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Preface xxi
Acknowledgments xxix
I INTRODUCTION AND BACKGROUND 1 (50)
1 Introduction 3 (10)
1.1 Causal Relationships and Ceteris 3 (1)
Paribus Analysis
1.2 Stochastic Setting and Asymptotic 4 (3)
Analysis
1.2.1 Data Structures 4 (3)
1.2.2 Asymptotic Analysis 7 (1)
1.3 Some Examples 7 (2)
1.4 Why Not Fixed Explanatory Variables? 9 (4)
2 Conditional Expectations and Related 13 (24)
Concepts in Econometrics
2.1 Role of Conditional Expectations in 13 (1)
Econometrics
2.2 Features of Conditional Expectations 14 (11)
2.2.1 Definition and Examples 14 (1)
2.2.2 Partial Effects, Elasticities, 15 (3)
and Semielasticities
2.2.3 Error Form of Models of 18 (1)
Conditional Expectations
2.2.4 Some Properties of Conditional 19 (3)
Expectations
2.2.5 Average Partial Effects 22 (3)
2.3 Linear Projections 25 (12)
Problems 27 (3)
Appendix 2A 30 (1)
2.A.1 Properties of Conditional 30 (2)
Expectations
2.A.2 Properties of Conditional 32 (2)
Variances and Covariances
2.A.3 Properties of Linear Projections 34 (3)
3 Basic Asymptotic Theory 37 (14)
3.1 Convergence of Deterministic Sequences 37 (1)
3.2 Convergence in Probability and 38 (2)
Boundedness in Probability
3.3 Convergence in Distribution 40 (1)
3.4 Limit Theorems for Random Samples 41 (1)
3.5 Limiting Behavior of Estimators and 42 (9)
Test Statistics
3.5.1 Asymptotic Properties of 42 (3)
Estimators
3.5.2 Asymptotic Properties of Test 45 (2)
Statistics
Problems 47 (4)
II LINEAR MODELS 51 (344)
4 Single-Equation Linear Model and Ordinary 53 (36)
Least Squares Estimation
4.1 Overview of the Single-Equation 53 (2)
Linear Model
4.2 Asymptotic Properties of Ordinary 55 (10)
Least Squares
4.2.1 Consistency 56 (3)
4.2.2 Asymptotic Inference Using 59 (1)
Ordinary Least Squares
4.2.3 Heteroskedasticity-Robust 60 (2)
Inference
4.2.4 Lagrange Multiplier (Score) Tests 62 (3)
4.3 Ordinary Least Squares Solutions to 65 (11)
the Omitted Variables Problem
4.3.1 Ordinary Least Squares Ignoring 65 (2)
the Omitted Variables
4.3.2 Proxy Variable-Ordinary Least 67 (6)
Squares Solution
4.3.3 Models with Interactions in 73 (3)
Unobservables: Random Coefficient Models
4.4 Properties of Ordinary Least Squares 76 (13)
under Measurement Error
4.4.1 Measurement Error in the 76 (2)
Dependent Variable
4.4.2 Measurement Error in an 78 (4)
Explanatory Variable
Problems 82 (7)
5 Instrumental Variables Estimation of 89 (34)
Single-Equation Linear Models
5.1 Instrumental Variables and Two-Stage 89 (9)
Least Squares
5.1.1 Motivation for Instrumental 89 (7)
Variables Estimation
5.1.2 Multiple Instruments: Two-Stage 96 (2)
Least Squares
5.2 General Treatment of Two-Stage Least 98 (14)
Squares
5.2.1 Consistency 98 (3)
5.2.2 Asymptotic Normality of Two-Stage 101 (2)
Least Squares
5.2.3 Asymptotic Efficiency of 103 (1)
Two-Stage Least Squares
5.2.4 Hypothesis Testing with Two-Stage 104 (2)
Least Squares
5.2.5 Heteroskedasticity-Robust 106 (1)
Inference for Two-Stage Least Squares
5.2.6 Potential Pitfalls with Two-Stage 107 (5)
Least Squares
5.3 IV Solutions to the Omitted Variables 112 (11)
and Measurement Error Problems
5.3.1 Leaving the Omitted Factors in 112 (1)
the Error Term
5.3.2 Solutions Using Indicators of the 112 (3)
Unobservables
Problems 115 (8)
6 Additional Single-Equation Topics 123 (38)
6.1 Estimation with Generated Regressors 123 (3)
and Instruments
6.1.1 Ordinary Least Squares with 123 (1)
Generated Regressors
6.1.2 Two-Stage Least Squares with 124 (1)
Generated Instruments
6.1.3 Generated Instruments and 125 (1)
Regressors
6.2 Control Function Approach to 126 (3)
Endogeneity
6.3 Some Specification Tests 129 (12)
6.3.1 Testing for Endogeneity 129 (5)
6.3.2 Testing Overidentifying 134 (3)
Restrictions
6.3.3 Testing Functional Form 137 (1)
6.3.4 Testing for Heteroskedasticity 138 (3)
6.4 Correlated Random Coefficient Models 141 (5)
6.4.1 When Is the Usual IV Estimator 142 (3)
Consistent?
6.4.2 Control Function Approach 145 (1)
6.5 Pooled Cross Sections and 146 (15)
Difference-in-Differences Estimation
6.5.1 Pooled Cross Sections over Time 146 (1)
6.5.2 Policy Analysis and 147 (5)
Difference-in-Differences Estimation
Problems 152 (5)
Appendix 6A 157 (4)
7 Estimating Systems of Equations by 161 (46)
Ordinary Least Squares and Generalized
Least Squares
7.1 Introduction 161 (1)
7.2 Some Examples 161 (5)
7.3 System Ordinary Least Squares 166 (7)
Estimation of a Multivariate Linear System
7.3.1 Preliminaries 166 (1)
7.3.2 Asymptotic Properties of System 167 (5)
Ordinary Least Squares
7.3.3 Testing Multiple Hypotheses 172 (1)
7.4 Consistency and Asymptotic Normality 173 (3)
of Generalized Least Squares
7.4.1 Consistency 173 (2)
7.4.2 Asymptotic Normality 175 (1)
7.5 Feasible Generalized Least Squares 176 (7)
7.5.1 Asymptotic Properties 176 (4)
7.5.2 Asymptotic Variance of Feasible 180 (2)
Generalized Least Squares under a
Standard Assumption
7.5.3 Properties of Feasible 182 (1)
Generalized Least Squares with
(Possibly Incorrect) Restrictions on
the Unconditional Variance Matrix
7.6 Testing the Use of Feasible 183 (2)
Generalized Least Squares
7.7 Seemingly Unrelated Regressions, 185 (6)
Revisited
7.7.1 Comparison between Ordinary Least 185 (3)
Squares and Feasible Generalized Least
Squares for Seemingly Unrelated
Regressions Systems
7.7.2 Systems with Cross Equation 188 (1)
Restrictions
7.7.3 Singular Variance Matrices in 189 (2)
Seemingly Unrelated Regressions Systems
7.8 Linear Panel Data Model, Revisited 191 (16)
7.8.1 Assumptions for Pooled Ordinary 191 (3)
Least Squares
7.8.2 Dynamic Completeness 194 (2)
7.8.3 Note on Time Series Persistence 196 (1)
7.8.4 Robust Asymptotic Variance Matrix 197 (1)
7.8.5 Testing for Serial Correlation 198 (2)
and Heteroskedasticity after Pooled
Ordinary Least Squares
7.8.6 Feasible Generalized Least 200 (2)
Squares Estimation under Strict
Exogeneity
Problems 202 (5)
8 System Estimation by Instrumental 207 (32)
Variables
8.1 Introduction and Examples 207 (3)
8.2 General Linear System of Equations 210 (3)
8.3 Generalized Method of Moments 213 (9)
Estimation
8.3.1 General Weighting Matrix 213 (3)
8.3.2 System Two-Stage Least Squares 216 (1)
Estimator
8.3.3 Optimal Weighting Matrix 217 (2)
8.3.4 The Generalized Method of Moments 219 (3)
Three-Stage Least Squares Estimator
8.4 Generalized Instrumental Variables 222 (4)
Estimator
8.4.1 Derivation of the Generalized 222 (2)
Instrumental Variables Estimator and
Its Asymptotic Properties
8.4.2 Comparison of Generalized Method 224 (2)
of Moment, Generalized Instrumental
Variables, and the Traditional
Three-Stage Least Squares Estimator
8.5 Testing Using Generalized Method of 226 (3)
Moments
8.5.1 Testing Classical Hypotheses 226 (2)
8.5.2 Testing Overidentification 228 (1)
Restrictions
8.6 More Efficient Estimation and Optimal 229 (3)
Instruments
8.7 Summary Comments on Choosing an 232 (7)
Estimator
Problems 233 (6)
9 Simultaneous Equations Models 239 (46)
9.1 Scope of Simultaneous Equations Models 239 (2)
9.2 Identification in a Linear System 241 (11)
9.2.1 Exclusion Restrictions and 241 (4)
Reduced Forms
9.2.2 General Linear Restrictions and 245 (6)
Structural Equations
9.2.3 Unidentified, Just Identified, 251 (1)
and Overidentified Equations
9.3 Estimation after Identification 252 (4)
9.3.1 Robustness-Efficiency Trade-off 252 (2)
9.3.2 When Are 2SLS and 3SLS Equivalent? 254 (1)
9.3.3 Estimating the Reduced Form 255 (1)
Parameters
9.4 Additional Topics in Linear 256 (6)
Simultaneous Equations Methods
9.4.1 Using Cross Equation Restrictions 256 (1)
to Achieve Identification
9.4.2 Using Covariance Restrictions to 257 (3)
Achieve Identification
9.4.3 Subtleties Concerning 260 (2)
Identification and Efficiency in Linear
Systems
9.5 Simultaneous Equations Models 262 (9)
Nonlinear in Endogenous Variables
9.5.1 Identification 262 (4)
9.5.2 Estimation 266 (2)
9.5.3 Control Function Estimation for 268 (3)
Triangular Systems
9.6 Different Instruments for Different 271 (14)
Equations
Problems 273 (12)
10 Basic Linear Unobserved Effects and 285 (60)
Explanatory Variables
10.1 Motivation: Omitted Variables Problem 281 (4)
10.2 Assumptions about the Unobserved 285 (6)
Effects and Explanatory Variables
10.2.1 Random or Fixed Effects? 285 (2)
10.2.2 Strict Exogeneity Assumptions on 287 (2)
the Explanatory Variables
10.2.3 Some Examples of Unobserved 289 (2)
Effects Panel Data Models
10.3 Estimating Unobserved Effects Models 291 (1)
by Pooled Ordinary Least Squares
10.4 Random Effects Methods 291 (9)
10.4.1 Estimation and Inference under 291 (6)
the Basic Random Effects Assumptions
10.4.2 Robust Variance Matrix Estimator 297 (1)
10.4.3 General Feasible Generalized 298 (1)
Least Squares Analysis
10.4.4 Testing for the Presence of an 299 (1)
Unobserved Effect
10.5 Fixed Effects Methods 300 (15)
10.5.1 Consistency of the Fixed Effects 300 (4)
Estimator
10.5.2 Asymptotic Inference with Fixed 304 (3)
Effects
10.5.3 Dummy Variable Regression 307 (3)
10.5.4 Serial Correlation and the 310 (2)
Robust Variance Matrix Estimator
10.5.5 Fixed Effects Generalized Least 312 (3)
Squares
10.5.6 Using Fixed Effects Estimation 315 (1)
for Policy Analysis
10.6 First Differencing Methods 315 (6)
10.6.1 Inference 315 (3)
10.6.2 Robust Variance Matrix 318 (1)
10.6.3 Testing for Serial Correlation 319 (1)
10.6.4 Policy Analysis Using First 320 (1)
Differencing
10.7 Comparison of Estimators 321 (24)
10.7.1 Fixed Effects versus First 321 (5)
Differencing
10.7.2 Relationship between the Random 326 (2)
Effects and Fixed Effects Estimators
10.7.3 Hausman Test Comparing Random 328 (6)
Effects and Fixed Effects Estimators
Problems 334 (11)
11 More Topics in Linear Unobserved Effects 345 (50)
Models
11.1 Generalized Method of Moments 345 (4)
Approaches to the Standard Linear
Unobserved Effects Model
11.1.1 Equivalance between GMM 3SLS and 345 (2)
Standard Estimators
11.1.2 Chamberlain's Approach to 347 (2)
Unobserved Effects Models
11.2 Random and Fixed Effects 349 (9)
Instrumental Variables Methods
11.3 Hausman and Taylor-Type Models 358 (3)
11.4 First Differencing Instrumental 361 (4)
Variables Methods
11.5 Unobserved Effects Models with 365 (3)
Measurement Error
11.6 Estimation under Sequential 368 (6)
Exogeneity
11.6.1 General Framework 368 (3)
11.6.2 Models with Lagged Dependent 371 (3)
Variables
11.7 Models with Individual-Specific 374 (21)
Slopes
11.7.1 Random Trend Model 375 (2)
11.7.2 General Models with 377 (5)
Individual-Specific Slopes
11.7.3 Robustness of Standard Fixed 382 (2)
Effects Methods
11.7.4 Testing for Correlated Random 384 (3)
Slopes
Problems 387 (8)
III GENERAL APPROACHES TO NONLINEAR ESTIMATION 395 (164)
12 M-Estimation, Nonlinear Regression, and 397 (72)
Quantile Regression
12.1 Introduction 397 (4)
12.2 Identification, Uniform Convergence, 401 (4)
and Consistency
12.3 Asymptotic Normality 405 (4)
12.4 Two-Step M-Estimators 409 (4)
12.4.1 Consistency 410 (1)
12.4.2 Asymptotic Normality 411 (2)
12.5 Estimating the Asymptotic Variance 413 (7)
12.5.1 Estimation without Nuisance 413 (5)
Parameters
12.5.2 Adjustments for Two-Step 418 (2)
Estimation
12.6 Hypothesis Testing 420 (11)
12.6.1 Wald Tests 420 (1)
12.6.2 Score (or Lagrange Multiplier) 421 (7)
Tests
12.6.3 Tests Based on the Change in the 428 (2)
Objective Function
12.6.4 Behavior of the Statistics under 430 (1)
Alternatives
12.7 Optimization Methods 431 (5)
12.7.1 Newton-Raphson Method 432 (1)
12.7.2 Berndt, Hall, Hall, and Hausman 433 (1)
Algorithm
12.7.3 Generalized Gauss-Newton Method 434 (1)
12.7.4 Concentrating Parameters out of 435 (1)
the Objective Function
12.8 Simulation and Resampling Methods 436 (6)
12.8.1 Monte Carlo Simulation 436 (2)
12.8.2 Bootstrapping 438 (4)
12.9 Multivariate Nonlinear Regression 442 (7)
Methods
12.9.1 Multivariate Nonlinear Least 442 (2)
Squares
12.9.2 Weighted Multivariate Nonlinear 444 (5)
Least Squares
12.10 Quantile Estimation 449 (20)
12.10.1 Quantiles, the Estimation 449 (5)
Problem, and Consistency
12.10.2 Asymptotic Inference 454 (5)
12.10.3 Quantile Regression for Panel 459 (3)
Data
Problems 462 (7)
13 Maximum Likelihood Methods 469 (56)
13.1 Introduction 469 (1)
13.2 Preliminaries and Examples 470 (3)
13.3 General Framework for Conditional 473 (2)
Maximum Likelihood Estimation
13.4 Consistency of Conditional Maximum 475 (1)
Likelihood Estimation
13.5 Asymptotic Normality and Asymptotic 476 (5)
Variance Estimation
13.5.1 Asymptotic Normality 476 (3)
13.5.2 Estimating the Asymptotic 479 (2)
Variance
13.6 Hypothesis Testing 481 (1)
13.7 Specification Testing 482 (3)
13.8 Partial (or Pooled) Likelihood 485 (9)
Methods for Panel Data
13.8.1 Setup for Panel Data 486 (4)
13.8.2 Asymptotic Inference 490 (2)
13.8.3 Inference with Dynamically 492 (2)
Complete Models
13.9 Panel Data Models with Unobserved 494 (5)
Effects
13.9.1 Models with Strictly Exogenous 494 (3)
Explanatory Variables
13.9.2 Models with Lagged Dependent 497 (2)
Variables
13.10 Two-Step Estimators Involving 499 (3)
Maximum Likelihood
13.10.1 Second-Step Estimator Is 499 (1)
Maximum Likelihood Estimator
13.10.2 Surprising Efficiency Result 500 (2)
When the First-Step Estimator Is
Conditional Maximum Likelihood Estimator
13.11 Quasi-Maximum Likelihood Estimation 502 (23)
13.11.1 General Misspecification 502 (3)
13.11.2 Model Selection Tests 505 (4)
13.11.3 Quasi-Maximum Likelihood 509 (5)
Estimation in the Linear Exponential
Family
13.11.4 Generalized Estimating 514 (3)
Equations for Panel Data
Problems 517 (5)
Appendix 13A 522 (3)
14 Generalized Method of Moments and 525 (34)
Minimum Distance Estimation
14.1 Asymptotic Properties of Generalized 525 (5)
Method of Moments
14.2 Estimation under Orthogonality 530 (2)
Conditions
14.3 Systems of Nonlinear Equations 532 (6)
14.4 Efficient Estimation 538 (7)
14.4.1 General Efficiency Framework 538 (2)
14.4.2 Efficiency of Maximum Likelihood 540 (2)
Estimator
14.4.3 Efficienct Choice of Instruments 542 (3)
under Conditional Moment Restrictions
14.5 Classical Minimum Distance Estimation 545 (2)
14.6 Panel Data Applications 547 (12)
14.6.1 Nonlinear Dynamic Models 547 (2)
14.6.2 Minimum Distance Approach to the 549 (2)
Unobserved Effects Model
14.6.3 Models with Time-Varying 551 (4)
Coefficients on the Unobserved Effects
Problems 555 (3)
Appendix 14A 558 (1)
IV NONLINEAR MODELS AND RELATED TOPICS 559 (466)
15 Binary Response Models 561 (82)
15.1 Introduction 561 (1)
15.2 Linear Probability Model for Binary 562 (3)
Response
15.3 Index Models for Binary Response: 565 (2)
Probit and Logit
15.4 Maximum Likelihood Estimation of 567 (2)
Binary Response Index Models
15.5 Testing in Binary Response Index 569 (4)
Models
15.5.1 Testing Multiple Exclusion 570 (1)
Restrictions
15.5.2 Testing Nonlinear Hypotheses 571 (1)
about β
15.5.3 Tests against More General 571 (2)
Alternatives
15.6 Reporting the Results for Probit and 573 (9)
Logit
15.7 Specification Issues in Binary 582 (26)
Response Models
15.7.1 Neglected Heterogeneity 582 (3)
15.7.2 Continuous Endogenous 585 (9)
Explanatory Variables
15.7.3 Binary Endogenous Explanatory 594 (5)
Variable
15.7.4 Heteroskedasticity and 599 (5)
Nonnormality in the Latent Variable
Model
15.7.5 Estimation under Weaker 604 (4)
Assumptions
15.8 Binary Response Models for Panel Data 608 (35)
15.8.1 Pooled Probit and Logit 609 (1)
15.8.2 Unobserved Effects Probit Models 610 (9)
under Strict Exogeneity
15.8.3 Unobserved Effects Logit Models 619 (6)
under Strict Exogeneity
15.8.4 Dynamic Unobserved Effects Models 625 (5)
15.8.5 Probit Models with Heterogeneity 630 (2)
and Endogenous Explanatory Variables
15.8.6 Semiparametric Approaches 632 (3)
Problems 635 (8)
16 Multinomial and Ordered Response Models 643 (24)
16.1 Introduction 643 (1)
16.2 Multinomial Response Models 643 (12)
16.2.1 Multinomial Logit 643 (3)
16.2.2 Probabilistic Choice Models 646 (5)
16.2.3 Endogenous Explanatory Variables 651 (2)
16.2.4 Panel Data Methods 653 (2)
16.3 Ordered Response Models 655 (12)
16.3.1 Ordered Logit and Ordered Probit 655 (3)
16.3.2 Specification Issues in Ordered 658 (2)
Models
16.3.3 Endogenous Explanatory Variables 660 (2)
16.3.4 Panel Data Methods 662 (1)
Problems 663 (4)
17 Corner Solution Responses 667 (56)
17.1 Motivation and Examples 667 (4)
17.2 Useful Expressions for Type I Tobit 671 (5)
17.3 Estimation and Inference with the 676 (1)
Type I Tobit Model
17.4 Reporting the Results 677 (3)
17.5 Specification Issues in Tobit Models 680 (10)
17.5.1 Neglected Heterogeneity 680 (1)
17.5.2 Endogenous Explanatory Models 681 (4)
17.5.3 Heteroskedasticity and 685 (2)
Nonnormality in the Latent Variable
Model
17.5.4 Estimating Parameters with 687 (3)
Weaker Assumptions
17.6 Two-Part Models and Type II Tobit 690 (13)
for Corner Solutions
17.6.1 Truncated Normal Hurdle Model 692 (2)
17.6.2 Lognormal Hurdle Model and 694 (3)
Exponential Conditional Mean
17.6.3 Exponential Type II Tobit Model 697 (6)
17.7 Two-Limit Tobit Model 703 (2)
17.8 Panel Data Methods 705 (18)
17.8.1 Pooled Methods 705 (2)
17.8.2 Unobserved Effects Models under 707 (6)
Strict Exogeneity
17.8.3 Dynamic Unobserved Effects Tobit 713 (2)
Models
Problems 715 (8)
18 Count, Fractional, and Other Nonnegative 723 (54)
Responses
18.1 Introduction 723 (1)
18.2 Poisson Regression 724 (12)
18.2.1 Assumptions Used for Poission 724 (3)
Regression and Quantities of Interest
18.2.2 Consistency of the Poisson QMLE 727 (1)
18.2.3 Asymptotic Normality of the 728 (4)
Poisson QMLE
18.2.4 Hypothesis Testing 732 (2)
18.2.5 Specification Testing 734 (2)
18.3 Other Count Data Regression Models 736 (4)
18.3.1 Negative Binomial Regression 736 (3)
Models
18.3.2 Binomial Regression Models 739 (1)
18.4 Gamma (Exponential) Regression Model 740 (2)
18.5 Endogeneity with an Exponential 742 (6)
Regression Function
18.6 Fractional Responses 748 (7)
18.6.1 Exogenous Explanatory Variables 748 (5)
18.6.2 Endogenous Explanatory Variables 753 (2)
18.7 Panel Data Methods 755 (22)
18.7.1 Pooled QMLE 756 (2)
18.7.2 Specifying Models of Conditional 758 (1)
Expectations with Unobserved Effects
18.7.3 Random Effects Methods 759 (3)
18.7.4 Fixed Effects Poisson Estimation 762 (2)
18.7.5 Relaxing the Strict Exogeneity 764 (2)
Assumption
18.7.6 Fractional Response Models for 766 (3)
Panel Data
Problems 769 (8)
19 Censored Data, Sample Selection, and 777 (76)
Attrition
19.1 Introduction 777 (1)
19.2 Data Censoring 778 (12)
19.2.1 Binary Censoring 780 (3)
19.2.2 Interval Coding 783 (2)
19.2.3 Censoring from Above and Below 785 (5)
19.3 Overview of Sample Selection 790 (2)
19.4 When Can Sample Selection Be Ignored? 792 (7)
19.4.1 Linear Models: Estimation by OLS 792 (6)
and 2SLS
19.4.2 Nonlinear Models 798 (1)
19.5 Selection on the Basis of the 799 (3)
Response Variable: Truncated Regression
19.6 Incidental Truncation: A Probit 802 (13)
Selection Equation
19.6.1 Exogenous Explanatory Variables 802 (7)
19.6.2 Endogenous Explanatory Variables 809 (4)
19.6.3 Binary Response Model with 813 (1)
Sample Selection
19.6.4 An Exponential Response Function 814 (1)
19.7 Incidental Truncation: A Tobit 815 (6)
Selection Equation
19.7.1 Exogenous Explanatory Variables 815 (2)
19.7.2 Endogenous Explanatory Variables 817 (2)
19.7.3 Estimating Structural Tobit 819 (2)
Equations with Sample Selection
19.8 Inverse Probability Weighting for 821 (6)
Missing Data
19.9 Sample Selection and Attrition in 827 (26)
Linear Panel Data Models
19.9.1 Fixed and Random Effects 828 (4)
Estimation with Unbalanced Panels
19.9.2 Testing and Correcting for 832 (5)
Sample Selection Bias
19.9.3 Attrition 837 (8)
Problems 845 (8)
20 Stratified Sampling and Cluster Sampling 853 (50)
20.1 Introduction 853 (1)
20.2 Stratified Sampling 854 (9)
20.2.1 Standard Stratified Sampling and 854 (2)
Variable Probability Sampling
20.2.2 Weighted Estimators to Account 856 (5)
for Stratification
20.2.3 Stratification Based on 861 (2)
Exogenous Variables
20.3 Cluster Sampling 863 (31)
20.3.1 Inference with a Large Number of 864 (12)
Clusters and Small Cluster Sizes
20.3.2 Cluster Samples with 876 (7)
Unit-Specific Panel Data
20.3.3 Should We Apply Cluster-Robust 883 (1)
Inference with Large Group Sizes?
20.3.4 Inference When the Number of 884 (10)
Clusters Is Small
20.4 Complex Survey Sampling 894 (9)
Problems 899 (4)
21 Estimating Average Treatment Effects 903 (80)
21.1 Introduction 903 (1)
21.2 A Counterfactual Setting and the 904 (4)
Self-Selection Problem
21.3 Methods Assuming Ignorability (or 908 (29)
Unconfoundedness) of Treatment
21.3.1 Identification 911 (4)
21.3.2 Regression Adjustment 915 (5)
21.3.3 Propensity Score Methods 920 (10)
21.3.4 Combining Regression Adjustment 930 (4)
and Propensity Score Weighting
21.3.5 Matching Methods 934 (3)
21.4 Instrumental Variables Methods 937 (17)
21.4.1 Estimating the Average Treatment 937 (8)
Effect Using IV
21.4.2 Correction and Control Function 945 (6)
Approaches
21.4.3 Estimating the Local Average 951 (3)
Treatment Effect by IV
21.5 Regression Discontinuity Designs 954 (6)
21.5.1 The Sharp Regression 954 (3)
Discontinuity Design
21.5.2 The Fuzzy Regression 957 (2)
Discontinuity Design
21.5.3 Unconfoundedness versus the 959 (1)
Fuzzy Regression Discontinuity
21.6 Further Issues 960 (23)
21.6.1 Special Considerations for 960 (1)
Responses with Discreteness or Limited
Range
21.6.2 Multivalued Treatments 961 (3)
21.6.3 Multiple Treatments 964 (4)
21.6.4 Panel Data 968 (7)
Problems 975 (8)
22 Duration Analysis 983 (42)
22.1 Introduction 983 (1)
22.2 Hazard Functions 984 (7)
22.2.1 Hazard Functions without 984 (4)
Covariates
22.2.2 Hazard Functions Conditional on 988 (1)
Time-Invariant Covariates
22.2.3 Hazard Functions Conditional on 989 (2)
Time-Varying Covariates
22.3 Analysis of Single-Spell Data with 991 (19)
Time-Invariant Covariates
22.3.1 Flow Sampling 992 (1)
22.3.2 Maximum Likelihood Estimation 993 (7)
with Censored Flow Data
22.3.3 Stock Sampling 1000(3)
22.3.4 Unobserved Heterogeneity 1003(7)
22.4 Analysis of Grouped Duration Data 1010(8)
22.4.1 Time-Invariant Covariates 1011(4)
22.4.2 Time-Varying Covariates 1015(2)
22.4.3 Unobserved Heterogeneity 1017(1)
22.5 Further Issues 1018(7)
22.5.1 Cox's Partial Likelihood Method 1018(1)
for the Proportional Hazard Model
22.5.2 Multiple-Spell Data 1018(1)
22.5.3 Competing Risks Models 1019(1)
Problems 1019(6)
References 1025(20)
Index 1045
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