 670<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6.3 Random Effects Methods 671<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6.4 Fixed Effects Poisson Estimation 674<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">19.6.5 Relaxing the Strict Exogeneity Assumption 676<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 678<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xv<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20 Duration Analysis 685<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.1 Introduction 685<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.2 Hazard Functions 686<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.2.1 Hazard Functions without Covariates 686<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.2.2 Hazard Functions Conditional on Time-Invariant<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Covariates 690<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.2.3 Hazard Functions Conditional on Time-Varying<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Covariates 691<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.3 Analysis of Single-Spell Data with Time-Invariant Covariates 693<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.3.1 Flow Sampling 694<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.3.2 Maximum Likelihood Estimation with Censored Flow<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Data 695<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.3.3 Stock Sampling 700<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.3.4 Unobserved Heterogeneity 703<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.4 Analysis of Grouped Duration Data 706<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.4.1 Time-Invariant Covariates 707<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.4.2 Time-Varying Covariates 711<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.4.3 Unobserved Heterogeneity 713<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.5 Further Issues 714<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.5.1 Cox’s Partial Likelihood Method for the Proportional<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Hazard Model 714<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.5.2 Multiple-Spell Data 714<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">20.5.3 Competing Risks Models 715<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Problems 715<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">References 721<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Index 737<o:p></o:p></FONT></P>
<P align=left><FONT face="Times New Roman">Contents xvi<o:p></o:p></FONT></P>
<P><FONT face="Times New Roman"><o:p></o:p></FONT></P><br>[/Money]

[此贴子已经被作者于2006-11-13 14:17:19编辑过]