Handbook of econometrics,

HandbookofEconometricsVolu1128_f.jpg......Page 1
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References......Page 12
Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation......Page 13
Abstract......Page 14
Keywords......Page 15
Introduction......Page 16
The relationship of this chapter to the literature on causal inference in statistics......Page 18
The plan of this chapter and our other contributions......Page 22
Policy evaluation problems considered in this chapter......Page 24
Notation and definition of individual level treatment effects......Page 26
More general criteria......Page 32
The evaluation problem......Page 33
Population level treatment parameters......Page 35
Criteria of interest besides the mean: Distributions of counterfactuals......Page 39
Option values......Page 40
Accounting for private and social uncertainty......Page 42
Roy and generalized Roy examples......Page 44
A generalized Roy model under perfect certainty......Page 45
Scalar income......Page 46
Treatment effects and evaluation parameters......Page 47
A two-outcome normal example under perfect certainty......Page 49
Examples of Roy models......Page 55
Adding uncertainty......Page 58
Generating counterfactuals......Page 60
Fixing vs. conditioning......Page 65
The econometric model vs. the Neyman-Rubin model......Page 67
Nonrecursive (simultaneous) models of causality......Page 72
Relationship to Pearl\'s analysis......Page 77
The multiplicity of causal effects that can be defined from a simultaneous equations system......Page 78
Structure as invariance to a class of modifications......Page 79
Alternative definitions of ``structure\'\'......Page 81
Marschak\'s Maxim and the relationship between the structural literature and the statistical treatment effect literature......Page 82
Identification problems: Determining models from data......Page 85
The identification problem......Page 86
The sources of nonidentifiability......Page 88
Using parametric assumptions to generate population level treatment parameters......Page 90
Two paths toward relaxing distributional, functional form and exogeneity assumptions......Page 93
The value of precisely formulated economic models in making policy forecasts......Page 95
Nonparametric identification of counterfactual outcomes for a multinomial discrete choice model with state-contingent outcomes......Page 97
Normal selection model results......Page 100
References......Page 101
Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New Environments......Page 109
Keywords......Page 112
Introduction......Page 113
The basic principles underlying the identification of the major econometric evaluation estimators......Page 114
A prototypical policy evaluation problem......Page 124
An index model of choice and treatment effects: Definitions and unifying principles......Page 128
Definitions of treatment effects in the two outcome model......Page 131
Policy relevant treatment parameters......Page 137
Instrumental variables......Page 141
IV in choice models......Page 147
Instrumental variables and local instrumental variables......Page 148
Conditions on the MTE that justify the application of conventional instrumental variables......Page 149
Estimating the MTE using local instrumental variables......Page 151
What does linear IV estimate?......Page 154
Further properties of the IV weights......Page 158
Discrete instruments......Page 159
Identifying margins of choice associated with each instrument and unifying diverse instruments within a common framework......Page 160
Yitzhaki\'s derivation of the weights......Page 161
Monotonicity, uniformity and conditional instruments......Page 162
Treatment effects vs. policy effects......Page 164
Some examples of weights in the generalized Roy model and the extended Roy model......Page 165
Discrete instruments and weights for LATE......Page 168
Continuous instruments......Page 173
Comparing selection and IV models......Page 184
Effect of the GED on wages......Page 187
Monotonicity, uniformity, nonseparability, independence and policy invariance: The limits of instrumental variables......Page 193
Implications of nonseparability......Page 195
Implications of dependence......Page 197
Regression discontinuity estimators and LATE......Page 198
Econometric cost benefit analysis based on the MTE......Page 201
Constructing the PRTE in new environments......Page 205
Constructing weights for new policies in a common environment......Page 206
A comparison of three approaches to policy evaluation......Page 210
Background for our analysis of the ordered choice model......Page 212
Analysis of an ordered choice model......Page 214
What do instruments identify in the ordered choice model?......Page 218
Some theoretical examples of the weights in the ordered choice model......Page 220
Some numerical examples of the IV weights......Page 222
Extension to multiple treatments that are unordered......Page 232
Model and assumptions......Page 236
Definition of treatment effects and treatment parameters......Page 240
Treatment parameters......Page 242
Heterogeneity in treatment effects......Page 243
LIV and nonparametric Wald estimands for one choice vs. the best alternative......Page 244
Identification: Effect of best option in K versus best option not in K......Page 249
Identification: Effect of one fixed choice versus another......Page 251
Summarizing the results for the unordered model......Page 254
Continuous treatment......Page 255
Matching......Page 260
Matching assumption (M-1) implies a flat MTE......Page 263
Matching and MTE using mean independence conditions......Page 265
Implementing the method of matching......Page 267
Comparing matching and control functions approaches......Page 270
Comparing matching and classical control function methods for a generalized Roy model......Page 276
The informational requirements of matching and the bias when they are not satisfied......Page 277
The economist uses the minimal relevant information: sigma( IR ) sigma( IE )......Page 280
Adding information to the econometrician\'s information set IE: Using some but not all the information from the minimal relevant information set IR......Page 282
Adding information to the econometrician\'s information set: Using proxies for the relevant information......Page 286
The case of a discrete outcome variable......Page 287
On the use of model selection criteria to choose matching variables......Page 290
Randomized evaluations......Page 291
Randomization as an instrumental variable......Page 294
What does randomization identify?......Page 297
Randomization bias......Page 300
Compliance......Page 301
The dynamics of dropout and program participation......Page 302
Evidence on randomization bias......Page 310
Evidence on dropping out and substitution bias......Page 312
Bounding and sensitivity analysis......Page 315
Outcome is bounded......Page 317
Latent index model: Roy model......Page 318
Instrumental variables: Mean independence condition......Page 320
Instrumental variables: Statistical independence condition......Page 322
Instrumental variables: Nonparametric selection model/LATE conditions......Page 323
Combining comparative advantage and instrumental variables......Page 325
Control functions, replacement functions, and proxy variables......Page 328
Relationships among parameters using the index structure......Page 332
Relaxing additive separability and independence......Page 336
Derivation of PRTE and implications of noninvariance for PRTE......Page 345
Deriving the IV weights on MTE......Page 346
Yitzhaki\'s Theorem and the IV weights [Yitzhaki (1989)]......Page 348
Relationship of our weights to the Yitzhaki weights......Page 350
Derivation of the weights for the mixture of normals example......Page 351
Local instrumental variables for the random coefficient model......Page 354
Generalized ordered choice model with stochastic thresholds......Page 356
Derivation of PRTE weights for the ordered choice model......Page 358
Derivation of the weights for IV in the ordered choice model......Page 359
Proof of Theorem 6......Page 361
Flat MTE within a general nonseparable matching framework......Page 363
The relationship between exclusion conditions in IV and exclusion conditions in matching......Page 364
Selection formulae for the matching examples......Page 367
References......Page 368
Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation......Page 378
Keywords......Page 381
Introduction......Page 382
Identifying distributions of treatment effects......Page 383
Why bother identifying joint distributions?......Page 384
Bounds from classical probability inequalities......Page 386
The common coefficient approach......Page 391
More general dependence assumptions......Page 392
Random coefficient regression approaches......Page 395
Information from revealed preference......Page 396
Using additional information......Page 399
Some examples......Page 401
Nonparametric extensions......Page 406
General models......Page 407
Steps 1 and 2: Solving the selection problem within each treatment state......Page 408
Step 3: Constructing counterfactual distributions using factor models......Page 412
Distinguishing ex ante from ex post returns......Page 414
An approach based on factor structures......Page 417
Operationalizing the method......Page 420
The estimation of the components in the information set......Page 421
Outcome and choice equations......Page 422
Two empirical studies......Page 427
Dynamic models......Page 442
The evaluation problem......Page 443
The treatment-effect approach......Page 447
Dynamic policy evaluation......Page 448
Dynamic treatment and dynamic outcomes......Page 450
Identification of treatment effects......Page 453
The effects of policies......Page 457
Policy choice and optimal policies......Page 458
The information structure of policies......Page 460
Selection on unobservables......Page 462
The event-history approach to policy analysis......Page 463
Dynamically assigned binary treatments and duration outcomes......Page 464
Identifiability without exclusion restrictions......Page 468
Inference based on instrumental variables......Page 469
The mixed semi-Markov event-history model......Page 470
Applications to program evaluation......Page 473
A structural perspective......Page 475
Dynamic discrete choice and dynamic treatment effects......Page 476
Semiparametric duration models and counterfactuals......Page 478
Single spell duration model......Page 479
Identification of duration models with general error structures and duration dependence......Page 480
Reduced form dynamic treatment effects......Page 483
Identification of outcome and treatment time distributions......Page 486
Using factor models to identify joint distributions of counterfactuals......Page 489
A sequential structural model with option values......Page 491
Identification at infinity......Page 498
Comparing reduced form and structural models......Page 499
A short survey of dynamic discrete-choice models......Page 501
Summary of the state of the art in analyzing dynamic treatment effects......Page 506
Accounting for general equilibrium, social interactions, and spillover effects......Page 507
General equilibrium approaches based on microdata......Page 508
Subsequent research......Page 514
Analyses of displacement......Page 515
Summary of general equilibrium approaches......Page 518
Deconvolution......Page 519
The Matzkin conditions......Page 520
Proof of Theorem 2......Page 521
Proof of a more general version of Theorem 4......Page 523
References......Page 527
Nonparametric identification......Page 537
Abstract......Page 538
Keywords......Page 539
Introduction......Page 540
From the economic model to the econometric model......Page 543
Dependence between epsilon and X......Page 545
Additive models......Page 546
Nonadditive models......Page 547
Triangular nonadditive model......Page 548
Nonadditive index models......Page 549
Nonadditive simultaneous equations models......Page 550
Discrete choice models......Page 552
Definition of identification......Page 553
Identification in additive models......Page 554
Identification in nonadditive models......Page 556
Identification of derivatives......Page 558
Identification in triangular systems......Page 559
Identification in nonadditive index models......Page 561
Identification in simultaneous equations models......Page 563
Identification in discrete choice models......Page 568
Subutilities additive in the unobservables......Page 569
Subutilities nonadditive in the unobservables......Page 570
Identification of functions and distributions in a nonadditive model using conditional independence......Page 571
Identification of average derivatives in a nonadditive model using conditional independence......Page 574
Instrumental variables in nonadditive models......Page 576
Unobservable instruments......Page 578
Instrumental variables in additive models with measurement error......Page 579
Exchangeability restrictions in the nonadditive model......Page 580
Local independence restrictions in the nonadditive model......Page 581
Independent nonadditive model......Page 582
Independent index model......Page 583
Discrete choice model......Page 584
Additivity in a known function......Page 585
A control function in an additive model......Page 586
Linear factor models......Page 588
Index models with fixed effects......Page 591
Single equation models with multivariate unobservables......Page 592
References......Page 593
Implementing Nonparametric and Semiparametric Estimators......Page 599
Abstract......Page 600
Keywords......Page 601
The nature of recent progress......Page 602
Benefits of flexible modeling approaches for empirical research......Page 603
Implementation issues......Page 604
Related literature......Page 606
Density estimation......Page 607
Earnings function estimation......Page 608
Analysis of consumer demand......Page 610
Analysis of sample selection......Page 611
Convergence rates, asymptotic bias, and the curse of dimensionality......Page 612
Using semiparametric models......Page 618
Changing the parameter......Page 620
Specifying different stochastic assumptions within a semiparametric model......Page 621
Nonparametric estimation methods......Page 623
How do we estimate densities?......Page 624
Moment based estimators......Page 625
Likelihood-based approaches......Page 630
Local likelihood estimation......Page 631
How do we estimate conditional mean functions?......Page 632
The global approach......Page 633
The local approach......Page 634
Bias......Page 638
Variance......Page 639
Semiparametric estimation......Page 642
Additively separable models......Page 643
An estimator based on integration......Page 644
Single index model......Page 646
Partially linear regression model......Page 648
Improving the convergence rate by changing the parameter of interest......Page 653
Usage of different stochastic assumptions......Page 656
Censored regression model......Page 657
Binary response model......Page 658
Smoothing parameter choice and trimming......Page 659
Rule of thumb......Page 660
Least square cross validation......Page 661
A brief discussion of other methods......Page 663
Methods for selecting smoothing parameters in the local polynomial estimator of a regression function......Page 664
Rule of thumb......Page 665
Least square cross validation......Page 666
Residual squares criterion......Page 667
Fan and Gijbels\'s finite sample method......Page 668
Other methods......Page 669
Optimal bandwidth choice in average derivative estimation......Page 670
Other works......Page 672
Three reasons for trimming......Page 673
How trimming is done......Page 674
Asymptotic distribution of semiparametric estimators......Page 675
Assumptions......Page 676
Main results on asymptotic distribution......Page 679
Description of an approximation method......Page 682
A simple binning estimator......Page 683
Fast Fourier transform (FFT) binning for density estimation......Page 684
Making the grid......Page 686
Performance evaluation......Page 687
Conclusions......Page 688
References......Page 689
The Econometrics of Data Combination......Page 699
Keywords......Page 700
Introduction......Page 701
Broken random samples......Page 704
Matching with imperfect identifiers......Page 707
Matching errors and estimation......Page 710
Fréchet bounds and conditional Fréchet bounds on the joint distribution......Page 714
Statistical matching of independent samples......Page 721
Conditional independence......Page 724
Exclusion restrictions......Page 725
Conditional independence......Page 728
Exclusion restrictions......Page 731
The origin of two-sample estimation and applications......Page 737
Combining samples to correct for measurement error......Page 740
General principles......Page 743
Consistency and related issues......Page 747
Binary choice models......Page 750
Applications......Page 753
Biased samples and marginal information......Page 755
Identification in biased samples......Page 758
Case-control with contaminated controls......Page 761
Efficient non-parametric estimation in biased samples......Page 762
Efficient parametric estimation in endogenously stratified samples......Page 763
Random sample with marginal information......Page 767
Biased samples with marginal information......Page 769
References......Page 773
Large Sample Sieve Estimation of Semi-Nonparametric Models......Page 778
Abstract......Page 779
Keywords......Page 780
Introduction......Page 781
Empirical examples of semi-nonparametric econometric models......Page 784
Semi-nonparametric conditional moment models.......Page 787
Ill-posed versus well-posed problem, sieve extremum estimation......Page 789
Sieve M-estimation......Page 791
Series estimation, concave extended linear models......Page 792
Sieve MD estimation......Page 796
Typical smoothness classes and (finite-dimensional) linear sieves......Page 798
Trigonometric polynomials.......Page 799
Wavelets.......Page 800
Orthogonal wavelets.......Page 801
Weighted smoothness classes and (finite-dimensional) linear sieves......Page 802
Sigmoid ANN.......Page 803
General ANN.......Page 804
Infinite-dimensional (nonlinear) sieves and method of penalization......Page 805
Cardinal B-spline wavelets.......Page 806
Choice of a sieve space......Page 808
A small Monte Carlo study......Page 809
An incomplete list of sieve applications in econometrics......Page 814
Large sample properties of sieve estimation of unknown functions......Page 816
Consistency of sieve extremum estimators......Page 817
Convergence rates of sieve M-estimators......Page 822
Example: Additive mean regression with a monotone constraint......Page 825
Example: Multivariate quantile regression......Page 827
Convergence rates of series estimators......Page 829
Univariate splines.......Page 830
Tensor product spaces.......Page 831
Asymptotic normality of the spline series LS estimator......Page 832
Asymptotic normality of functionals of series LS estimator......Page 833
Large sample properties of sieve estimation of parametric parts in semiparametric models......Page 835
Asymptotic normality......Page 836
Asymptotic normality of smooth functionals of sieve M-estimators......Page 840
Asymptotic normality of sieve GLS......Page 842
Example: Partially additive mean regression with a monotone constraint......Page 845
Efficiency of sieve MLE......Page 846
Sieve simultaneous MD estimation: Normality and efficiency......Page 848
Concluding remarks......Page 851
References......Page 852
Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization......Page 862
Keywords......Page 865
Structural models and functional estimation......Page 866
Notation......Page 868
Generalized method of moments (GMM)......Page 869
Instrumental variables......Page 870
Deconvolution......Page 871
Additive models......Page 872
Measurement-error models or nonparametric analysis of panel data......Page 873
Game theoretic model......Page 874
Instrumental variables in a nonseparable model......Page 875
Organization of the chapter......Page 876
Hilbert spaces......Page 877
Definitions and basic properties of operators......Page 881
Spectral decomposition of compact operators......Page 889
Definitions......Page 891
Central limit theorem for mixing processes......Page 892
Estimation of an operator......Page 893
Estimation of the adjoint of a conditional expectation operator......Page 894
Computation of the spectrum of finite dimensional operators......Page 897
Ill-posed and well-posed problems......Page 898
Regularity spaces......Page 901
Regularization schemes......Page 905
Operator interpretation and implementation of regularization schemes......Page 909
Landweber-Fridman regularization......Page 911
Estimation bias......Page 912
Consistency......Page 914
Discussion on the rate of convergence......Page 915
Assumption WC......Page 916
Assumption G......Page 917
Discussion of Proposition 4.3......Page 918
Ridge regression......Page 919
Principal components and factor models......Page 922
First approach: Ridge regression......Page 923
Second approach: Moment conditions......Page 924
A new estimator based on Tikhonov regularization......Page 927
Comparison with the deconvolution kernel estimator......Page 929
Instrumental variables......Page 931
Reproducing kernel......Page 939
Definitions and basic properties of RKHS......Page 940
RKHS for covariance operators of stochastic processes......Page 943
GMM in Hilbert spaces......Page 945
Identification assumption......Page 946
Optimal choice of the weighting operator......Page 948
Implementation of GMM......Page 950
Asymptotic efficiency of GMM......Page 951
Testing overidentifying restrictions......Page 953
Extension to time series......Page 954
Introduction......Page 956
Riesz theory and Fredholm alternative......Page 957
Well-posed equations of the second kind......Page 958
Estimation......Page 966
Backfitting estimation in additive models......Page 969
Identification assumption......Page 970
Estimation of the bias function in a measurement error equation......Page 974
References......Page 975
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