Horowitz Semiparametric and Nonparametric Methods in Econometrics

1. Auflage 2010
ISBN: 978-0-387-92870-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 276 Seiten

Reihe: Springer Series in Statistics

Standard methods for estimating empirical models in economics and many other fields rely on strong assumptions about functional forms and the distributions of unobserved random variables. Often, it is assumed that functions of interest are linear or that unobserved random variables are normally distributed. Such assumptions simplify estimation and statistical inference but are rarely justified by economic theory or other a priori considerations. Inference based on convenient but incorrect assumptions about functional forms and distributions can be highly misleading. Nonparametric and semiparametric statistical methods provide a way to reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. These methods are applicable to a wide variety of estimation problems in empirical economics and other fields, and they are being used in applied research with increasing frequency. The literature on nonparametric and semiparametric estimation is large and highly technical. This book presents the main ideas underlying a variety of nonparametric and semiparametric methods. It is accessible to graduate students and applied researchers who are familiar with econometric and statistical theory at the level taught in graduate-level courses in leading universities. The book emphasizes ideas instead of technical details and provides as intuitive an exposition as possible. Empirical examples illustrate the methods that are presented. This book updates and greatly expands the author's previous book on semiparametric methods in econometrics. Nearly half of the material is new.

Autoren/Hrsg.

Horowitz, Joel L.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;12
3.1;1.1 The Goals of This Book;12
3.2;1.2 Dimension Reduction;14
3.3;1.3 Are Semiparametric and Nonparametric Methods Really Different from Parametric Ones?;17
4;2 Single-Index Models;18
4.1;2.1 Definition of a Single-Index Model of a Conditional Mean Function;18
4.2;2.2 Multiple-Index Models;21
4.3;2.3 Identification of Single-Index Models;23
4.3.1;2.3.1 Conditions for Identification of ß and G ;23
4.3.2;2.3.2 Identification Analysis When X Is Discrete;26
4.4;2.4 Estimating G in a Single-Index Model;28
4.5;2.5 Optimization Estimators of ;30
4.5.1;2.5.1 Nonlinear Least Squares;31
4.5.2;2.5.2 Choosing the Weight Function;36
4.5.3;2.5.3 Semiparametric Maximum-Likelihood Estimation of Binary-Response Models;38
4.5.4;2.5.4 Semiparametric Maximum-Likelihood Estimation of Other Single-Index Models;40
4.5.5;2.5.5 Semiparametric Rank Estimators;40
4.6;2.6 Direct Semiparametric Estimators;41
4.6.1;2.6.1 Average-Derivative Estimators;42
4.6.2;2.6.2 An Improved Average-Derivative Estimator;46
4.6.3;2.6.3 Direct Estimation with Discrete Covariates;48
4.6.4;2.6.4 One-Step Asymptotically Efficient Estimators;53
4.7;2.7 Bandwidth Selection;55
4.8;2.8 An Empirical Example;57
4.9;2.9 Single-Index Models of Conditional Quantile Functions;58
5;3 Nonparametric Additive Models and Semiparametric Partially Linear Models;63
5.1;3.1 Nonparametric Additive Models with Identity Link Functions;65
5.1.1;3.1.1 Marginal Integration;65
5.1.2;3.1.2 Backfitting;73
5.1.3;3.1.3 Two-Step, Oracle-Efficient Estimation;74
5.1.3.1;3.1.3.1 Informal Description of the Estimator;75
5.1.3.2;3.1.3.2 Asymptotic Properties of the Two-Stage Estimator;76
5.2;3.2 Estimation with a Nonidentity Link Function;80
5.2.1;3.2.1 Estimation;81
5.2.2;3.2.2 Bandwidth Selection;85
5.3;3.3 Estimation with an Unknown Link Function;87
5.4;3.4 Estimation of a Conditional Quantile Function;90
5.5;3.5 An Empirical Example;93
5.6;3.6 The Partially Linear Model;95
5.6.1;3.6.1 Identification;95
5.6.2;3.6.2 Estimation of ;96
5.6.3;3.6.3 Partially Linear Models of Conditional Quantiles;100
5.6.4;3.6.4 Empirical Applications;101
6;4 Binary-Response Models;104
6.1;4.1 Random-Coefficients Models;104
6.2;4.2 Identification;105
6.2.1;4.2.1 Identification Analysis When X Has Bounded Support;109
6.2.2;4.2.2 Identification When X Is Discrete;110
6.3;4.3 Estimation;112
6.3.1;4.3.1 Estimating ;113
6.3.2;4.3.2 Estimating ß: The Maximum-Score Estimator;114
6.3.3;4.3.3 Estimating ß: The Smoothed Maximum-Score Estimator;117
6.4;4.4 Extensions of the Maximum-Score and Smoothed Maximum-Score Estimators;127
6.4.1;4.4.1 Choice-Based Samples;128
6.4.2;4.4.2 Panel Data;132
6.4.3;4.4.3 Ordered-Response Models;137
6.5;4.5 Other Estimators for Heteroskedastic Binary-Response Models;140
6.6;4.6 An Empirical Example;141
7;5 Statistical Inverse Problems;143
7.1;5.1 Deconvolution in a Model of Measurement Error;144
7.1.1;5.1.1 Rate of Convergence of the Density Estimator;146
7.1.2;5.1.2 Why Deconvolution Estimators Converge Slowly;149
7.1.3;5.1.3 Asymptotic Normality of the Density Estimator;151
7.1.4;5.1.4 A Monte Carlo Experiment;152
7.2;5.2 Models for Panel Data;152
7.2.1;5.2.1 Estimating fU and fe;154
7.2.2;5.2.2 Large Sample Properties of fne and fnU;156
7.2.3;5.2.3 Estimating First-Passage Times;159
7.2.4;5.2.4 Bias Reduction;160
7.2.5;5.2.5 Monte Carlo Experiments;162
7.3;5.3 Nonparametric Instrumental-Variables Estimation;164
7.3.1;5.3.1 Regularization Methods;172
7.3.1.1;5.3.1.1 Tikhonov Regularization;173
7.3.1.2;5.3.1.2 Regularization by Series Truncation;177
7.4;5.4 Nonparametric Instrumental-Variables Estimation When T Is Unknown;179
7.4.1;5.4.1 Estimation by Tikhonov Regularization When T Is Unknown;179
7.4.1.1;5.4.1.1 Computation of ˆg;185
7.4.2;5.4.2 Estimation by Series Truncation When T Is Unknown;186
7.4.2.1;5.4.2.1 Computation of ˆg;192
7.5;5.5 Other Approaches to Nonparametric Instrumental-Variables Estimation;193
7.5.1;5.5.1 Nonparametric Quantile IV;193
7.5.2;5.5.2 Control Functions;194
7.6;5.6 An Empirical Example;195
8;6 Transformation Models;197
8.1;6.1 Estimation with Parametric T and Nonparametric F;198
8.1.1;6.1.1 Choosing the Instruments;201
8.1.2;6.1.2 The Box--Cox Regression Model;202
8.1.3;6.1.3 The Weibull Hazard Model with Unobserved Heterogeneity;204
8.2;6.2 Estimation with Nonparametric T and Parametric F;209
8.2.1;6.2.1 The Proportional Hazards Model;209
8.2.2;6.2.2 The Proportional Hazards Model with Unobserved Heterogeneity;212
8.2.3;6.2.3 The Case of Discrete Observations of Y;216
8.2.4;6.2.4 Estimating ;217
8.2.5;6.2.5 Other Models in Which F Is Known;221
8.3;6.3 Estimation When Both T and F Are Nonparametric;223
8.3.1;6.3.1 Derivation of Horowitz’s Estimators of T and F;224
8.3.2;6.3.2 Asymptotic Properties of Tn and Fn;227
8.3.3;6.3.3 Chen’s Estimator of T;229
8.3.4;6.3.4 The Proportional Hazards Model with Unobserved Heterogeneity;231
8.4;6.4 Predicting Y Conditional on X;238
8.5;6.5 An Empirical Example;238
9;Appendix: Nonparametric Density Estimationand Nonparametric Regression;241
9.1;6.1 Nonparametric Density Estimation;241
9.1.1;A.1.1 Density Estimation When X Is Multidimensional;245
9.1.2;A.1.2 Estimating Derivatives of a Density;247
9.2;6.2 Nonparametric Mean Regression;248
9.2.1;A.2.1 The Nadaraya--Watson Kernel Estimator;248
9.2.2;A.2.2 Local-Linear Mean Regression;250
9.2.3;A.2.3 Series Estimation of a Conditional Mean Function;253
9.2.3.1;A.2.3.1 Hilbert Spaces;253
9.2.3.2;A.2.3.2 Nonparametric Regression;256
9.3;6.3 Nonparametric Quantile Regression;257
9.3.1;A.3.1 A Kernel-Type Estimator of qa(x);258
9.3.2;A.3.2 Local-Linear Estimation of qa(x);259
9.3.3;A.3.3 Series Estimation of qa(x);261
10;References;264
11;Index;274