A. Colin Cameron              Pravin K. Trivedi

Contents
List of Figures page xv
List of Tables xvii
Preface xxi
I Preliminaries
1 Overview 3
1.1 Introduction 3
1.2 Distinctive Aspects of Microeconometrics 5
1.3 Book Outline 10
1.4 How to Use This Book 14
1.5 Software 15
1.6 Notation and Conventions 16
2 Causal and Noncausal Models 18
2.1 Introduction 18
2.2 Structural Models 20
2.3 Exogeneity 22
2.4 Linear Simultaneous Equations Model 23
2.5 Identification Concepts 29
2.6 Single-Equation Models 31
2.7 Potential Outcome Model 31
2.8 Causal Modeling and Estimation Strategies 35
2.9 Bibliographic Notes 38
3 Microeconomic Data Structures 39
3.1 Introduction 39
3.2 Observational Data 40
3.3 Data from Social Experiments 48
3.4 Data from Natural Experiments 54
vii
CONTENTS
3.5 Practical Considerations 58
3.6 Bibliographic Notes 61
II Core Methods
4 Linear Models 65
4.1 Introduction 65
4.2 Regressions and Loss Functions 66
4.3 Example: Returns to Schooling 69
4.4 Ordinary Least Squares 70
4.5 Weighted Least Squares 81
4.6 Median and Quantile Regression 85
4.7 Model Misspecification 90
4.8 Instrumental Variables 95
4.9 Instrumental Variables in Practice 103
4.10 Practical Considerations 112
4.11 Bibliographic Notes 112
5 Maximum Likelihood and Nonlinear Least-Squares Estimation 116
5.1 Introduction 116
5.2 Overview of Nonlinear Estimators 117
5.3 Extremum Estimators 124
5.4 Estimating Equations 133
5.5 Statistical Inference 135
5.6 Maximum Likelihood 139
5.7 Quasi-Maximum Likelihood 146
5.8 Nonlinear Least Squares 150
5.9 Example: ML and NLS Estimation 159
5.10 Practical Considerations 163
5.11 Bibliographic Notes 163
6 Generalized Method of Moments and Systems Estimation 166
6.1 Introduction 166
6.2 Examples 167
6.3 Generalized Method of Moments 172
6.4 Linear Instrumental Variables 183
6.5 Nonlinear Instrumental Variables 192
6.6 Sequential Two-Step m-Estimation 200
6.7 Minimum Distance Estimation 202
6.8 Empirical Likelihood 203
6.9 Linear Systems of Equations 206
6.10 Nonlinear Sets of Equations 214
6.11 Practical Considerations 219
6.12 Bibliographic Notes 220
viii
CONTENTS
7 Hypothesis Tests 223
7.1 Introduction 223
7.2 Wald Test 224
7.3 Likelihood-Based Tests 233
7.4 Example: Likelihood-Based Hypothesis
Tests
241
7.5 Tests in Non-ML Settings 243
7.6 Power and Size of Tests 246
7.7 Monte Carlo Studies 250
7.8 Bootstrap Example 254
7.9 Practical Considerations 256
7.10 Bibliographic Notes 257
8 Specification Tests and Model Selection 259
8.1 Introduction 259
8.2 m-Tests 260
8.3 Hausman Test 271
8.4 Tests for Some Common Misspecifications 274
8.5 Discriminating between Nonnested
Models
278
8.6 Consequences of Testing 285
8.7 Model Diagnostics 287
8.8 Practical Considerations 291
8.9 Bibliographic Notes 292
9 Semiparametric Methods 294
9.1 Introduction 294
9.2 Nonparametric Example: Hourly Wage 295
9.3 Kernel Density Estimation 298
9.4 Nonparametric Local Regression 307
9.5 Kernel Regression 311
9.6 Alternative Nonparametric Regression
Estimators
319
9.7 Semiparametric Regression 322
9.8 Derivations of Mean and Variance
of Kernel Estimators
330
9.9 Practical Considerations 333
9.10 Bibliographic Notes 333
10 Numerical Optimization 336
10.1 Introduction 336
10.2 General Considerations 336
10.3 Specific Methods 341
10.4 Practical Considerations 348
10.5 Bibliographic Notes 352
ix
CONTENTS
III Simulation-Based Methods
11 Bootstrap Methods 357
11.1 Introduction 357
11.2 Bootstrap Summary 358
11.3 Bootstrap Example 366
11.4 Bootstrap Theory 368
11.5 Bootstrap Extensions 373
11.6 Bootstrap Applications 376
11.7 Practical Considerations 382
11.8 Bibliographic Notes 382
12 Simulation-Based Methods 384
12.1 Introduction 384
12.2 Examples 385
12.3 Basics of Computing Integrals 387
12.4 Maximum Simulated Likelihood Estimation 393
12.5 Moment-Based Simulation Estimation 398
12.6 Indirect Inference 404
12.7 Simulators 406
12.8 Methods of Drawing Random Variates 410
12.9 Bibliographic Notes 416
13 Bayesian Methods 419
13.1 Introduction 419
13.2 Bayesian Approach 420
13.3 Bayesian Analysis of Linear Regression 435
13.4 Monte Carlo Integration 443
13.5 Markov Chain Monte Carlo Simulation 445
13.6 MCMC Example: Gibbs Sampler for SUR 452
13.7 Data Augmentation 454
13.8 Bayesian Model Selection 456
13.9 Practical Considerations 458
13.10 Bibliographic Notes 458
IV Models for Cross-Section Data
14 Binary Outcome Models 463
14.1 Introduction 463
14.2 Binary Outcome Example: Fishing Mode Choice 464
14.3 Logit and Probit Models 465
14.4 Latent Variable Models 475
14.5 Choice-Based Samples 478
14.6 Grouped and Aggregate Data 480
14.7 Semiparametric Estimation 482
x
CONTENTS
14.8 Derivation of Logit from Type I Extreme Value 486
14.9 Practical Considerations 487
14.10 Bibliographic Notes 487
15 Multinomial Models 490
15.1 Introduction 490
15.2 Example: Choice of Fishing Mode 491
15.3 General Results 495
15.4 Multinomial Logit 500
15.5 Additive Random Utility Models 504
15.6 Nested Logit 507
15.7 Random Parameters Logit 512
15.8 Multinomial Probit 516
15.9 Ordered, Sequential, and Ranked Outcomes 519
15.10 Multivariate Discrete Outcomes 521
15.11 Semiparametric Estimation 523
15.12 Derivations for MNL, CL, and NL Models 524
15.13 Practical Considerations 527
15.14 Bibliographic Notes 528
16 Tobit and Selection Models 529
16.1 Introduction 529
16.2 Censored and Truncated Models 530
16.3 Tobit Model 536
16.4 Two-Part Model 544
16.5 Sample Selection Models 546
16.6 Selection Example: Health Expenditures 553
16.7 Roy Model 555
16.8 Structural Models 558
16.9 Semiparametric Estimation 562
16.10 Derivations for the Tobit Model 566
16.11 Practical Considerations 568
16.12 Bibliographic Notes 569
17 Transition Data: Survival Analysis 573
17.1 Introduction 573
17.2 Example: Duration of Strikes 574
17.3 Basic Concepts 576
17.4 Censoring 579
17.5 Nonparametric Models 580
17.6 Parametric Regression Models 584
17.7 Some Important Duration Models 591
17.8 Cox PH Model 592
17.9 Time-Varying Regressors 597
17.10 Discrete-Time Proportional Hazards 600
17.11 Duration Example: Unemployment Duration 603
xi
CONTENTS
17.12 Practical Considerations 608
17.13 Bibliographic Notes 608
18 Mixture Models and Unobserved Heterogeneity 611
18.1 Introduction 611
18.2 Unobserved Heterogeneity and Dispersion 612
18.3 Identification in Mixture Models 618
18.4 Specification of the Heterogeneity Distribution 620
18.5 Discrete Heterogeneity and Latent Class Analysis 621
18.6 Stock and Flow Sampling 625
18.7 Specification Testing 628
18.8 Unobserved Heterogeneity Example: Unemployment Duration 632
18.9 Practical Considerations 637
18.10 Bibliographic Notes 637
19 Models of Multiple Hazards 640
19.1 Introduction 640
19.2 Competing Risks 642
19.3 Joint Duration Distributions 648
19.4 Multiple Spells 655
19.5 Competing Risks Example: Unemployment Duration 658
19.6 Practical Considerations 662
19.7 Bibliographic Notes 663
20 Models of Count Data 665
20.1 Introduction 665
20.2 Basic Count Data Regression 666
20.3 Count Example: Contacts with Medical Doctor 671
20.4 Parametric Count Regression Models 674
20.5 Partially Parametric Models 682
20.6 Multivariate Counts and Endogenous Regressors 685
20.7 Count Example: Further Analysis 690
20.8 Practical Considerations 690
20.9 Bibliographic Notes 691
V Models for Panel Data
21 Linear Panel Models: Basics 697
21.1 Introduction 697
21.2 Overview of Models and Estimators 698
21.3 Linear Panel Example: Hours and Wages 708
21.4 Fixed Effects versus Random Effects Models 715
21.5 Pooled Models 720
21.6 Fixed Effects Model 726
21.7 Random Effects Model 734
xii
CONTENTS
21.8 Modeling Issues 737
21.9 Practical Considerations 740
21.10 Bibliographic Notes 740
22 Linear Panel Models: Extensions 743
22.1 Introduction 743
22.2 GMM Estimation of Linear Panel Models 744
22.3 Panel GMM Example: Hours and Wages 754
22.4 Random and Fixed Effects Panel GMM 756
22.5 Dynamic Models 763
22.6 Difference-in-Differences Estimator 768
22.7 Repeated Cross Sections and Pseudo Panels 770
22.8 Mixed Linear Models 774
22.9 Practical Considerations 776
22.10 Bibliographic Notes 777
23 Nonlinear Panel Models 779
23.1 Introduction 779
23.2 General Results 779
23.3 Nonlinear Panel Example: Patents and R&D 762
23.4 Binary Outcome Data 795
23.5 Tobit and Selection Models 800
23.6 Transition Data 801
23.7 Count Data 802
23.8 Semiparametric Estimation 808
23.9 Practical Considerations 808
23.10 Bibliographic Notes 809
VI Further Topics
24 Stratified and Clustered Samples 813
24.1 Introduction 813
24.2 Survey Sampling 814
24.3 Weighting 817
24.4 Endogenous Stratification 822
24.5 Clustering 829
24.6 Hierarchical Linear Models 845
24.7 Clustering Example: Vietnam Health Care Use 848
24.8 Complex Surveys 853
24.9 Practical Considerations 857
24.10 Bibliographic Notes 857
25 Treatment Evaluation 860
25.1 Introduction 860
25.2 Setup and Assumptions 862
xiii
CONTENTS
25.3 Treatment Effects and Selection Bias 865
25.4 Matching and Propensity Score Estimators 871
25.5 Differences-in-Differences Estimators 878
25.6 Regression Discontinuity Design 879
25.7 Instrumental Variable Methods 883
25.8 Example: The Effect of Training on Earnings 889
25.9 Bibliographic Notes 896
26 Measurement Error Models 899
26.1 Introduction 899
26.2 Measurement Error in Linear Regression 900
26.3 Identification Strategies 905
26.4 Measurement Errors in Nonlinear Models 911
26.5 Attenuation Bias Simulation Examples 919
26.6 Bibliographic Notes 920
27 Missing Data and Imputation 923
27.1 Introduction 923
27.2 Missing Data Assumptions 925
27.3 Handling Missing Data without Models 928
27.4 Observed-Data Likelihood 929
27.5 Regression-Based Imputation 930
27.6 Data Augmentation and MCMC 932
27.7 Multiple Imputation 934
27.8 Missing Data MCMC Imputation Example 935
27.9 Practical Considerations 939
27.10 Bibliographic Notes 940
A Asymptotic Theory 943
A.1 Introduction 943
A.2 Convergence in Probability 944
A.3 Laws of Large Numbers 947
A.4 Convergence in Distribution 948
A.5 Central Limit Theorems 949
A.6 Multivariate Normal Limit Distributions 951
A.7 Stochastic Order of Magnitude 954
A.8 Other Results 955
A.9 Bibliographic Notes 956
B Making Pseudo-Random Draws 957
References 961
Index 999