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Nonparametric Econometrics : Themes in Modern Econometrics - Adrian Pagan

Nonparametric Econometrics

Themes in Modern Econometrics


Published: 26th June 2004
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  • Paperback View Product Published: 25th October 1999

This book systematically and thoroughly covers a vast literature on the nonparametric and semiparametric statistics and econometrics that has evolved over the past five decades. Within this framework, this is the first book to discuss the principles of the nonparametric approach to the topics covered in a first year graduate course in econometrics, e.g., regression function, heteroskedasticity, simultaneous equations models, logit-probit and censored models. Professors Pagan and Ullah provide intuitive explanations of difficult concepts, heuristic developments of theory, and empirical examples emphasizing the usefulness of modern nonparametric approach. The book should provide a new perspective on teaching and research in applied subjects in general and econometrics and statistics in particular.

'The authors of this well-produced volume merit high praise for their endeavours. This will be the most comprehensive summary of nonparametric statistics that we are likely to see for a long time. I can recommend it as a guide to recent work in an important area of mathematical statistics.' Short Book Reviews

Prefacep. xvii
Introductionp. 1
Methods of Density Estimationp. 5
Introductionp. 5
Nonparametric Density Estimationp. 7
A "Local" Histogram Approachp. 7
A Formal Derivation of andfirac;[subscript 1] (x)p. 9
Rosenblatt-Parzen Kernel Estimatorp. 9
The Nearest Neighborhood Estimatorp. 11
Variable Window-Width Estimatorsp. 12
Series Estimatorsp. 13
Penalized Likelihood Estimatorsp. 15
The Local Log-Likelihood Estimatorsp. 17
Summaryp. 19
Estimation of Derivatives of a Densityp. 19
Finite-Sample Properties of the Kernel Estimatorp. 20
The Exact Bias and Variance of the Estimator andfirac;p. 21
Approximations to the Bias and Variance and Choices of h and Kp. 23
Reduction of Biasp. 29
Asymptotic Properties of the Kernel Density Estimator andfirac; with Independent Observationsp. 32
Asymptotic Unbiasednessp. 33
Consistencyp. 34
Asymptotic Normalityp. 39
Small-Sample Confidence Intervalsp. 42
Sampling Properties of the Kernel Density Estimator with Dependent Observationsp. 43
Unbiasednessp. 43
Consistencyp. 43
Asymptotic Normalityp. 48
Bibliographical Summary (Approximate and Asymptotic Results)p. 48
Choices of Window Width and Kernel: Further Discussionp. 49
Choice of hp. 49
Choice of Higher Order Kernelsp. 54
Choice of h for Density Derivativesp. 56
Multivariate Density Estimationp. 57
Testing Hypotheses about Densitiesp. 60
Comparison with a Known Density Functionp. 61
Testing for Symmetryp. 67
Comparison of Unknown Densitiesp. 68
Testing for Independencep. 69
Examplesp. 71
Density of Stock Market Returnsp. 71
Estimating the Dickey-Fuller Densityp. 74
Conditional Moment Estimationp. 78
Introductionp. 78
Estimating Conditional Moments by Kernel Methodsp. 79
Parametric Estimationp. 80
Nonparametric Estimation: A "Local" Regression Approachp. 81
Kernel-Based Estimation: A Formal Derivationp. 83
A General Nonparametric Estimator of m(x)p. 84
Unifying Nonparametric Estimatorsp. 86
Estimation of Higher Order Conditional Momentsp. 95
Finite-Sample Propertiesp. 95
Approximate Results: Stochastic xp. 96
The Local Linear Regression Estimatorp. 104
Combining Parametric and Nonparametric Estimatorsp. 106
Asymptotic Propertiesp. 108
Asymptotic Properties of the Kernel Estimator with Independent Observationsp. 108
Asymptotic Properties of the Kernel Estimator with Dependent Observationsp. 115
Bibliographical Summary (Asymptotic Results)p. 116
Implementing the Kernel Estimatorp. 118
Choice of Window Widthp. 118
Robust Nonparametric Estimation of Momentsp. 122
Estimating Conditional Moments by Series Methodsp. 123
Asymptotic Properties of Series Estimators with Independent Observationsp. 126
Asymptotic Properties of Series Estimators with Dependent Observationsp. 133
Implementing the Estimatorp. 133
Imposing Structure on the Conditional Momentsp. 137
Generalized Additive Modelsp. 137
Projection Pursuit Regressionp. 139
Neural Networksp. 140
Measuring the Affinity of Parametric and Nonparametric Modelsp. 141
Examplesp. 150
A Model of Strike Durationp. 150
Earnings-Age Profilesp. 152
Review of Applied Work on Nonparametric Regressionp. 157
Nonparametric Estimation of Derivativesp. 160
Introductionp. 160
The Model and Partial Derivative Formulaep. 161
Estimationp. 164
Estimation of Partial Derivatives by Kernel Methodsp. 164
Estimation of Partial Derivatives by Series Methodsp. 167
Estimation of Average Derivativesp. 167
Local Linear Derivative Estimatorsp. 170
Pointwise Versus Average Derivativesp. 172
Restricted Estimation and Hypothesis Testingp. 173
Imposing Linear Equality Restriction on Partial Derivativesp. 174
Imposing Linear Inequality Restrictionsp. 175
Hypothesis Testingp. 176
Asymptotic Properties of Partial Derivative Estimatorsp. 177
Asymptotic Properties of Kernel-Based Estimatorsp. 178
Series-Based Estimatorsp. 182
Higher Order Derivativesp. 182
Local Linear Estimatorsp. 183
Asymptotic Properties of Kernel-Based Average Derivative Estimatorsp. 184
Implementing the Derivative Estimatorsp. 189
Illustrative Examplesp. 190
A Monte Carlo Experiment with a Production Functionp. 190
Earnings-Age Relationshipp. 192
Review of Applied Workp. 194
Semiparametric Estimation of Single-Equation Modelsp. 196
Introductionp. 196
Semiparametric Estimation of the Linear Part of a Regression Modelp. 198
General Resultsp. 198
Diagnostic Tests after Nonparametric Regressionp. 208
Semiparametric Estimation of Some Macro Modelsp. 210
The Asymptotic Covariance Matrix of SP Estimators without Asymptotic Independencep. 212
Efficient Estimation of Semiparametric Models in the Presence of Heteroskedasticity of Unknown Formp. 214
Conditions for Adaptive Estimationp. 217
Efficient Estimation of Regression Parameters with Unknown Error Densityp. 225
Efficient Estimation by Likelihood Approximationp. 225
Efficient Estimation by Kernel-Based Score Approximationp. 227
Efficient Estimation by Moment-Based Score Approximationp. 230
Estimation of Scale Parametersp. 234
Optimal Diagnostic Tests in Linear Modelsp. 234
Adaptive Estimation with Dependent Observationsp. 235
M-Estimatorsp. 237
Estimationp. 237
Diagnostic Tests with M-Estimatorsp. 242
Sequential M-Estimatorsp. 243
The Semiparametric Efficiency Bound for Moment-Based Estimatorsp. 245
Approximating the SP Efficiency Bound by a Conditional Moment Estimatorp. 246
Applicationsp. 248
Semiparametric Estimation of a Heteroskedastic Modelp. 248
Adaptive Estimation of a Model of House Pricesp. 250
Review of Other Applicationsp. 251
Semiparametric and Nonparametric Estimation of Simultaneous Equation Modelsp. 254
Introductionp. 254
Single-Equation Estimatorsp. 255
Parametric Estimationp. 256
Rilstone's Semiparametric Two-Stage Least Squares Estimatorp. 258
Systems Estimationp. 260
A Parametric Estimatorp. 260
The SP3SLS Estimatorp. 261
Newey's Estimatorp. 262
Newey's Efficient Distribution-Free Estimatorsp. 264
Finite-Sample Propertiesp. 267
Nonparametric Estimationp. 269
Identificationp. 269
Nonparametric Two-Stage Least Squares (2SLS) Estimationp. 270
Semiparametric Estimation of Discrete Choice Modelsp. 272
Introductionp. 272
Parametric Estimation of Binary Discrete Choice Modelsp. 273
Semiparametric Efficiency Bounds for Binary Discrete Choice Modelsp. 275
Semiparametric Estimation of Binary Discrete Choice Modelsp. 279
Ichimura's Estimatorp. 280
Klein and Spady's Estimatorp. 283
The SNP Maximum Likelihood Estimatorp. 285
Local Maximum Likelihood Estimationp. 286
Alternative Consistent SP Estimatorsp. 286
Manski's Maximum Score Estimatorp. 286
Horowitz's Smoothed Maximum Score Estimatorp. 287
Han's Maximum Rank Correlation Estimatorp. 291
Cosslett's Approximate MLEp. 292
An Iterative Least Squares Estimatorp. 293
Derivative-Based Estimatorsp. 294
Models with Discrete Explanatory Variablesp. 295
Multinomial Discrete Choice Modelsp. 296
Some Specification Tests for Discrete Choice Modelsp. 297
Applicationsp. 299
Semiparametric Estimation of Selectivity Modelsp. 300
Introductionp. 300
Some Parametric Estimatorsp. 300
Some Sequential Semiparametric Estimatorsp. 304
Cosslett's Dummy Variable Methodp. 306
Powell's Kernel Estimatorp. 306
Newey's Series Estimatorp. 308
Newey's GMM Estimatorp. 310
Maximum Likelihood-Type Estimatorsp. 310
Gallant and Nychka's Estimatorp. 310
Newey's Estimatorp. 311
Estimation of the Intercept in Selection Modelsp. 315
Applications of the Estimatorsp. 315
Conclusionsp. 316
Semiparametric Estimation of Censored Regression Modelsp. 317
Introductionp. 317
Some Parametric Estimatorsp. 319
Semiparametric Efficiency Bounds for the Censored Regression Modelp. 322
The Kaplan-Meier Estimator of the Distribution Function of a Censored Random Variablep. 324
Semiparametric Density-Based Estimatorsp. 326
The Semiparametric Generalized Least Squares Estimator (SGLS)p. 327
Estimators Replacing Part of the Samplep. 328
Maximum Likelihood Type Estimatorsp. 329
Semiparametric Nondensity-Based Estimatorsp. 329
Powell's Censored Least Absolute Deviation (CLAD) Estimatorp. 330
Powell's (1986a) Censored Quantile Estimatorsp. 333
Powell's Symmetrically Censored Least Squares Estimatorsp. 333
Newey's Efficient Estimator under Conditional Symmetryp. 336
Comparative Studies of the Estimatorsp. 337
Retrospect and Prospectp. 339
Statistical Methodsp. 342
Probability Conceptsp. 342
Random Variable and Distribution Functionp. 345
Conditional Distribution and Independencep. 347
Borel Measurable Functionsp. 348
Inequalities Involving Expectationsp. 350
Characteristic Function (c.f.)p. 351
Results on Convergencep. 352
Weak and Strong Convergence of Random Variablesp. 352
Laws of Large Numbersp. 354
Convergence of Distribution Functionsp. 355
Central Limit Theoremsp. 357
Further Results on the Law of Large Numbers and Convergence in Moments and Distributionsp. 360
Convergence in Momentsp. 361
Some Probability Inequalitiesp. 365
Order of Magnitudes (Small o and Large O)p. 368
Asymptotic Theory for Dependent Observationsp. 370
Ergodicityp. 371
Mixing Sequencesp. 372
Near-Epoch Dependent Sequencesp. 376
Martingale Differences and Mixingalesp. 377
Rosenblatt's (1970) Measure of Dependence [beta][subscript n]p. 379
Stochastic Equicontinuityp. 379
Referencesp. 383
Indexp. 419
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521355643
ISBN-10: 0521355648
Series: Themes in Modern Econometrics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 444
Published: 26th June 2004
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 2.87
Weight (kg): 0.82